Deductive way of thinking. What is deduction - the advantages and disadvantages of the method

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

In the broadest sense of the word, induction is a form of thinking that develops general judgments about single objects; it is a way of movement of thought from the particular to the general, from knowledge that is less universal to knowledge that is more universal (the path of cognition "from the bottom up").

Observing and studying individual objects, facts, events, a person comes to knowledge of general laws. No human knowledge can do without them. The immediate basis of inductive inference is the recurrence 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 set of single facts. Usually 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. Induction gives a probabilistic conclusion from true premises. Induction is characteristic of experimental sciences, it makes it possible to construct hypotheses, does not provide reliable knowledge, and suggests an idea.

Speaking of induction, induction is usually distinguished 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 inference by summarizing observation and experiment data. From the point of view of cognitive tasks, induction is also distinguished as a method of discovering new knowledge and induction as a method of substantiating hypotheses and theories.

Induction plays an important role in empirical (experimental) cognition. Here she speaks:

· One of the methods of formation of empirical concepts;

· The basis for the construction of natural classifications;

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

· One of the methods of confirmation and substantiation of empirical laws.

Induction is widely used in science. With its help, all the most important natural classifications in botany, zoology, geography, astronomy, etc. The laws of planetary motion discovered by Johannes Kepler were obtained by induction based on the analysis of astronomical observations by 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), which contains various schemes for establishing cause-and-effect relationships.

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

General induction is an induction in which one moves from knowledge of several objects to knowledge of their totality. This is a typical induction. It is general induction that gives us general knowledge. General induction can be represented by two types of complete and incomplete induction. Full 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 inference obtained 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 such that contradict the inductive inference. Therefore, it is natural that the truth obtained in this way is incomplete, here we get probabilistic knowledge that requires additional confirmation.

The inductive method was studied and applied already by the ancient Greeks, in particular Socrates, Plato and Aristotle. But special interest in the problems of induction manifested itself in the 17th-18th centuries. with the development of new science. The English philosopher Francis Bacon, criticizing scholastic logic, considered induction based on observation and experiment to be the main method of knowing the truth. By this induction, Bacon intended to search for the cause of the properties of things. Logic should become the logic of inventions and discoveries, Bacon believed, the Aristotelian logic presented in the work "Organon" does not 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 extolled induction. He can be considered the founder of classical inductive logic. In his logic, Mill gave a large place to the development of methods for the study of causal relationships.

In the course of experiments, material is accumulated for analyzing objects, identifying some of their properties and characteristics; the scientist draws conclusions, preparing the basis for scientific hypotheses, axioms. That is, there is a movement of thought from the particular to the general, which is called induction. The line of knowledge, according to the supporters of inductive logic, is built as follows: experience - inductive method - generalization and conclusions (knowledge), their verification in experiment.

The principle of induction states that the universal statements of science are based on inductive inference. This principle is referred to when it is said that the truth of a statement is known from experience. In the modern methodology of science, it is realized that it is generally impossible to establish the truth of a universal generalizing judgment by empirical data. No matter how much any law is tested by empirical data, there is no guarantee that new observations will not appear that will contradict it.

Unlike inductive inference, which only suggests thought, deductive inference draws some thought from other thoughts. The process of logical inference, as a result of which the transition from premises to consequences is carried out based on the application of the rules of logic, is called deduction. Deductive inferences are: conditionally categorical, dividing-categorical, dilemmas, conditional inferences, etc.

Deduction is a method of scientific knowledge, which consists in the transition from some general premises to particular results-consequences. Deduction derives general theorems, special conclusions from experimental sciences. Provides reliable knowledge if the premise is correct. The deductive method of research is as follows: in order to obtain new knowledge about an object or a group of similar objects, it is necessary, firstly, to find the closest genus that these objects belong to, and, secondly, to apply the corresponding law inherent in all given kind of objects; transition from knowledge of more general provisions to knowledge of less general provisions.

In general, deduction as a method of knowledge proceeds from the already known laws and principles. Therefore, the deduction method does not allow one to obtain meaningfully new knowledge. Deduction is only a method for the logical deployment of a system of provisions on the basis of initial knowledge, a method for revealing the specific content of generally accepted premises.

