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Induction (from Latin inductio - guidance, motivation) is a formal logical conclusion that leads to a general conclusion based on particular premises. In other words, it is the movement of our thinking from the particular to the general.

Induction is widely used in scientific knowledge. Finding similar features, properties in many objects of a certain class, the researcher concludes that these features, properties are inherent in all objects of this class. Along with other methods of cognition, the inductive method played a role important role in the discovery of certain laws of nature (universal gravity, atmospheric pressure, thermal expansion of bodies, etc.).

Induction used in scientific knowledge (scientific induction) can be implemented in the form of the following methods:

1. The method of single similarity (in all cases of observing a phenomenon, only one common factor is found, all others are different; therefore, this single similar factor is the cause of this phenomenon).
2. The method of a single difference (if the circumstances of the occurrence of a phenomenon and the circumstances under which it does not occur are similar in almost everything and differ only in one factor that is present only in the first case, then we can conclude that this factor is the cause of this phenomena).
3. Combined method of similarity and difference (is a combination of the above two methods).
4. The method of concomitant changes (if certain changes in one phenomenon each time entail some changes in another phenomenon, then this implies the conclusion about causation these events).
5. Method of residuals (if a complex phenomenon is caused by a multifactorial cause, and some of these factors are known as the cause of some part of this phenomenon, then the conclusion follows: the cause of another part of the phenomenon is the remaining factors included in the general cause of this phenomenon).

The founder of the classical inductive method of cognition is F. Bacon. But he interpreted induction extremely broadly, considered it the most important method of discovering new truths in science, the main means scientific knowledge nature.

In fact, the above methods of scientific induction serve mainly to find empirical relationships between the experimentally observed properties of objects and phenomena.

But the especially great cognitive significance of deduction is manifested in the case when the general premise is not just an inductive generalization, but some kind of hypothetical assumption, for example, a new scientific idea. In this case, deduction is the starting point for the birth of a new theoretical system. The theoretical knowledge created in this way predetermines the further course of empirical research and directs the construction of new inductive generalizations.

The acquisition of new knowledge through deduction exists in all natural sciences, but especially great importance the deductive method has in mathematics. In terms of mathematical abstractions and building their reasoning on a very general provisions, mathematicians are forced most often to use deduction. And mathematics is, perhaps, the only proper deductive science.

In the science of modern times, the prominent mathematician and philosopher R. Descartes was the propagandist of the deductive method of cognition.

But, despite the attempts that have taken place in the history of science and philosophy to separate induction from deduction, to oppose them in the real process of scientific knowledge, these two methods are not used as isolated, isolated from each other. Each of them is used at a corresponding stage of the cognitive process.

Moreover, in the process of using the inductive method, deduction is often “hidden” as well. “Generalizing the facts in accordance with some ideas, we thereby indirectly derive the generalizations we receive from these ideas, and we are far from always aware of this. It seems that our thought moves directly from facts to generalizations, that is, that there is pure induction here.

In fact, in conformity with some ideas, in other words, being implicitly guided by them in the process of generalizing facts, our thought indirectly proceeds from ideas to these generalizations, and, consequently, deduction also takes place here ... We can say that in in all cases when we generalize, in accordance with any philosophical provisions, our conclusions are not only induction, but also hidden deduction.

Emphasizing the necessary connection between induction and deduction, F. Engels strongly advised scientists: “Induction and deduction are interconnected in the same necessary way as synthesis and analysis. Instead of one-sidedly exalting one of them to the skies at the expense of the other, one should try to apply each in its place, and this can be achieved only if one does not lose sight of their connection with each other, their mutual complement to each other.

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

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

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

What is the essence of deductive logic

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

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

The deductive method allows our thinking to be more concrete and efficient.

The bottom line is that deduction is based on the derivation of the particular on the basis of general premises. In other words, these are arguments based on confirmed, generally accepted and well-known general data, which lead to a logical factual conclusion.

