Definition of deduction: through the general to the specific. Deductive thinking - trust specific facts The direction of logical consequence in the deductive method of thinking

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

What is this deduction?

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

Deduction in philosophy

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

Deduction in psychology

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

Deduction - advantages and disadvantages

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

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

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

Deduction and induction

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

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

How to develop deduction?

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

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

Deduction - exercises

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

Deductive method of thinking - books

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

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

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

In the broad sense of the word, induction is a form of thinking that develops general judgments about individual objects; this 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”).

By observing and studying individual objects, facts, events, a person comes to know general patterns. No human knowledge can do without them. The immediate basis of inductive inference is the repeatability of features in a number of objects of a certain class. A conclusion by induction is a conclusion about the general properties of all objects belonging to a given class, based on the observation of a fairly wide variety of individual facts. Typically, inductive generalizations are viewed 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, it makes it possible to construct hypotheses, but does not provide reliable knowledge, but is suggestive.

Speaking about induction, we usually distinguish 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 observational and experimental data. From the point of view of cognitive tasks, they also distinguish between induction as a method of discovering new knowledge and induction as a method of substantiating hypotheses and theories.

Induction plays a major role in empirical (experiential) knowledge. Here she speaks:

· one of the methods for the formation of empirical concepts;

· the basis for constructing natural classifications;

· one of the methods for discovering cause-and-effect patterns and hypotheses;

· one of the methods of confirming and justifying empirical laws.

Induction is widely used in science. With its help, all the most important natural classifications in botany, zoology, geography, astronomy, etc. were built. The laws of planetary motion discovered by Johannes Kepler were obtained using induction based on an analysis of the astronomical observations of Tycho Brahe. In turn, Keplerian laws served as an inductive basis for 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 for establishing cause-and-effect relationships.

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

General induction is an induction in which one moves from knowledge about several objects 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: 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 no ones that contradict the inductive inference. 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 special interest in the problems of induction appeared 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 cognition of truth. With the help of such induction, Bacon intended to look for the cause of the properties of things. Logic should become the logic of inventions and discoveries, Bacon believed; Aristotelian logic, set out in the work “Organon,” cannot cope with this task. Therefore, Bacon writes the work “New Organon”, which was supposed to replace the old logic. Another English philosopher, economist and logician John Stuart Mill also extolled induction. He can be considered the founder of classical inductive logic. In his logic, Mill devoted much attention to the development of methods for studying causal relationships.

During the experiments, material is accumulated for analyzing objects, identifying 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 like this: experience - inductive method - generalization and conclusions (knowledge), their verification in an experiment.

The principle of induction states that universal statements of science are based on inductive conclusions. This principle is referred to when it is said that the truth of a statement is known from experience. In modern scientific methodology, it is realized that it is generally impossible to establish the truth of a universal generalizing judgment using 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 derives a certain thought from other thoughts. The process of logical inference, which results in the transition from premises to consequences based on the application of the rules of logic, is called deduction. There are deductive inferences: conditionally categorical, separative-categorical, dilemmas, conditional inferences, etc.

Deduction is a method of scientific knowledge, which consists in the transition from certain general premises to particular results and consequences. Deduction derives general theorems and special conclusions from experimental sciences. Gives reliable knowledge if the premise is true. 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 closest genus into which these objects belong, and, secondly, to apply to them the corresponding law inherent to all this kind of objects; transition from knowledge of more general provisions to knowledge of less general provisions.

In general, deduction as a method of cognition is based on already known laws and principles. Therefore, the deduction method does not allow us to obtain meaningful new knowledge. Deduction is only a way of logical development of a system of propositions based on initial knowledge, a way of identifying the specific content of generally accepted premises.