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

1. What is clear and distinct is true.

2. The complex must be divided into private, simple problems.

3. To the unknown and unproven to go from the known and proven.

4. Lead logical reasoning consistently, without gaps.

The method of reasoning based on the conclusion (deduction) of consequences-conclusions from hypotheses is called the hypothetical-deductive method. Since there is no logic of scientific discovery, no methods that guarantee the receipt of true scientific knowledge, scientific statements are hypotheses, i.e. are scientific assumptions or assumptions whose truth value is uncertain. This provision forms the basis of a hypothetical-deductive model of scientific knowledge. In accordance with this model, the scientist puts forward a hypothetical generalization, various kinds of consequences are deduced from it, which are then compared with empirical data. The rapid development of the hypothetical-deductive method began in the 17th-18th centuries. This method has been successfully applied in mechanics. The researches of Galileo Galilei and especially of Isaac Newton turned mechanics into a harmonious hypothetical-deductive system, thanks to which mechanics became a model of scientificity for a long time, and mechanistic views were tried for a long time to be transferred to other natural phenomena.

The deductive method plays a huge role in mathematics. It is known that all provable propositions, that is, theorems, are deduced in a logical way 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 hypothetical-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 hypothetical-deductive method rather plays the role of a controller, checking the consequences arising from hypotheses.

In the modern era, extreme points of view about the meaning of induction and deduction began to be overcome. Galileo, Newton, Leibniz, recognizing for experience, and hence for induction, a large role 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 the important role of deduction in the construction and verification of scientific theories and noted that hypothesis, not reducible to induction and deduction, occupies an important place in scientific knowledge. However, it was not possible for a long time to completely overcome the opposition of inductive and deductive methods of cognition.

In modern scientific knowledge, induction and deduction are always intertwined with each other. Real scientific research takes place in the 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, probabilistic methods play a huge role in modern inductive logic. Evaluation of the probability of generalizations, the search for criteria for justifying hypotheses, the establishment of the full reliability of which is often impossible, require more and more sophisticated research methods.

Sherlock Holmes is one of the everlasting illustrations of the appeal of a sharp mind. The skills this character possessed (and borrowed from his prototype Joseph Bell, Conan Doyle's brilliant physician and mentor) will come in handy in any profession, from diagnostics to journalism. T&P drew up a rough outline of teaching his deductive method.

Thinking training

The most spontaneous answer to the question of how to become a Sherlock might sound like this: "First, buy yourself a black coat." To use the terminology of the American psychologist, Nobel laureate Daniel Kahneman, who published the book Think Slow ... Decide Fast in 2011, this is the reaction of the so-called “quick thinking” - a system that is responsible for momentary knowledge of the world and cataloging instinctive sensations. "Fast thinking" reacts to circumstances instantly and very directly, as a result of which it often makes mistakes, forcing us to make irrational decisions.

But in order to think like Sherlock Holmes, you need to use a different system - "slow". It is she, according to Kahneman, who is responsible for the deliberate and conscious formation of thoughts, decisions, conclusions and evaluations. Like any function of the human brain, the slow thinking system can be strengthened and developed.

As in sports, training should start with light exercises in small amounts, gradually moving on to more complex and lengthy ones. To begin with, you can borrow several school textbooks from friends on various subjects: mathematics, physics, chemistry and other disciplines that involve solving problems. This will help not only train the system of slow thinking (after all, it is she who is used in the process of intellectual activity), but also broaden the horizons, restoring the knowledge lost since the time of schooling and identifying interesting scientific areas for study.

Corrosiveness is another quality that a future master of deduction requires. To cultivate it in yourself, you need to find areas that truly arouse curiosity. What exactly they will be, by and large, does not matter: the emotional response always pushes a person to a deep study of the subject, makes him constantly increase the amount of knowledge, and with it the length of the border of contact with the unknown, the existence of which invariably prompts the mind to new searches.

