The deductive method is direct. How to develop deduction: recommendations, games and methods. How to develop logic and deduction. What does deductive logic give in life?

Deduction is a special method of thinking based on the ability to build a logical connection and draw small private conclusions from the overall picture. How did everyone use it? legendary hero Sherlock Holmes?

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 happens chaotically and sometimes unpredictably, 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 information as possible, analyzed various scenarios for the development of events and looked at them from 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 all possible options for 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 the attention of ordinary people. He was a specialist 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 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 something interesting 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 - classical literature and modern detective stories or novels will be useful. 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 at the same time, 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. It is recommended to read fiction - this will develop impressionability and the ability to think figuratively. Special attention must be paid to mastering 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 problem 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 various approaches, you need to find the best option. Try to conduct a comparative analysis of the expected paths of development of events.

The deductive way of thinking is a fascinating journey through 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.

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

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

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

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

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

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

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

What does the mind of Sherlock Holmes do?

Deductive method

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

Attention

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

Knowledge base

The detective himself said it best:

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

The palaces of the mind

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

Constant analysis

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

How to learn it

Pay attention to the little things

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

Develop your memory

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

Learn to formulate

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

Go deeper into the area

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

Concentrate

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

Learn body language

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

Develop your intuition

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

Take notes

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

Ask questions

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

Solve problems and puzzles

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

Create puzzles

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

Read. More. Better

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

Listen more, talk less

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

Love what you do

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

Practice

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

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

If you ask a person what guides him when he makes decisions, seeks answers to important questions in life or to the simplest everyday questions, you will often hear two polar opinions. Some people claim that they rely on their own sensations, feelings, intuition, while others trust only “common sense” and logic. This means that the first category of people is guided by the experience of the emotional sphere, and the second draws conclusions using the intellect, through logical conclusions.

A person is beautiful in his integrity; “cold” logical thinking in interaction with bright emotional colors makes a person’s experience unique and gives the ability to be creative. Therefore, in the process of personal development, it is worth evenly developing both the ability to empathy, intuition, and logical thinking.

In the process of logical analysis, a person uses various operations and methods of thinking, among which the inductive and hypothetico-deductive method of thinking are important. They are parts of one holistic process of testing put forward hypotheses in order to find the most optimal solution to the problem.

True inference

In order to better understand how deductive thinking works, you should understand and distinguish between the concepts of induction and deduction, and study their definition. When using induction, a person first observes some fact, and then, based on it, draws conclusions about the phenomenon as a whole.

You can give examples: you noticed that your teenage sister loves watching TV series, her friend watches them too, and then you found out that their entire class is passionate about this series. Based on this, you conclude that most teenagers are addicted to TV series. This means that with the help of induction you observe different objects, and then proceed to put forward a general hypothesis.

The scientific definition of induction states that inductive reasoning is built on the basis of factual premises, which ultimately lead to the formation general conclusion, which contains unconfirmed information. That is why the induction method very often influences the formation of thinking stereotypes. Everyone knows how some women, based on several unsuccessful relationships, like to conclude that “all men are assholes.” Or the common conclusion in our society that all politicians are liars, because previous experience has confirmed this hypothesis many times.

Unlike induction, the hypothetico-deductive method is entirely based on logic. Its definition seems very simple, but in order to understand its meaning and learn to use it in everyday life to solve problems different levels falsity, you should study it in detail and provide examples.

The deductive method makes our thinking more accurate and effective. Its essence is that a particular conclusion is made on the basis of general premises. Simply put, it is reasoning based on confirmed general data that leads to the same confirmed factual conclusion. To give examples: if it rains, then one can argue that the ground is wet; all people will die someday, you are a human, therefore, you are also doomed to death. It is obvious that deduction, unlike induction, makes it possible to draw competent conclusions based on verified and irrefutable facts.

What is the genius of Sherlock Holmes?

The hypothetico-deductive method in our time has long gone beyond the scope of science and has become widely used in all spheres of human life. With its help, you can think through your actions in more detail and deeply, plan them several steps ahead, and also better understand the motives and behavior of other people. To understand the power of deduction, you can study the genius of the famous character in Arthur Conan Doyle's books, detective Sherlock Holmes. His insight amazes readers, and his talent for solving the most complicated crimes is simply shocking.

Deduction with “humor”:

How to independently develop deductive thinking?

In our society, there is a tendency among people to generalize, which often leads to negative consequences not only for a specific person, but also for the entire society as a whole. Based on generalizations, people are capable of blaming and ruining relationships. A person who builds relationships based on facts, not versions, commands respect. To develop deductive thinking, which, among other things, helps in difficult life situations, use the following tips:

• Dig Deeper. If you take on the study of any material, fact, subject, then try to become interested in it so as to study it in all details. For example, when reading a book, do not just follow the main events, but carefully study the characters of each hero in their interrelation. This way, you can predict the outcome of the story well before its end. This is especially true for books in the detective genre. The same can be said about cinema.
• Expand your horizons. Try to become a well-rounded person. Improve your knowledge all the time, because the pace modern life dictates the conditions for constant development, stopping which even for a while can cost you a lot. This is a loss of professional and personal guidelines, as well as mutual understanding with other people. Expand your social circle, read a lot, try yourself in new areas of activity, cast aside doubts. Deep theoretical and practical knowledge will help you solve problems based not on guesswork, but on the basis of their experience.
• Develop flexibility of thinking. It consists of always looking for different options and examples of solving a problem, even if you go for, at first glance, the obvious correct answer. Don't reject other people's opinions, listen to different versions. The presence of different options, opinions of other people, plus rich personal experience and deep knowledge will help you come to a competent deductive conclusion.
• Observe your interlocutor. Use the examples of Sherlock Holmes in your daily interactions with other people. Try not only to delve into the general meaning of what was said, but also to pay close attention to individual repeated words, to non-verbal means of communication: facial expressions, intonation, timbre, gestures, tone of voice. At first it will be difficult for you to grasp all these points, but over time you will learn to read the message of your interlocutor “between the lines” and draw more accurate conclusions about the person, and recognize lies.
• Solve problems. Now there are a lot of books with tasks and puzzles for development logical thinking. Buy yourself such a book and get to work. But keep in mind that it is better to start with easier tasks, gradually increasing their level of difficulty.