The deductive method is successfully applied in mathematics, physics, scientific philosophy and the economy. Doctors and lawyers also need to apply the skills of deductive reasoning, but they will be useful for representatives of any profession. Even for writers working on books, the ability to understand characters and draw conclusions based on empirical knowledge is important.

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

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

Examples of using the method

A person who conducts deductive reasoning in its entirety is likely to be mistaken for a pedant. Indeed, arguing on the example of the following syllogism, such conclusions may be too artificial.

The first part: "All Russian officers cherish military traditions." Second: "All keepers of martial traditions are patriots." Finally, the conclusion: "Some patriots are Russian officers."

Another example: "Platinum is a metal, all metals conduct electricity, so platinum is electrically conductive."

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

Examples of Deductive Logic in Conan Doyle's Novel and McGuigan's Sherlock Holmes Series

What is deduction in the artistic interpretation of Paul McGuigan becomes clear in the following examples. A quote embodying the deductive method from the series: “This man has the bearing of an ex-military man. His face is tanned, but it's not his skin tone, since his wrists aren't as dark. The face is tired, as after a serious illness. Keeps his hand motionless, most likely, was once wounded in it. Here Benedict Cumberbatch uses the method of inference from the general to the particular.

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

Quote from Detective Conan Doyle: “Because I have been using deductive logic for so long, inferences flow through my head at such a speed that I do not even notice intermediate conclusions or relationships between two positions.”

What gives deductive logic in life

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

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

The incredible interest shown in deductive reasoning in various fields scientific activity, absolutely explain. After all, deduction allows one to obtain new laws and axioms from an already existing fact, event, empirical knowledge, moreover, exclusively theoretically, without applying it in experiments, solely thanks to observations. Deduction gives a full guarantee that the facts obtained as a result of a logical approach, operations will be reliable and true.

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

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

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with the method of induction, the study of individual facts, principles and the formation of general theoretical concepts on the basis of obtaining results (from the particular to the general) take place. The method of deduction involves the study of general principles, laws, when the provisions of the theory are distributed into separate phenomena.

Induction (from Latin Inductio - guidance, motivation) is a method of cognition based on a formal logical conclusion, which leads to a general conclusion based on particular premises. In other words, it is the movement of our thinking from the particular, the individual to the general.

Induction is widely used in scientific knowledge. Finding similar features, properties in many objects of a certain class, the researcher concludes that these features, properties are inherent in all objects of this class. For example, in the process of experimental study of electrical phenomena, current conductors made of various metals were used. Based on numerous individual experiments, a general conclusion was formed about the electrical conductivity of all metals. Along with other methods of cognition, the inductive method played an important role in the discovery of certain laws of nature (universal gravity, atmospheric pressure, thermal expansion of bodies, etc.).

Induction used in scientific knowledge (scientific induction) can be implemented in the form of the following methods:

1. The method of single similarity (in all cases of observing a phenomenon, only one common factor is found, all others are different; therefore, this single similar factor is the cause of this phenomenon).

2. The method of a single difference (if the circumstances of the occurrence of a phenomenon and the circumstances under which it does not occur are similar in almost everything and differ only in one factor that is present only in the first case, then we can conclude that this factor is the cause of this phenomena).

3. Combined method of similarity and difference (is a combination of the above two methods).

4. The method of concomitant changes (if certain changes in one phenomenon each time entail some changes in another phenomenon, then the conclusion follows about the causal relationship of these phenomena).

5. Method of residuals (if a complex phenomenon is caused by a multifactorial cause, and some of these factors are known as the cause of some part of this phenomenon, then the conclusion follows: the cause of another part of the phenomenon is the remaining factors included in the general cause of this phenomenon).

In fact, the above methods of scientific induction serve mainly to find empirical relationships between the experimentally observed properties of objects and phenomena. They systematize the simplest formal logical techniques that were spontaneously used by natural scientists in any empirical study. With the development of natural science, it became more and more clear that the methods of classical induction do not play that all-encompassing role in scientific knowledge, which was attributed to them by F. Bacon and his followers up to late XIX century.