Aristotle understood deduction as evidence using syllogisms. The great French scientist Rene Descartes extolled deduction. He contrasted it with intuition. In his opinion, intuition directly perceives the truth, and with the help of deduction, the truth is comprehended indirectly, i.e. by reasoning. Distinct intuition and necessary deduction are the way to know the truth, according to Descartes. He also deeply developed the deductive-mathematical method in the study of natural science issues. For a rational method of research, Descartes formulated four basic rules, the so-called. "rules for guiding the mind":

1. That which is clear and distinct is true.

2. Complex things must be divided into specific, simple problems.

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

4. Conduct logical reasoning consistently, without gaps.

A method of reasoning based on the deduction of consequences and conclusions from hypotheses is called the hypothetico-deductive method. Since there is no logic of scientific discovery, no methods guaranteeing the acquisition of true scientific knowledge, scientific statements are hypotheses, i.e. are scientific assumptions or assumptions whose truth value is uncertain. This position forms the basis of the hypothetico-deductive model of scientific knowledge. In accordance with this model, the scientist puts forward a hypothetical generalization, from which various kinds of consequences are deductively derived, which are then compared with empirical data. The rapid development of the hypothetico-deductive method began in the 17th-18th centuries. This method was successfully applied in mechanics. The studies of Galileo Galilei and especially Isaac Newton turned mechanics into a harmonious hypothetico-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 a huge role in mathematics. It is known that all provable propositions, that is, theorems, are derived logically using 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 hypothetico-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 hypothetico-deductive method rather plays the role of a controller, checking the consequences arising from the hypotheses.

In the modern era, extreme points of view about the meaning of induction and deduction began to be overcome. Galileo, Newton, Leibniz, recognizing the great role of experience, and therefore induction 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 assigned an important role to deduction in constructing and testing scientific theories and noted that in scientific knowledge an important place is occupied by a hypothesis, which cannot be reduced to induction and deduction. However, for a long time it was not possible to completely overcome the opposition between inductive and deductive methods of cognition.

In modern scientific knowledge, induction and deduction are always intertwined with each other. Real scientific research takes place in an 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, in modern inductive logic, probabilistic methods play a huge role. Assessing the likelihood of generalizations, searching for criteria for substantiating hypotheses, the establishment of complete reliability of which is often impossible, requires increasingly sophisticated research methods.

Deduction is a method of thinking, the consequence of which is a logical conclusion, where a particular conclusion is deduced from a general one.

“From just one drop of water, a person who knows how to think logically can deduce the existence of the Atlantic Ocean or Niagara Falls, even if he has not seen either of them,” this is how the most famous literary detective reasoned. Taking into account small details invisible to other people, he built impeccable logical conclusions using the method of deduction. It was thanks to Sherlock Holmes that the whole world learned what deduction is. In his reasoning, the great detective always started from the general picture - the whole picture of the crime with the alleged criminals, and moved to specific moments - he considered each individual, everyone who could commit the crime, studied the motives, behavior, evidence.

This amazing Conan Doyle hero could guess from the soil particles on his shoes which part of the country a person came from. He also distinguished one hundred and forty types of tobacco ash. Sherlock Holmes was interested in absolutely everything and had extensive knowledge in all areas.

What is the essence of deductive logic

The deductive method begins with a hypothesis that a person believes to be true a priori, and then he must test it through observations. Books on philosophy and psychology define this concept as an inference built on the principle from the general to the particular according to the laws of logic.

Unlike other types of logical reasoning, deduction derives a new idea from others, leading to a specific conclusion applicable to a given situation.

The deductive method allows our thinking to be more specific and effective.

The bottom line is that deduction is based on deducing the particular on the basis of general premises. In other words, this is reasoning based on confirmed, generally accepted and generally known general data, which leads to a logical factual conclusion.

The deductive method is successfully used in mathematics, physics, scientific philosophy and economics. Doctors and lawyers also need to use deductive reasoning skills, but they are useful for any profession. Even for writers working on books, the ability to understand characters and draw conclusions based on empirical knowledge is important.

Deductive logic is a philosophical concept, it has been known since the time of Aristotle, but it began to be intensively developed only in the nineteenth century, when developing mathematical logic gave impetus to the development of the doctrine of the deductive method. Aristotle understood deductive logic as evidence with syllogisms: reasoning with two premises and one conclusion. Rene Descartes also emphasized the high cognitive or cognitive function of deduction. In his works, the scientist contrasted it with intuition. In his opinion, it directly reveals the truth, and deduction comprehends this truth indirectly, that is, through additional reasoning.

