Definitions of deduction and induction. Inductive and deductive methods

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 and there was a strong wind at night. 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 were identified important types conclusions:

• 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 valid reasoning was viewed 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 obtaining 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 their “enduring” value, in contrast to the “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 how Sherlock Holmes unravels detective stories using the deductive method, it can be adopted by investigators, lawyers, employees law enforcement. 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 have become brand names Sherlock Holmes, as well as the heroes of the series “True Detective” or “The Mentalist”. Columnist The New Yorker 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 prone you are to making mistakes and the more likely you are to miss things. 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, 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 comes down to learning how to give meaning 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 skills 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 post, 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 simply ignore. 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 also easily understand the works of Renaissance artists, the latest trends in the cryptocurrency market and discoveries in the most progressive theories quantum physics, your deductive thinking methods have a much higher 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 is increased intellectual abilities and contribute 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 they will help various encyclopedias, trips to museums, documentaries and, of course, travel.
3. Pedantry. The ability to thoroughly study an object that interests 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. To choose the best 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 availability of several options for resolving the issue, will help you choose the most optimal conclusion.
5. Observation. When communicating with people, it is recommended not only to hear what they say, but also to observe their facial expressions, gestures, voice and intonation. Thus, one can recognize whether a person is sincere or not, what his intentions are, etc.

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 in a broad sense words, 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 knowledge that is less universal to knowledge that is more universal (the path of knowledge “from the bottom up”).

By observing and studying individual objects, facts, events, a person comes to knowledge general patterns. Nothing can do without them human cognition. 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 development new science. The English philosopher Francis Bacon, criticizing scholastic logic, considered induction, based on observation and experiment, to be the main method of knowing the truth. With the help of such induction, Bacon intended to look for the cause of the properties of things. Logic should become the logic of inventions and discoveries, Bacon believed; Aristotle’s 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 great place devoted 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, axiom. 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 to more general provisions to knowledge of less general provisions.

In general, deduction as a method of knowledge 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 rational way 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. Because there is no logic scientific discovery, no methods guaranteeing obtaining true scientific knowledge, to the extent that 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 hypothesis, which cannot be reduced to induction and deduction. However, to completely overcome the opposition between inductive and deductive methods of cognition for a long time it didn't work out.

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 (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 and there was a strong wind at night. 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 valid reasoning was viewed 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 particular judgment, is brought under a 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, logical thinking, memory and simply makes you think, preventing the brain from aging prematurely. 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 other negative emotions that are processed in the amygdala impair the brain's ability to solve problems or absorb information. Positive emotions, on the contrary, improve this brain function and even help you think more creatively and strategically.

Develop memory

Having tuned in 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 makes 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 other board games that develop 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 skills 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 post, 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 force you to make better decisions about what's really important and what's not."

Taking field notes, whether during a regular work meeting or a walk in a city park, will develop the right approach to exploring the environment. Over time, you begin to pay attention to small details in any situation, and the more you do this 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. It is not easy to describe in a few sentences how to develop your critical thinking abilities. 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 simply ignore. 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 for developing 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 your personality from different angles, but will also help you gain experience, rather than relying 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 that interests 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. To choose the best 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 availability of several options for resolving the issue, will help you choose the most optimal conclusion.
5. Observation. When communicating with people, it is recommended not only to hear what they say, but also to observe their facial expressions, gestures, voice and intonation. Thus, one can recognize whether a person is sincere or not, what his intentions are, etc.

Deduction is special method thinking, based on the ability to build a logical connection and draw small private conclusions from the overall picture. How did the well-known legendary hero Sherlock Holmes use this?

Sherlock Holmes method

Sherlock Holmes' deductive method can be described in one phrase that the detective uttered in A Study in Scarlet: "All life is a huge chain of causes and effects, and we can know its nature one by one." Undoubtedly, everything in life is chaotic and sometimes unpredictable, but despite this, the skills that the detective possessed helped him solve even the most complicated crimes.

Observation and details

Sherlock Holmes collected as much as possible more information, analyzed all possible scenarios for the development of events and looked at them under different angles. This allowed the detective to discard the unimportant, thus, the hero of Arthur Conan Doyle singled out one or more more significant ones from the many possible versions.