Deduction and induction

When the mind is prepared and saturated with various useful information, you can proceed to exercises for the development of logical thinking: deductive and inductive. After all, Conan Doyle's character used both methods - which, alas, is shown in the BBC series "Sherlock" somewhat weaker than in the books of Arthur Conan-Doyle.

Deduction is a method in which the particular is logically derived from the general: “All metals conduct current. Gold is a metal. This means that gold conducts current. " Induction, on the contrary, deduces the general from the particular: “I am a Muscovite and I remember that it snowed every winter. This means that it always snows in Moscow in winter ”. Sherlock Holmes, examining a crime scene or assessing others, often went from private to general and back, freely moving in both logical directions: “John has a military bearing, a tan on his arms only up to his sleeves, a psychosomatic limp, which means he has been in a war. Where have the military operations been lately? In Afghanistan. So, in the war in Afghanistan. "

However, his main conclusions were deductive and appeared in the mind of the great detective when he tormented his violin or pondered while smoking a pipe. At these moments, Sherlock Holmes turned to his phenomenal knowledge of history and forensic science and classified the case based on the "family tree of crimes." He assigned him a place in the group: "Murder by inheritance", "Murder out of jealousy", "Theft of the will", etc. This gave the motive, and the motive gave the suspects. This was the essence of Sherlock Holmes's deductive method. Induction gave him food for thought, while deduction provided the answer.

There are many exercises for training logical thinking. For example, "Concepts in order", within which it is necessary to arrange several words from particular meanings to general ones or vice versa. Chess or poker may also be helpful. In addition, it is important to learn to avoid logical errors in judgments, having studied them, for example, according to the book by Abner Uemov “Logical errors. How they interfere with right thinking. "

How to Raise a Detective in You

Learning to notice details, interpret them correctly and not be distracted during observation and analysis will require exercises to develop voluntary and involuntary attention, as well as training in flexibility of thinking.

Involuntary attention is a system of reaction to stimuli, a kind of "peripheral vision" in terms of the perception of reality. To develop it, you can make it a rule to observe familiar objects and places with a lack of lighting and a different sound background (in natural conditions, with pleasant music and harsh unpleasant sounds), as well as learn to mark the details that attract attention when moving from one species activities to others. This allows you to cultivate a sensitivity to fluctuations in reality and learn not to miss out on interesting details that may be the key to a situation or a person's character.

Voluntary attention, or, simply, concentration also plays a huge role in cultivating the ability to think clearly. On average, thanks to volitional effort, a person is able to maintain attention on an object for only 20 minutes. To increase this indicator, training with the so-called "Entertaining table" and its analogues are suitable. Each such table is a structure with chaotically located and differently depicted numbers from 1 to 35 or from 1 to 90. The task is to find all the numbers in ascending or descending order, spending the least amount of time.

You can also train your attention to detail by making it a habit to observe strangers: at work, on the street, on social networks. In this case, it is important to evaluate a person from different angles, giving several answers to questions about what profession he can engage in, what is his marital status, character and habits. This will allow you to develop flexibility in thinking and stop being satisfied with the only answer every time, which may turn out to be wrong with a greater degree of probability.

However, the main secret of diabolical observation seems to lie not in the amount of training, but in the presence of a strong interest. Indeed, with an increase in the emotional value of the subject of study and the appearance of work experience sufficient to automate actions, a person develops so-called post-voluntary attention, the focus of which may not subside for hours. It was this post-spontaneous attention that allowed Sherlock Holmes to solve crimes. It also helps scientists make discoveries, writers find the best formulations, and so on. In addition, the presence of post-involuntary attention is still pleasant: it relieves the psyche, since the brain stops spending energy on maintaining focus and can throw energy on solving the tasks.

Maria Konnikova,

Sherlock Holmes does not just think slowly - he understands that it is necessary to separate objective and subjective thinking. When you see a person, you inevitably have associations associated with him, and you quickly decide whether he is good or bad. An exercise Sherlock would use to combat this is to ask, “What is my subjective judgment in what I think and feel? I'll just keep that in mind when I form my real opinion. "

In addition, if we want to assess the surrounding reality more objectively, it is necessary every time to realize why we made this or that judgment, and to check ourselves, learning from the person himself, his acquaintances or on the Internet whether we were right or not. This is not always possible, so you can use the video courses posted on the network for training. Within their framework, you can observe the participants in special scenes, evaluate whether they are lying or not, and then find out the correct answer.