And remember that to achieve results you need regular training. Our brain needs it just like our muscles. Good luck!

Thinking is a complex mental process through which we understand the world around us.

Deduction is a method of thinking in which conclusions are derived by logic from the general.

For example, the sun is always in the sky, therefore it is in the sky every day. When using the deductive method, our thinking becomes more accurate. It is based on a particular conclusion, which is made from general premises. The deductive method makes it possible to make correct conclusions based on accurate and indisputable facts.

Now almost every person develops and uses it. Using the deductive method of thinking, you can think through your actions many steps ahead down to the smallest detail.

The benefits of deductive thinking

The education system tries to equate high and low intelligent children, because the former pose a considerable danger to the entire system. It is impossible to control them; they will not look for someone who would tell them what to do.

The advantage of the deductive method is that you grow above yourself, the ability to think in new ways, and you:

• learn to quickly find the right solutions and cope with the task faster;
• gain original, out-of-the-box thinking;
• you can find an approach to any person, problem, situation;
• you will have flexibility of mind, well-developed intuition;
• learn to better understand the behavior and motives of other people.

By developing the method of deductive thinking, you will not only develop all the functions of your brain, but it will also be easier for you to work in life. No one is born an intellectual, you need to learn this and constantly work on yourself.

Intuition and the deductive method

Deductive thinking is important in every person's life. But in order to avoid mistakes in its application, it should be understood that each individual case has a generalization. To do it correctly, you need to continuously acquire new knowledge, look for details and connections between events, i.e. develop observation skills. Of course, at first there may be difficulties, because the brain is aimed at searching for little things. However, when mindfulness becomes a habit, you will notice details automatically.

Although this method of thinking is a search for solutions using logic, intuition is also important. Because it is unconscious, it is a “gut feeling” that knows for sure and remembers much more than the conscious.

Presentation: "Basic concepts of logic. Inference"

Intuition also needs to be developed. It should work without failures. For example, the well-known Sherlock Holmes used deductive thinking, but he also used intuition. When a couple of clues are available, the investigation can be turned in any direction, and there are many of them, and each can be justified logically. You need to spend a lot of time on this.

Development of the deductive method of thinking

It has been proven that mechanical activity slows down brain performance. Our task is to make it work actively, which means it is necessary to attract new events that require analysis.

By performing various techniques listed below, you can learn to look for non-standard solutions to posed questions using the deductive method of thinking.

• Use of sensors. For example, while eating food, close your eyes and inhale its smell. Think about it, and then touch it with your hand if the dish allows it.
• Development of flexibility of thinking. There are no hopeless situations. Therefore, it is recommended to consider the problem from different angles. For example, you can listen to other people's points of view, look at your experience in solving these issues, and then combine the data using the method of deductive reasoning, i.e. construction of logical chains.
• A prerequisite is to find a connection not only between events, but also between thoughts.

• Learning and development. Regardless of age and occupation, you need to constantly develop, learn new hobbies or sports interests. Even attempts to understand the operation of some mechanism help develop deduction abilities. Important rule– do not stop the learning process, because Your goal is to develop a brain function such as analysis.
• Changing the course of events during the day. For example, when returning home after a hard day, take a different road. When visiting a cafe, choose a dish that you previously did not dare to try.
• Traveling is another useful hobby. Exploring the world, a person learns a lot of new things, communicates with different people living in a different culture and having a different temperament from yours. The purpose of each trip is to immerse yourself in the culture of another people and adapt to their living conditions. At such times, brain functions such as analysis, memory, and perception are involved.

With the help of these exercises, you will not only learn the method of deductive thinking, but also have a pleasant time doing interesting things. To achieve good results, continuous training is needed.

Anyone can develop this method. This requires a sincere desire, systematic repetition of tasks and the will to reach the end.

Exercises to develop 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 of interest to you allows you to comprehensively and thoroughly gain a complete understanding. It is important that this object evokes a response in the emotional spectrum, then the result will be effective.
4. Flexibility of mind. When solving a task or problem, it is necessary to use different approaches. 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 presence of several options for solving the issue, will help you choose the most optimal conclusion.
5. Observation. When communicating with people, it is recommended not only to hear what they say, but also to observe their facial expressions, gestures, voice and intonation. Thus, one can recognize whether a person is sincere or not, what his intentions are, etc.

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

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

Let us analyze induction as a method of empirical knowledge.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Baconian induction is based on the recognition:

material unity of nature;

uniformity of its actions;

universal causation.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Difference method:"a" occurs in ABC, but does not occur in BC, where A is absent. It follows from this that A is necessary for “a” to arise (i.e., is the cause of “a”).

United method of similarities and differences:“a” occurs with AB and AS , but does not arise with BC. It follows that A is necessary and sufficient for the determination of “a” (i.e., is its cause).

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

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

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

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

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

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

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

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

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

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

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

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

The first premise: crucian carp is a fish;

second premise: crucian carp lives in water;

conclusion (inference): fish live in water.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Firstly, creating the most complete classification possible;

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

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

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

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

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

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

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

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

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

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

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

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

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