In everyday reasoning, deduction is extremely rarely used in the form of a syllogism or two premises and one conclusion. Most often, only one message is indicated, and the second message, as well-known and accepted by everyone, is omitted. The conclusion is also not always formulated explicitly. The logical connection between premises and conclusions is expressed by the words “here”, “therefore”, “therefore”, “therefore”.

Examples of using the method

A person who engages in full deductive reasoning is likely to be mistaken for a pedant. Indeed, when reasoning using the following syllogism as an example, such conclusions may be too artificial.

First part: “All Russian officers carefully preserve military traditions.” Second: “All keepers of military traditions are patriots.” Finally, the conclusion: “Some patriots are Russian officers.”

Another example: “Platinum is a metal, all metals conduct electricity, which means platinum is electrically conductive.”

Quote from a joke about Sherlock Holmes: “The cabman greets Conan Doyle’s hero, saying that he is glad to see him after Constantinople and Milan. To Holmes’ surprise, the cab driver explains that he learned this information from the tags on the luggage.” And this is an example of using the deductive method.

Examples of deductive logic in Conan Doyle's novel and McGuigan's Sherlock Holmes series

What deduction is in the artistic interpretation of Paul McGuigan becomes clear in the following examples. A quote that embodies the deductive method from the series: “This man has the bearing of a former military man. His face is tanned, but this is not his skin tone, since his wrists are not so dark. The face is tired, as if after a serious illness. He holds his hand motionless, most likely he was once wounded in it.” Here Benedict Cumberbatch uses the method of inference from the general to the specific.

Often deductive conclusions are so limited that they can only be guessed at. It can be difficult to restore deduction in full, indicating two premises and a conclusion, as well as logical connections between them.

Quote from detective Conan Doyle: “Because I have been using deductive logic for so long, conclusions arise in my head so quickly that I do not even notice intermediate conclusions or relationships between two positions.”

What does deductive logic give in life?

Deduction will be useful in everyday life, business, and work. The secret of many people who have achieved outstanding success in various fields of activity lies in the ability to use logic and analyze any actions, calculating their outcome.

When studying any subject, the deductive thinking approach will allow you to consider the object of study more carefully and from all sides; at work, you will be able to make the right decisions and calculate efficiency; and in everyday life - to better navigate in building relationships with other people. Therefore, deduction can improve quality of life when used correctly.

The incredible interest shown in deductive reasoning in various fields of scientific activity is absolutely understandable. After all, deduction allows you to obtain new laws and axioms from an existing fact, event, empirical knowledge, moreover, exclusively through theoretical means, without applying it experimentally, solely through observations. Deduction provides a complete guarantee that the facts obtained as a result of a logical approach and operation will be reliable and true.

Speaking about the importance of the logical deductive operation, we should not forget about the inductive method of thinking and justifying new facts. Almost all general phenomena and conclusions, including axioms, theorems and scientific laws, appear as a result of induction, that is, the movement of scientific thought from the particular to the general. Thus, inductive reasoning is the basis of our knowledge. True, this approach in itself does not guarantee the usefulness of the acquired knowledge, but the inductive method raises new assumptions and connects them with knowledge established empirically. Experience in this case is the source and basis of all our scientific ideas about the world.

Deductive argumentation is a powerful means of cognition, used to obtain new facts and knowledge. Together with induction, deduction is a tool for understanding the world.

Logical thinking is based on two methods of inference. These are deduction and induction.

The concept of deduction comes from the Latin word deductio - deduction. This is a method of thinking through which conclusions are obtained along the way from the general case to the particular. Induction, on the contrary, means obtaining conclusions from a particular rule to a general one.

Why develop inductive and deductive abilities?

Deductive methods are known to many from the books of Arthur Conan Doyle, who glorifies the talent of a detective named Sherlock Holmes. This detective masterfully found the criminal every time, since he first suspected everyone, and then examined each of the potential villains, cutting off the unsuitable ones. Not a single detail escaped Holmes's attentive gaze, which is why he unraveled seemingly dead-end cases as quickly as possible.

Why does a person need deductive abilities in the modern world? This is a basic part of logical thinking, without which intellectual abilities will be at a low level. Deductive inferences for the most part take place at an automatic level, that is, a person hardly strains to draw, for example, the following consistent conclusions:

• All children love cartoons.
• Vasya is a child.
• Therefore, Vasya loves cartoons.