Doctors and lawyers use logical thinking skills and the habit of being focused all the time, but these abilities are useful in any profession. Even for writers, it's important to understand people and be able to focus on work without constantly checking email or social networks. Working on the book Outstanding Mind, for example, I realized that I have no habit of keeping the focus of attention. I tried to force myself not to be distracted by the Internet, but it was incredibly difficult. Then I installed the Freedom program on my computer, which blocks the global network for a specified time: from two minutes to eight hours. It helped me a lot. We can recall that Sherlock Holmes also deliberately created conditions for the thought process: he played the violin, smoked his pipe and even kicked out Dr. Watson so that he would not interfere with him.

But what about when we cannot isolate ourselves from external conditions? Conan Doyle seems to help answer that question as well. Many say that Sherlock Holmes was cold, but this is not so: he has all the same emotions that any other person has, but he knows how to push them aside and perceive the situation without a subjective assessment. Such a skill must be cultivated in oneself on purpose. To do this, you can have a notebook with two or three columns: Objective Observations, Subjective Assessment, and What May Be Subjective Assessment. Holmes had it all in mind, but we need to take notes before it becomes a habit.

I think in the modern world of investigations there are fewer Sherlock Holmes due to the dominance of technology. Instead of trying to use logic to figure out if a suspect is lying, we try to estimate their heart rate or analyze how their brain works. However, in my opinion, we know too little about the brain to fully rely on existing technologies for analyzing its reactions.