Such an unjustifiably extended understanding of the role of induction in scientific knowledge has received the name of all-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. F. Engels criticized all-inductivism, pointing out that induction cannot, in particular, be separated from another method of cognition - deduction.

Deduction (from lat. deductio - inference) is the receipt of particular conclusions based on the knowledge of some general provisions. In other words, it is the movement of our thinking from the general to the particular, the individual. For example, from the general position that all metals have electrical conductivity, one can make a deductive conclusion about the electrical conductivity of a particular copper wire (knowing that copper is a metal). If the initial general propositions are an established scientific truth, then the true conclusion will always be obtained by the method of deduction. General principles and laws do not allow scientists to go astray in the process of deductive research: they help to correctly understand the specific phenomena of reality.

The acquisition of new knowledge through deduction exists in all natural sciences, but the deductive method is especially important in mathematics. Operating with mathematical abstractions and building their reasoning on very general principles, mathematicians are forced most often to use deduction. And mathematics is, perhaps, the only proper deductive science.

In the science of modern times, the prominent mathematician and philosopher R. Descartes was the propagandist of the deductive method of cognition. Inspired by his mathematical successes, being convinced of the infallibility of a correctly reasoning mind, Descartes one-sidedly exaggerated the importance of the intellectual side at the expense of the experienced in the process of knowing the truth. Descartes' deductive methodology was in direct opposition to Bacon's empirical inductivism.

Moreover, in the process of using the inductive method, deduction is often “hidden” as well.

“Generalizing the facts in accordance with some ideas, we thereby indirectly derive the generalizations we receive from these ideas, and we are far from always aware of this. It seems that our thought moves directly from facts to generalizations, that is, that there is pure induction here. In fact, in conformity with some ideas, in other words, being implicitly guided by them in the process of generalizing facts, our thought indirectly proceeds from ideas to these generalizations, and, consequently, deduction also takes place here ... We can say that in in all cases when we generalize according to some philosophical propositions, our conclusions are not only induction, but also hidden deduction.

Emphasizing the necessary connection between induction and deduction, F. Engels urgently advised scientists: from the view of their connection with each other, their mutual complement to each other.

Logical reasoning often becomes the subject of philosophical reflection, especially when we are talking about epistemology. This happened with such types of cognition as induction and deduction. Both of these methods are a means of obtaining information and new knowledge. It's just that philosophers understand by induction a logical transition from the particular to the general, and by deduction - the art of deducing conclusions from theoretical positions. However, do not assume that both of these methods are opposites.

Of course, when Francis Bacon said his famous phrase that knowledge is power, he had in mind precisely the potency of induction. But the second method should not be underestimated. AT modern understanding deduction is more of a control character and helps to verify the hypotheses obtained with the help of induction.

What's the Difference?

The method of deduction and induction in philosophy is associated with logic, but at the same time we are talking about two different types inferences. When we go from one premise to another, and then to conclusions, the truth of the latter depends on the correctness of our initial foundations. This is what deduction looks like. It relies on the clarity and necessity of logical laws. If we are talking about induction, then in this case the conclusions come first from the facts - material, psychological, legal, and so on. Such conclusions are less formal than deductive ones. Therefore, the connections between the facts that follow from these conclusions are probabilistic (or hypothetical). They need further testing and verification.

How did the concept of "induction" appear in philosophy

The English thinker Francis Bacon, analyzing the state of contemporary science, considered it deplorable due to the lack of the necessary method. He proposed it in his New Organon to replace the rules of logic proposed by Aristotle. Bacon believed that four obstacles stand in the way of knowledge, which he called idols. This admixture to knowledge human nature, individual subjectivity, incorrect terminology and misconceptions based on axioms or authorities of the past. From the point of view of the English scientist, real knowledge can only come from a generalization sensory experience. This is how induction in philosophy appeared.