The reverse method of inference is called induction. It is worth noting that in life we ​​are not so categorical and do not make hasty conclusions based on deductive or inductive methods. Statements can be based on specific facts, life experiences and previously made conclusions. Otherwise, erroneous conclusions may appear. So, in the case of the above example, not all children love cartoons, since there are children with impaired vision or hearing, and there are simply those who have not seen cartoons and cannot say whether they like them.

Deductive and inductive methods of logical thinking are very useful in everyday life. Every day a person makes hundreds of conclusions based on only a small amount of information. Seeing a crowd of people and remembering that today is Saturday, a person can confidently announce that a sale has begun. Knowing the characteristics of other people's behavior, we can cheer up a person who is sad, without even asking him about the reasons for his bad mood.

Deductive thinking in the life of every professional

It is important for all people to develop deductive abilities, but they will be most useful for representatives of professions from law enforcement agencies:

• Investigator
• Judge
• Lawyer
• Detective

For human learners, deduction is very useful. It is this property of logical thinking that allows you not only to remember, but to assimilate the material.

Deductive methods help doctors make decisions that may affect a person’s life.

Every person needs deductive abilities, but they should be developed. This is part of logical thinking, which can be developed with regular training.

So, deductive abilities should be developed in conjunction with logical thinking. Here it is very important to have a sufficient amount of patience and attentiveness, because deduction does not tolerate haste, its methods can be compared to unraveling a ball of tangled threads - one careless movement and the knot is pulled tighter. To train deductive abilities, it is important to follow several rules.

Keep your brain alert at all times

Try to regularly challenge your brain with new and new tasks. It is during intellectual activity that the formation of logical thinking occurs. For the development of deduction, tasks that require not a momentary solution, but a balanced and reasoned answer are suitable. Games that train deduction are classic poker and, of course, chess.

Study not superficially, but deeply

Man is a creature that strives to understand the world. Broaden your horizons, discovering more and more facets of science, culture and art. Each subject of study must be viewed from different perspectives. There are no small details in deduction; everything is important, which is why try to pay attention to small details that help you draw certain conclusions. You can train by watching films and watching characters, as well as in everyday life, trying to predict the development of a particular situation depending on the available details. To make deduction training not too boring, you should set aside a certain part of your life for travel. It is during travel and relaxation that the human brain receives incomparable impulses that allow one to train intellectual abilities.

Harmonious combination of deduction and induction

Deduction combined with induction allows you to come to the right conclusions. Despite the fact that a person mainly uses these methods “automatically,” the very opportunity to try to change the point of view helps to reach the necessary conclusions. Logic loves order, but not everything obeys its laws, so not only deductive and inductive approaches are very important, but also the ability to use various information, determine its essence and create new conclusions.

Observation and attentiveness are two assistants to deduction

Careful observation of many details helps not only to draw the right conclusions, but also to identify several solutions and development options for the situation. Life experience and past conclusions help to predict the development of a situation with great accuracy and make the right conclusions.

Observation in life is a very useful skill that contributes to the development of deductive thinking. You can observe people, their behavior, their manner of voice. You can also observe natural phenomena, weather, and animals. In any case, an observant person will subconsciously process the information received and draw conclusions.

Attention is a very important characteristic of a person that allows you to concentrate. An inattentive person will certainly miss important details and will not be able to draw complete conclusions.

By the way, the genius of the deductive method, Sherlock Holmes, used his pipe and also played the violin to increase concentration. Today, many people are helped to concentrate by a simple rule - giving up gadgets for a while. If you remove the phone, computer and TV from your sight, a person is more likely to be able to successfully concentrate on the task at hand.