DEDUCTION

DEDUCTION

(from Lat. deductio - deduction) - the transition from premises to a conclusion, based on, by virtue of which it follows with logical necessity from the accepted premises. A characteristic feature of D. is that it always leads from true premises only to a true conclusion.
Dialectic, as an inference based on a law and necessarily giving a true conclusion from true premises, is opposed - not based on the law of logic and leading from true premises to a probable, or problematic, conclusion.
Conclusions are deductive, for example:
If the ice heats up, it melts.
The ice is heating up.
The ice is melting.
The line separating from the conclusion stands in place of the word "therefore".
Examples of induction are the following reasoning:
Brazil is a republic; Argentina is a republic.
Brazil and Argentina are South American states.
All South American states are republics.
Italy is a republic; Portugal is a republic; Finland is a republic; France is a republic.
Italy, Portugal, Finland, France - Western European countries.
All Western European countries are republics.
Inductive inference is based on some factual or psychological basis. In such a conclusion, the conclusion may contain information that is absent in the premises. The reliability of the premises does not mean, therefore, the reliability of the inductive statement derived from them. The induction conclusion is problematic and needs further investigation. So, the premises of both the first and the second of the above inductive inferences are true, but the conclusion of the first of them is true, and the second is false. Indeed, all South American states are republics; but among the Western European countries there are not only republics, but also monarchies.
Logical transitions from general knowledge to a particular type are especially characteristic of D.
All people are mortal.
All Greeks are human.
All Greeks are mortal.
In all cases when it is required to consider something on the basis of an already known general rule and to draw the necessary conclusion regarding this phenomenon, we conclude in the form D. Reasoning leading from knowledge about a part of objects (private knowledge) to knowledge about all objects of a certain class (common knowledge) are typical inductions. There always remains that which turns out to be hasty and unreasonable ("Socrates is a skillful debater; Plato is a skillful debater; hence, everyone is a skillful debater").
At the same time, it is impossible to identify dialecticism with the transition from the general to the particular, and induction with the transition from the particular to the general. In the discourse “Shakespeare wrote sonnets; therefore, it is not true that Shakespeare did not write sonnets. ”There is D., but there is no transition from the general to the particular. The reasoning “If aluminum is plastic or clay is plastic, then aluminum is plastic” is, as it is commonly thought, inductive, but there is no transition from the particular to the general. D. is the derivation of conclusions that are as reliable as the accepted premises, induction is the derivation of probable (plausible) conclusions. Inductive inferences include transitions from the particular to the general, as well as the canons of induction, etc.
Deductive inferences allow one to obtain new truths from existing knowledge, and, moreover, with the help of pure reasoning, without resorting to experience, intuition, common sense, etc. D. gives one hundred percent guarantee of success. Starting from the true premises and reasoning deductively, we will definitely get the reliable in all cases.
However, one should not separate D. from induction and underestimate the latter. Almost all general propositions, including scientific laws, are the results of inductive generalization. In this sense, induction is the basis of our knowledge. By itself, it does not guarantee its truth and validity, but it generates assumptions, connects them with experience and thereby gives them a certain likelihood, a more or less high degree of probability. Experience is the source and foundation of human knowledge. Induction, starting from what is comprehended in experience, is a necessary means of its generalization and systematization.
In ordinary reasoning, D. only in rare cases appears in full and expanded form. Most often, not all used parcels are indicated, but only some. General statements that seem to be well known are omitted. The conclusions arising from the accepted premises are not always clearly formulated. The logical itself, which exists between the initial and the deduced statements, is only sometimes marked by words like "therefore" and "means." Often D. is so abbreviated that one can only guess about it. Conducting deductive reasoning without omitting or reducing anything is burdensome. However, whenever it arises in the validity of the conclusion made, it is necessary to return to the beginning of the reasoning and reproduce it in the fullest possible form. Without this, it is difficult or even impossible to detect the mistake made.
Deductive is the derivation of the substantiated position from other, previously adopted provisions. If the advanced position can be logically (deductively) deduced from the already established positions, this means that it is acceptable to the same extent as these positions themselves. Justification of some statements by reference to or the acceptability of other statements is not the only one performed by D. in the processes of argumentation. Deductive reasoning also serves to verify (indirectly confirm) statements: from the verified position, its empirical consequences are deduced; these consequences is evaluated as an inductive argument in favor of the original position. Deductive reasoning is also used to falsify claims by showing that the consequences that follow from them are false. Failure is a weakened version of verification: failure to disprove the empirical implications of the hypothesis being tested is an argument, albeit a very weak one, in support of this hypothesis. And finally, dialectic is used to systematize a theory or a system of knowledge, to trace the logical connections of the statements included in it, to construct explanations and understandings based on the general principles proposed by the theory. Clarifying the logical structure of a theory, strengthening its empirical base and identifying its general premises is a contribution to its constituent statements.
Deductive argumentation is universal, applicable in all areas of reasoning and in any audience. "And if bliss is nothing but eternal life, and eternal life is truth, then bliss is nothing but the knowledge of the truth" - John Scotus (Eriugena). This theological reasoning is deductive reasoning, viz.
The specific weight of deductive argumentation in different areas of knowledge is significantly different. It is widely used in mathematics and mathematical physics, and only occasionally - in history or aesthetics. Keeping in mind the scope of D.'s application, Aristotle wrote: "One should not demand scientific evidence from an orator, just as one should not demand emotional persuasion from the speaker." Deductive reasoning is a very powerful tool, but like anything, it must be used in a narrow way. An attempt to build argumentation in the form of a dialectic in those areas or in the audience that are not suitable for this leads to superficial reasoning that can only create the illusion of persuasiveness.
Depending on how widely deductive argumentation is used, all sciences are usually divided into deductive and inductive. The first uses primarily or even solely deductive argumentation. Secondly, such argumentation plays only a knowingly auxiliary role, and in the first place is empirical argumentation, which has inductive, probabilistic. Typically deductive science is mathematics, the example of inductive sciences are. However, the sciences on deductive and inductive, widespread in the beginning. 20th century, has now largely lost its own. It is focused on science, considered statically, as a system of reliably and definitively established truths.
The concept of "D." is a general methodological concept. In logic, evidence corresponds to it.