Concentration

A detached face, ignoring people and their questions, as well as events around oneself - this is how Conan Doyle portrays his hero. However, such behavior is by no means a sign of bad taste. No. This is the result of a special focus on the investigation. Sherlock Holmes constantly thinks about everything possible options solving a problem, abstracting from external factors.

Interest and outlook

The detective's main weapon was his broad outlook. It is worth remembering how he could easily determine from soil particles where a person came from in England. He was interested in literally everything, especially what escaped attention ordinary people. He was an expert in criminology and biochemistry, played the violin remarkably, was knowledgeable about opera and music, and knew several foreign languages, practiced fencing and knew how to box. A multifaceted personality, isn't it?..

The palaces of the mind

The deduction method is based on memorizing information using associations. The famous detective worked with a large amount of information. And in order not to get confused in it, he used a method called “paintings of the mind.” By the way, it is far from new; its essence was known to the ancient Greeks. Each fact, information, knowledge is tied to a specific object in the room, for example, a door, window, etc. This made it easier for the detective to remember information that came to him almost hourly.

Sign language

Sherlock Holmes was a wonderful psychologist. Observing the behavior of a particular person, the detective paid attention to facial expressions and gestures, as a result of which he could easily determine whether his client/suspect was lying or not. The ability to notice details - behavior, manner of speaking, dressing - helps to create an overall picture of a person’s life.

Intuition

Sherlock Holmes' intuition was more likely based not on a sixth sense, but on experience. But the line between the voice of the subconscious and high qualifications in work is quite blurred. Only the person himself can draw this fine line between the assumption and the action itself.

Practice

The method of deduction can only be developed through practice. Sherlock Holmes constantly practiced logic, even in his free time. This allowed him to constantly keep his mind “on its toes.” But without interesting things to do, he was bored and mopey.

The benefits of deduction

Deductive thinking skills will be useful in everyday life and labor activity. The secret of many successful people is the ability to think logically and analyze their actions, predicting the outcome of events. This helps them avoid patterns and achieve greater success in various areas:

In studies - helps to quickly master the subject being studied;

In work activity - make the right decisions and plan your actions several steps ahead;

In life - to understand people well and build effective relationships with others.

Thus, the deduction method will help make life much easier and avoid many unpleasant situations, as well as quickly achieve your goals.

How to develop deductive thinking

Mastering the way of thinking we are considering is a long and painstaking work on oneself, but at the same time it does not present any particular difficulties. The deduction method requires the participation of common sense, but emotions must be relegated to the background, they will only interfere with the process. There are a number of rules that will help develop a deductive way of thinking at any age.

1. If you are determined to achieve a positive result in this field, then you need to start reading a lot. But not glossy magazines and newspapers - they will be useful classic literature And modern detectives or novels. While reading, you need to think about the plot and remember the details. Compare the “material covered”: eras, genres, etc.

2. In everyday life, try to pay attention to little things: people’s behavior, their clothes, gestures, facial expressions, speech. This will help develop your powers of observation and teach you analysis. It would be nice to enlist the support of a like-minded person with whom you can discuss what you saw, and in the process of conversation you will learn to express your thoughts logically and build a chronological sequence of events.

3. Solving logical problems and puzzles will help you master deductive thinking skills.

4. Pay attention to your actions, analyze why you did what you did in a certain situation, look for other possible options for getting out of it and think about what result could have happened in this case.

5. The development of deductive thinking requires memory training. This is necessary in order to cover a large amount of information and keep it in your head. It is important to note that memory training needs to be done constantly. Scientists have found that a person loses acquired skills and abilities if brain activity is interrupted for some period of time (say, on vacation). Well-known methods will help develop memory:

Memorize a certain number of words by ear;

Repeat the phrases you read word for word;

List items.

It should be remembered that there are several sources of information perception: auditory, voice, visual and tactile. At the same time, it is important to develop everything simultaneously, focusing on weaknesses. To simplify the memorization process, you can come up with your own system of encoding and associations.

6. But you should not completely rely on memory, since its possibilities are not unlimited. You need to train yourself to take notes - in the form of graphs, tables, lists. This useful habit will help you find connections and create logical chains.