Examples of its application are given by the same Francis Bacon. If we watch the lilac every year and see that it is white, then in this garden all these trees bloom in only one color. That is, our conclusions are based on the assumption that if the experiment gives us such and such data, then this will happen in all similar cases.

What is dangerous one-way method

Conclusions in inductive reasoning can be erroneous. And if we constantly rely on them and do not check them deductively, then we can move away from real value links between facts. But aren't we guided in our lives - subconsciously and one-sidedly - only by inductive reasoning? For example, in given circumstances, we have always adopted such and such an approach to solving a problem, and this has brought us success. So, we will continue to act in this way, without changing anything. But after all, our experience is not facts, but only our idea of them. But often we treat our concepts as a kind of axioms. This leads to incorrect conclusions.

Why induction is imperfect

Although this method at one time looked very revolutionary, as we see, one cannot rely only on it. Now it's time to talk about what is complete and incomplete induction. Philosophy offers us the following definitions.

Full induction is an ideal situation where we are dealing with a certain number of special cases that exhaust all possible options. This means that we have collected all the facts, made sure that their number is finite, and on this basis we prove our assertion. Incomplete induction is much more common. From observation of individual facts, we draw some hypothetical conclusions. But since we do not know whether the same result will be in all particular cases, we must understand that our conclusion is only probabilistic in nature and needs to be verified. That is why we should constantly critically evaluate our experience and supplement it with new information.

Model that limits cognition

Induction in philosophy is the deliberate simplification of complex structures in order to create an intelligible picture of the world. When we observe different phenomena, we generalize them. From this we draw conclusions about the connections between phenomena and add up a single picture from them. It allows us to make choices and prioritize, to determine what is important to us and what is not. But if we lose control of the situation and begin to replace the facts with our own opinion about them, then we will inevitably begin to adjust everything that we see to ourselves. Thus, the presence of induction alone limits knowledge. After all, as a rule, it is incomplete. Therefore, almost all universal generalizations made with its help suggest the possibility of exceptions.

How to use induction

We need to understand that the use of this method alone replaces the diversity of the world with simplified models. This gives us a kind of weapon against the limitations that induction in philosophy is fraught with. This understanding is often justified by the thesis that there are no universal theories. Even Karl Popper said that any concept can either be recognized as falsified, and therefore it should be rejected, or it has not yet been sufficiently tested, and therefore we have not yet proven that it is incorrect.

Another thinker, Nassim Taleb, supports this argument with the observation that any great amount white swans does not give us the right to claim that all these birds are of the same color. Why? But because one black swan is enough to smash your conclusions to smithereens. Induction thus helps us to generalize information, but at the same time forms stereotypes in our brain. They are also needed, but we can use them until at least one fact appears that refutes our conclusion. And when we see this, we should not adjust it to fit our theory, but look for a new concept.

Deduction

Let us now consider the second method of cognition, its pros and cons. The very word "deduction" means derivation, logical connection. This is the transition from broad knowledge to specific information. If in philosophy induction is the receipt of general judgments based on empirical knowledge, then deduction proceeds from information and connections between facts that are already proven, that is, existing. This means she has more a high degree reliability. Therefore, it is often used to prove mathematical theorems. The founder of deduction is Aristotle, who described this method as a chain of inferences, also called syllogistics, where the conclusion is obtained from premises according to clear formal rules.

Deduction and Induction - Bacon vs. Aristotle

In the history of philosophy, these two methods of cognition were constantly opposed. Aristotle, by the way, was also the first to describe induction, but he called it dialectics. He stated that the conclusions drawn in this way are the opposite of the analytical ones. Bacon, as we have seen, preferred induction. He developed several rules for gaining knowledge using this method. Causal relationships between different phenomena, from his point of view, can be established by analogy of differences, similarities, residues, as well as the presence of concomitant changes. Having absolutized the role of experiment, Bacon declared that in philosophy induction is a universal method of epistemology. Just like in any science. However, eighteenth-century rationalism and the development of theoretical mathematics challenged his conclusions.