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

DEDUCTION

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

D.'s study is ch. the task of logic; sometimes formal logic is even defined as the theory of dialectic, although it is far from being one that studies the methods of dialectic: studies the realization of dialectic in the process of real individual thinking, but as one of main (along with others, in particular various forms of induction) methods scientific. knowledge.

Although the term "D." first used, but apparently by Boethius, the concept of D. - as k.-L. sentences through syllogism - already featured in Aristotle ("First Analytics")... In philosophy and logic, cf. centuries and modern times, there were different views on the role of D. in a number of dr. methods of cognition. So, Descartes opposed D. to intuition, by means of cut, but to his opinion, human. "Directly sees" the truth, while D. delivers to the mind only "mediated" (obtained by reasoning) knowledge. F. Bacon, and later dr. english logicians - "inductivists" (W. Wewell, J.S. Mill, A. Ben and dr.) considered D. a "secondary" method, while true knowledge, in their opinion, gives only induction. Leibniz and Wolff, proceeding from the fact that dialectic does not give "new facts," it was on this basis that they came to the opposite conclusion: the knowledge obtained by dialectic is "true in all possible worlds."

D.'s questions began to be intensively worked out in the late 19th century. in connection with the rapid development of mathematical. logic, clarifying the foundations of mathematics. This led to the expansion of the means of deductive proof (for example, was developed ""), to clarify many. D. concepts (for example, the concept of logical. consequence), the introduction of new problems in the theory of deductive proof (for example, questions about consistency, the completeness of deductive systems, decidability), etc.

Development of D.'s questions in the 20th century associated with the names of Buhl, Frege, Peano, Poretsky, Schroeder, Peirce, Russell, Gödel, Hilbert, Tarski, etc. Thus, for example, Buhl believed that dialectic consists only in the exclusion (elimination) of middle terms from the premises. Generalizing Boole's ideas and using their own algebra. methods, rus. the logician Poretsky showed that such a dialectic is too narrow (see "On the ways of solving logical equalities and the reverse way of mathematical logic", Kazan, 1884). According to Poretsky, D. is not the exclusion of middle terms, but the exclusion of information. The process of excluding information is that when you move from logical. expressions L \u003d 0 to one of its consequences, it is enough to discard in the left part of it, which is logical. polynomial in perfect normal form, some of its constituents.

V. sovr. bourgeois. philosophy is very widespread is the excessive exaggeration of the role of D. in knowledge. In a number of works on logic, it is customary to emphasize that it is supposedly completely excluded. the role that D. plays in mathematics, in contrast to other scientific. disciplines. Focusing on this "difference", they reach the conclusion that all sciences can be divided into the so-called. deductive and empirical. (see, for example, L. S. Stebbing, A modern introduction to logic, L., 1930). However, such a distinction is fundamentally illegal and it is denied not only by scientists who stand on the dialectical materialistic. positions, but also some bourges. researchers (for example, J. Lukasiewicz; see Lukasiewicz, Aristotelian from the point of view of modern formal logic, trans. from English, Moscow, 1959), who realized that both logical and mathematical. axioms are ultimately a reflection of certain experiments with material objects of the objective world, actions over them in the process of socio-historical. practice. And in this sense, mathematical. axioms are not opposed to the provisions of science and society. An important feature of D. is her analytic. character. Mill also noted that there is nothing in the conclusion of deductive reasoning that is not already contained in its premises. To describe the analytic. the nature of deductive following is formal, let us resort to the exact language of the algebra of logic. Let us assume that deductive reasoning is formalized by means of the algebra of logic, i.e. the relations between the volumes of concepts (classes) are precisely fixed both in the premises and in the conclusion. Then it turns out that the decomposition of premises into constituents (elementary) units contains all those constituents that are present in the decomposition of the corollary.

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

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

D. is sometimes used to check K.-L. judgments, when consequences are derived from it according to the rules of logic in order to then check these consequences in practice; this is one of the methods for testing hypotheses. D. is also used when revealing the content of certain concepts.