DEDUCTION

DEDUCTION

(from Latin deductio - deduction) - a transition from premises to a conclusion, based on, due to which it follows with logical necessity from the accepted premises. A characteristic feature of D. is that from true premises it always leads only to a true conclusion.
D., as an inference based on the law and necessarily giving a true conclusion from true premises, is contrasted with -, which is not based on the law of logic and leads from true premises to a probable, or problematic, conclusion.
For example, inferences are deductive:
If ice gets hot, it melts.
The ice is heating up.
The ice is melting.
The line separating from the conclusion stands in place of the word “therefore.”
Examples of induction include reasoning:
Brazil is a republic; Argentina is a republic.
Brazil and Argentina are South American countries.
All South American states are republics.
Italy is a republic; Portugal is a republic; Finland is a republic; France is a republic.
Italy, Portugal, Finland, France are Western European countries.
All Western European countries are republics.
Inductive inference relies on some factual or psychological basis. In such an inference, the conclusion may contain information not present in the premises. The reliability of the premises does not therefore mean the reliability of the inductive statement derived from them. The inductive conclusion is problematic and needs further investigation. Thus, the premises of both the first and second given inductive inferences are true, but the conclusion of the first of them is true, and the second is false. Indeed, all South American states are republics; but among Western European countries there are not only republics, but also monarchies.
Particularly characteristic of D. are logical transitions from general knowledge to specific knowledge:
All people are mortal.
All Greeks are people.
All Greeks are mortal.
In all cases when it is necessary to consider something on the basis of an already known general rule and draw the necessary conclusion regarding this phenomenon, we draw conclusions in the form D. Reasoning leading from knowledge about some objects (private knowledge) to knowledge about all objects of a certain class (to general knowledge) are typical inductions. There always remains something that turns out to be hasty and unfounded (“Socrates is a skillful debater; Plato is a skillful debater; therefore, everyone is a skillful debater”).
At the same time, it is impossible to identify D. with the transition from the general to the particular, and induction with the transition from the particular to the general. In the argument, “Shakespeare wrote sonnets; therefore, it is not true that Shakespeare did not write sonnets.” There is D., but there is no transition from the general to the specific. The reasoning “If aluminum is plastic or clay is plastic, then aluminum is plastic” is, as is commonly thought, inductive, but there is no transition from the particular to the general. D. is the derivation of conclusions that are as reliable as the accepted premises; induction is the derivation of probable (plausible) conclusions. Inductive inferences include both transitions from the particular to the general, and the canons of induction, etc.
Deductive inferences allow one to obtain new truths from existing knowledge, and moreover, using pure reasoning, without resorting to experience, intuition, common sense, etc. D. gives a 100% guarantee of success. Starting from true premises and reasoning deductively, we are sure to obtain a reliable result in all cases.
However, one should not separate D. from induction and underestimate the latter. Almost all general provisions, including scientific laws, are the results of inductive generalization. In this sense, induction is the basis of our knowledge. In itself, it does not guarantee its truth and validity, but it generates assumptions, connects them with experience and thereby gives them a certain credibility, a more or less high degree of probability. Experience is the source and foundation of human knowledge. Induction, starting from what is comprehended in experience, is a necessary means of its generalization and systematization.
In ordinary reasoning, D. appears in full and expanded form only in rare cases. Most often, not all used parcels are indicated, but only some. General statements that appear to be well known are omitted. The conclusions that follow from the accepted premises are not always clearly formulated. The logical itself, existing between the original and the deduced statements, is only sometimes marked by words like “therefore” and “means”. Often D. is so abbreviated that one can only guess about it. Carrying out deductive reasoning without omitting or shortening anything is cumbersome. However, whenever there is a question about the validity of the conclusion made, it is necessary to return to the beginning of the reasoning and reproduce it in the most complete form possible. Without this, it is difficult or even impossible to detect a mistake.
Deductive is the derivation of a substantiated position from other, previously accepted provisions. If the put forward position can be logically (deductively) deduced from already established provisions, this means that it is acceptable to the same extent as these provisions themselves. The justification of some statements by reference to or the acceptability of other statements is not the only thing performed by D. in the processes of argumentation. Deductive reasoning also serves to verify (indirectly confirm) statements: from the position being verified, its empirical consequences are deductively derived; These consequences are assessed as an inductive argument in favor of the original position. Deductive reasoning is also used to falsify statements by showing that their consequences are false. Failure to succeed is a weakened version of verification: failure to refute the empirical consequences of the hypothesis being tested is an argument, albeit a very weak one, in support of this hypothesis. And finally, d. is used to systematize a theory or system of knowledge, trace the logical connections of the statements included in it, and construct explanations and understandings based on the general principles proposed by the theory. Clarifying the logical structure of a theory, strengthening its empirical basis, and identifying its general premises are contributions to its propositions.
Deductive argumentation is universal, applicable to all areas of reasoning and to any audience. “And if bliss is nothing other than eternal life, and eternal life is truth, then bliss is nothing other than the knowledge of truth” - John Scotus (Eriugena). This theological reasoning is deductive reasoning, viz.
The proportion of deductive argumentation in different fields of knowledge is significantly different. It is used very widely in mathematics and mathematical physics and only sporadically in history or aesthetics. Keeping in mind the scope of application of D., Aristotle wrote: “One should not demand scientific proof from an orator, just as one should not demand emotional persuasion from an orator.” Deductive argumentation is a very powerful tool, but, like anything else, it must be used narrowly. An attempt to build argumentation in the form of D. in those areas or in the audience that are not suitable for this leads to superficial reasoning that can only create the illusion of persuasiveness.
Depending on how widely deductive argumentation is used, all sciences are usually divided into external and inductive ones. In the first, deductive argumentation is used primarily or even exclusively. Secondly, such argumentation plays only a obviously auxiliary role, and in the first place is empirical argumentation, which has an inductive, probabilistic one. Mathematics is considered a typical deductive science; an example of inductive sciences is. However, sciences into deductive and inductive, widespread in the beginning. 20th century, has now lost much of its character. It is focused on science, considered statically, as a system of reliably and finally established truths.
The concept of "D." is a general methodological concept. In logic it corresponds to evidence.