Descartes and Leibniz

These French and German philosophers brought back the interest in the deductive method. Descartes raised the question of authenticity. He stated that mathematical axioms are obvious propositions that do not require proof. Therefore, they are reliable. Therefore, if you follow the rules of logic, then the conclusions from them will also be true. Therefore, deduction will be a good scientific method if you follow a few simple rules. It is necessary to proceed only from what has been proven and verified, to divide the problem into its component parts, to move from simple to complex and not be one-sided, but to check all the details.

Leibniz also argued that deduction can be used in other branches of science. Even those studies that are carried out on the basis of experiments, he said, in the future will be carried out with a pencil in hand and using universal symbols. Deduction and induction thus divided scientists in the nineteenth century into two parties, who were for or against one method or the other.

Modern epistemology

The ability to reason logically and base one's knowledge on facts rather than assumptions was valued not only in the past. It will always come in handy in our world with you. Modern thinkers believe that in philosophy, induction is an argument based on a degree of probability. Its methods are applied depending on how they are suitable for solving the problem you are facing.

In practical life, it looks like this. If you want to go to some hotel, then you start looking at reviews about it and you see that the hotel has a high rating. This is an inductive argument. But for final decision, you need to understand whether you have enough budget for such a vacation, whether you personally like living there and how objective the assessments were. That is, you need more information.

Deduction, on the other hand, is used in cases where the so-called validity criterion can be applied. For example, your vacation is only possible in September. A highly rated hotel closes in August, but another hotel stays open until October. The answer is obvious - you can go on vacation only where it can be done in the fall. This is how deduction is used not only in philosophy, but also in everyday life.

Life is constantly forcing us to make decisions. And few people think about the fact that reflections on what is happening are built according to very specific schemes. Let's reveal this topic in more detail, or rather, find out how deduction differs from induction.

Definition

Deduction- such reasoning, in which the existing premises (statements) become the basis for the conclusion. Example: any number that is a multiple of four is also divisible by two (premise); eight times four (premise); hence eight is divisible by two (conclusion).

Induction- this is a mental method in which a certain general picture is drawn up on the basis of single facts. Example: raspberries are sweet, strawberries are sweet, grapes are sweet; raspberries, strawberries, grapes - berries; so all berries are sweet.

Comparison

There are two opposite ways of thinking. A typical model of deduction involves a movement in some reasoning from the general to the particular. In induction, on the other hand, knowledge of individual units leads to the conclusion that all objects of this series have the same characteristics.

The difference between deduction and induction is that in the reasoning carried out by the first method, pure logic operates. This allows you to draw unmistakable conclusions. But there is one condition: the initial positions must be true. Let's give an example: any drink is a liquid (certain premise); compote is a drink (a reliable premise); it follows from this that compote is a liquid (a true conclusion).

In turn, inductive reasoning is not derived strictly in accordance with logic, but through a guess and some ideas. As a result, the obtained consequence is only probabilistic and requires verification. Even with true premises, an incorrect conclusion can be obtained here. Example: Misha is a kindergartener, Kostya is a kindergartener, Sveta goes to Kindergarten(truth); Misha, Kostya, Sveta - children (true); all children attend kindergarten (false - there are those who are at home before school).

It should be noted that the most reliable knowledge is given by complete induction - the one in which each of a particular class of objects is examined, and only after that is formed general judgment about the multitude. But in practice this is not always possible. Often only a particular is considered, and then the definition is transferred to the whole group. In order for such conclusions to leave no doubts about their veracity, it is necessary to resort to repeated experiments and apply theoretical thinking.

Concluding the conversation on the topic, what is the difference between deduction and induction, it is worth mentioning that in scientific research the two described methods are organically linked. Through induction, many important hypotheses are put forward, and deduction allows you to obtain consequences from them that are subject to justification or refutation.