Lit .: Engels F., Dialectics of Nature, M., 1955; Lenin V.I., Soch., 4th ed., T. 38; Aristotle, Analysts First and Second, trans. from Greek., M., 1952; R. Descartes, Rules for the Guidance of the Mind, trans. from lat., M. - L., 1936; his, Discourse on the method, M., 1953; Leibniz G. V., New about the human mind, M. - L., 1936; Karinsky M.I., Classification of conclusions, in collection: Izbr. works of Russian logicians of the XIX century, M., 1956; L. Liar, English Reformers of Logic in the 19th Century, St. Petersburg, 1897; L. Coutyura, Algebra of Logic, Odessa, 1909; S. Povarnin, Logic, part 1 - General doctrine of proof, P., 1915; Gilbert D. and Ackerman V., Foundations of Theoretical Logic, trans. from it., M., 1947; Tarski Α., Introduction to the logic and methodology of deductive sciences, trans. from English, M., 1948; Asmus V. Φ., Doctrine of logic about proof and refutation, M., 1954; Boole G., An investigation of the laws of thought ..., N. Y., 1951; Schröder Ε., Vorlesungen über die Algebra der Logik, Bd 1–2, Lpz., 1890–1905; Reichenbach H. Elements of symbolic logic, Ν. Υ., 1948.

D. Gorsky. Moscow.

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

DEDUCTION

DEDUCTION (from Lat. Deductio - withdrawal) - transition from general to particular; in a more special sense, the term “deduction” denotes the process of logical inference, that is, the transition, according to one or another rule of logic, from some given sentences-premises to their consequences (conclusions). The term “deduction” is used both to denote specific conclusions of consequences from premises (ie, as a synonym for the term “inference” in one of its meanings), and as a generic name for the general theory of constructing correct conclusions. Sciences, the proposals of which are mainly obtained as a consequence of some general principles, postulates, axioms, are usually called deductive (mathematics, theoretical mechanics, some sections of physics, etc.), and the axiomatic method, by means of which conclusions of these particular sentences are made, axiomatic-deductive.

The study of deduction is the task of logic; sometimes formal logic is even defined as a theory of deduction. Although the term "deduction" was first used, apparently, by Boethius, the concept of deduction - as a proof of a proposition by means of a syllogism - appears already in Aristotle ("The First Analytics"). In the philosophy and logic of modern times, there were different views on the role of deduction in a number of methods of cognition. So, Descartes opposed deduction to intuition, through which, in his opinion, the mind “directly perceives” the truth, while deduction delivers to the mind only “mediated” (obtained through reasoning) knowledge. F. Bacon, and later other English "inductivist" logicians (W. Wewell, JS Mill, A. Ben, and others) considered deduction to be a "secondary" method, while only induction gives true knowledge. Leibniz and Wolff, proceeding from the fact that deduction does not give “new facts,” it was on this basis that they came to the opposite conclusion: knowledge obtained by deduction is “true in all possible worlds”. The relationship between deduction and induction was revealed by F. Engels, who wrote that “induction and deduction are interconnected in the same necessary way as synthesis and analysis. Instead of unilaterally exalting one of them to heaven at the expense of the other, one should try to apply each of them in its place, and this can be achieved only if one does not lose sight of their connection with each other, their mutual complementarity ”( K. Marx, F. Engels Soch., V. 20, pp. 542-543), the following statement applies to applications in any area: everything that is included in any logical truth obtained through deductive inference is already contained in the premises from which it is derived ... Each application of the rule consists in the fact that the general provision refers (applies) to some specific (particular) situation. Some inference rules fall under this characteristic and in a very explicit way. So, for example, various modifications of the so-called. the substitution rules state that the property of provability (or derivability from a given system of premises) is preserved for any replacement of the elements of an arbitrary formula of a given formal theory with specific expressions of the same kind. The same applies to the common way of specifying axiomatic systems by means of the so-called. schemes of axioms, that is, expressions that turn into concrete axioms after substituting specific formulas of a given theory instead of the general notation in them. Deduction is often understood as the process of logical following. This determines its close relationship with the concepts of inference and consequence, which is reflected in logical terminology. So, one of the important relationships between the logical connective of implication (formalizing the verbal phrase “if ... then ...”) and the relation of logical consequence (deducibility) is usually called the “deduction theorem”: if consequence B is derived from premise A, then AeB (“if A ... then B ...”) is provable (that is, deducible without any premises, from only axioms). Other logical terms associated with the concept of deduction are of a similar nature. Thus, sentences derived from each other are called deductively equivalent; a deductive system (with respect to a property) consists in the fact that all expressions of a given system that have this property (for example, truth under some interpretation) are provable in it.