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

DEDUCTION

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

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

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

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

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

V. modern bourgeois In philosophy, it is very common to over-exaggerate the role of D. in cognition. In a number of works on logic, it is customary to emphasize that which supposedly completely excludes. the role that D. plays in mathematics, in contrast to other scientific. disciplines. By focusing on this “difference,” they go so far as to claim that all sciences can be divided into so-called sciences. deductive and empirical. (see, for example, L. S. Stebbing, A modern introduction to logic, L., 1930). However, such a distinction is fundamentally illegitimate and it is denied not only by dialectical-materialistic scientists. positions, but also certain bourgeois. researchers (for example, J. Lukasiewicz; see Lukasiewicz, Aristotelian from the point of view of modern formal logic, translated from English, M., 1959), who realized that both logical and mathematical. axioms are ultimately a reflection of certain experiments with material objects of the objective world, actions on them in the process of social-historical. practices. And in this sense, mathematician. axioms do not contradict the provisions of science and society. An important feature of D. is its analytical nature. character. Mill also noted that there is nothing in the conclusion of deductive reasoning that is not already contained in its premises. To describe analytical the nature of deductive implication is formal, let us resort to the exact language of algebra of logic. Let us assume that deductive reasoning is formalized by means of the algebra of logic, i.e. The relationships between the volumes of concepts (classes) are precisely recorded both in the premises and in the conclusion. Then it turns out that the decomposition of premises into constituent (elementary) units contains all those constituents that are present in the decomposition of the consequence.

Due to the special significance that the disclosure of premises acquires in any deductive conclusion, deduction is often associated with analysis. Since in the process of D. (in the conclusion of a deductive inference) there is often a combination of knowledge given to us in the department. premises, D. is associated with synthesis.

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

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

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

D. Gorsky. Moscow.

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

DEDUCTION

DEDUCTION (from Latin deductio - deduction) - the transition from the general to the specific; in a more special sense, the term “deduction” denotes the process of logical inference, i.e., the transition, according to certain rules of logic, from certain given premise sentences to their consequences (conclusions). The term “deduction” is used both to denote specific conclusions of consequences from premises (i.e., as a synonym for the term “conclusion” in one of its meanings), and as a generic name for the general theory of constructing correct conclusions. Sciences whose propositions are primarily obtained as consequences of certain general principles, postulates, axioms are usually called deductive (mathematics, theoretical mechanics, some branches of physics, etc.), and the axiomatic method by which the conclusions of these particular propositions are drawn is axiomatic-deductive.

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

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

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

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