7. It is important to constantly learn new knowledge. They may not even be related to social life and interpersonal relationships. Recommended reading fiction- this will develop impressionability and the ability to think figuratively. Special attention must be paid to the development of special knowledge, such as psychology, physiognomy, sign language. They will help analyze human behavior in certain situations.

8. Practice plays an important role in mastering deductive thinking. Its essence is to create a problematic situation and find a way out of the current situation. To do this, it is necessary to put forward a hypothesis and determine ways to solve the problem. Next, considering all possible approaches, we need to find best option. Try to conduct a comparative analysis of the expected paths of development of events.

Deductive way of thinking is an amusing trip according to the expanses of logic. By making an effort and spending some time practicing, you will be able to pick up the keys to any locks using deduction and experience for yourself what it means to be Sherlock Holmes.

) the term “deduction” is used as a synonym for the more precise, but more cumbersome, term “deductive reasoning” and is understood in a narrower sense: as inference, in which the general conclusion is based on particular premises. It is believed that if the premises of deduction are true, then [subject to correct form reasoning] are true and its consequences (conclusions). In deductive reasoning, there is a relationship between premises and conclusion logical consequence(see), in which the logical content of the conclusion (its information without taking into account the meanings of non-logical terms) forms part of the total logical content of the premises. In this sense, the term “deduction” is used to denote specific conclusions of consequences from premises, that is, as a synonym for the term “conclusion” in one of its meanings. All this determines the close connection (and sometimes even identification) of the concept of deduction with the concepts of inference and consequence, which is reflected in logical terminology; Thus, the “theorem of deduction” is usually called one of the important relationships between the logical connective of implication (formalizing the verbal phrase “If ..., then ...”) and the relation of logical implication (derivability): if from the premise A a consequence is drawn B, then the implication A ≡ B("If A…, That B...") is provable (that is, deducible without any premises, from axioms alone). (A deduction theorem valid for some sufficiently general conditions for all “full-fledged” logical systems, in some cases it is simply postulated for them as original rule.) Other logical terms associated with the concept of deduction are of a similar nature; Thus, sentences derived from each other are called deductively equivalent; the deductive completeness of a system (with respect to some property) consists in the fact that all expressions of this system that have this property (for example, truth under some interpretation) are provable in it.

Along with this, the term “deduction” denotes the generic name for the general theory of constructing correct conclusions. In accordance with this last usage, sciences whose propositions are obtained (at least predominantly) as consequences of some general “basic laws” (principles, postulates, axioms, etc.) are usually called deductive (mathematics, theoretical mechanics, some branches of physics and others), and axiomatic method, by means of which the conclusions of these particular propositions are made, are often called axiomatic-deductive. The opposite of deduction is induction(see), in which the general conclusion is also built on the basis of particular premises, but the premises may confirm or imply the truth, but do not guarantee its receipt. Accordingly, examples of inductive sciences are natural Sciences. At the same time, the division of sciences into deductive and inductive, widespread at the beginning of the 20th century, has now largely lost its meaning, since it is focused on science viewed statically, that is, as a system of reliably and finally established truths.

Deduction method is widely used in all fields scientific knowledge, playing an important role in the construction of empirical knowledge and the transition from empirical to theoretical knowledge (see). In deduction, relying on general knowledge, a conclusion of a particular nature is made, therefore one of the premises of deduction is necessarily a general judgment. If it is obtained as a result of inductive reasoning, then deduction complements induction, expanding the amount of knowledge gained. The greatest cognitive value of deduction is manifested in the case when the general premise is not just an inductive generalization, but some kind of hypothetical assumption, a new scientific idea. In this case, deduction plays not just an auxiliary role, complementing induction, but is the starting point for the emergence of a new theoretical system. Created this way theoretical knowledge(see) predetermines the further course of empirical research and targets the construction of new inductive generalizations. Overall, on initial stage In scientific research, induction predominates; in the course of the development and substantiation of scientific knowledge, deduction begins to play a major role. Thus, these two operations of scientific knowledge are inextricably linked and complement each other.

The general scheme of organization of scientific-theoretical deductive systems includes:

1. initial basis, that is, a set of initial terms and statements;
2. the logical means used (inference and definition rules);
3. a set of statements (proposals) obtained from (1) by applying (2).

When studying such theories, the relationships between their individual components, abstracted from the genesis and development of knowledge, are analyzed. Therefore, it is advisable to consider them as a kind of formalized languages ​​that can be analyzed either syntactically (when the relationship between the signs and expressions included in the language is studied without taking into account their extra-linguistic meaning), or semantically (when the relationship between signs and expressions of the system is considered from the point of view of their meaning) aspects. Deductive systems are divided into axiomatic (axiomatic method) and constructive (constructive method). The deductive method, when used in knowledge based on experience and experiment, acts as hypothetico-deductive method(cm. ). The analysis of the deductive method of constructing scientific knowledge began already in ancient philosophy (Plato, Aristotle, Euclid, the Stoics), and occupied a significant place in the philosophy of modern times (R. Descartes, B. Pascal, B. Spinoza, G. V. Leibniz and others), but the principles of the deductive organization of knowledge were most fully and clearly formulated only at the end of the 19th - beginning of the 20th centuries with the use of the apparatus of mathematical logic. Until the end of the 19th century, the deductive method was used mainly in the fields of mathematics and logic. In the 20th century, attempts at deductive (in particular, axiomatic) construction of many non-mathematical disciplines - certain branches of physics, biology, linguistics, sociology and others - became widespread.

The study of deduction is the main task of logic; sometimes logic - anyway formal logic(see) - is even defined as the “theory of deduction.” Outside the bounds of deductive logic are the so-called plausible reasoning(mass media inductive methods, which are studied in inductive logic(cm. ). Deductive logic studies methods of reasoning with standard, typical statements; These methods are presented in the form logical systems, or calculus.

Although 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 was syllogistic inferences(see) - was carried out by Aristotle in the “First Analytics” (“First Analytics”, II 25, 69a 20–36) 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. Such important types of inferences were identified as conditionally categorical (modus ponens, modus tollens), dividing-categorical (modus tollendo ponens, modus ponendo tollens), conditionally dividing (lemmatic) and others. 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. (The primacy of intuition over deduction, proclaimed by Descartes, was revived much later and in significantly modified and developed forms in the concepts intuitionism- see) 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 (if expressed in modern language) no “information” that would not be contained (even if implicitly) 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 valid reasoning was viewed 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 by deduction, knowledge is “true in all possible worlds” (or, as I. Kant later said, “analytically true”), which determines their “enduring” value, in contrast to “factual” data obtained by inductive generalization of observation and experience ( or “synthetic”) truths that 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.”

Within the framework of traditional logic, only a small part of deductive reasoning was described and there were no precise criteria for the logical correctness of reasoning. In modern symbolic logic(see), thanks to the use of formalization methods, the construction of logical calculi and formal semantics, and the axiomatic method, the study of deductive inferences was raised to a qualitatively different, theoretical level. By means of modern logical theory, it is possible to define the entire set of forms of correct deductive inferences within the framework of a certain formalized language. Thus, if the theory is constructed semantically, then the transition from formulas A 1 A 2 , … A n to formula B declared to be a form of correct deductive reasoning in the presence of logical consequence B from A 1 A 2 , … A n ; this relation is usually defined as follows: for any interpretation of non-logical symbols admissible in a given theory, in which A 1 A 2 , … A n take the highlighted value (truth value), formula B also takes the highlighted value. In syntactically constructed logical systems (calculi), the criterion for the logical correctness of the transition from A 1 A 2 , … A n to B indicates the existence of a formal derivation of the formula B from formulas A 1 A 2 , … A n, carried out in accordance with the rules of this system.

The choice of a logical theory adequate for testing deductive inferences is determined by the type of statements included in its composition and the expressive capabilities of the language of the theory. Thus, inferences containing complex statements can be analyzed by means propositional logic(see), while the internal structure of simple statements within complex ones is ignored. Syllogistics(see) explores inferences from simple attributive statements based on volumetric relations in the sphere general terms. By means predicate logic(see) correct deductive inferences are highlighted based on taking into account the internal structure of simple statements of various types different types. Inferences containing modal statements are considered within the framework of systems modal logic(see), those that contain tense utterances - within temporal logic(see) and so on.