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

TRANSCENDENTAL DEDUCTION (German transzendentale Deduktion) is the key section of I. Kant's “Critique of Pure Reason”. The main task of deduction is to substantiate the legitimacy of the a priori application of categories (elementary concepts of pure reason) to objects and show them as principles of a priori synthetic cognition. The need for transcendental deduction was realized by Kant 10 years before the release of Critique, in 1771. The central deduction was first formulated in handwritten sketches in 1775. The text of deduction was completely revised by Kant in the 2nd edition of Critique. The solution to the main task of deduction implies the proof of the thesis that the necessary possibilities of things constitute. The first part of deduction (“objective deduction”) clarifies that such things, in principle, can only be objects of possible experience. The second part (“subjective deduction”) is the sought-for proof of the identity of categories with the a priori conditions of possible experience. The starting point of deduction is the concept of apperception. Kant asserts that all conceptions possible for us must be connected in the unity of apperception, that is, in I. The necessary conditions for such a connection are the categories. The proof of this central position is carried out by Kant by analyzing the structure of objective judgments of experience based on the use of categories, and the postulate of the parallelism of the transcendental object and the transcendental unity of apperception (this allows one to “reverse” categorical syntheses on the I to refer representations to the object). As a result, Kant concludes that all possible perceptions as conscious, that is, those related to the I, contemplation are necessarily subordinate to categories (first, Kant shows that this is true about “contemplations in general,” then about “our contemplations” in space and time) ... This means the possibility of anticipating objective forms of experience, i.e., a priori cognition of objects of possible experience with the help of categories. In the framework of deduction, Kant develops the doctrine of cognitive abilities, among which imagination plays a special role, which connects and reason. It is the imagination, obeying categorical “instructions”, which forms the phenomena in accordance with the law. Kant's deduction of categories has caused numerous discussions in modern historical and philosophical literature.

Dictionary of foreign words of the Russian language

In the science of correct thinking - logic - there are two types of inference. This is induction and deduction. In this article, we'll show you how to develop deduction.

What is deduction

The term "deduction" is derived from the Latin word deductio, meaning "deduction." Deduction is a method of thinking in which, as a result of a chain of inferences, in a logical way, a particular is derived from a general position. How to develop deduction, or learn to think and reason from the general to the particular?

Sherlock Holmes - master of the deductive method

Not so long ago, this term was known only to a narrow circle of scientists. However, thanks to Sherlock Holmes, the hero of a series of detective novels by Arthur Conan Doyle, deduction became known all over the world. This character was called the master of the deductive method. How to develop deduction like Sherlock Holmes? Is it possible?

Based on the complete picture of the crime committed with all the suspects, Sherlock Holmes considered each possible participant: he studied the possibilities, behavior, motives. That is, it went from the general to the particular. So, by logical reasoning, he determined which of the suspects was a criminal, and presented undeniable evidence of his guilt.

How to use the deductive method in practice

Having watched Sherlock Holmes unravel one crime after another using deduction, one might wonder how to develop logic and deduction. This method can be adopted not only by law enforcement officers, investigators and lawyers. Deduction can be useful in everyday life as well.

Mastering the deduction method is useful in every field of activity. So, students will be able to understand and memorize material for the test easier and faster, doctors and managers - to quickly make the right decision, and so on.

Is there an area of \u200b\u200bhuman life where the method of deduction would be useless? With the help of it, you can draw conclusions about the people around you, which is extremely important for building relationships with them. It develops logical thinking, observation, memory and simply makes you think, which does not allow the brain to grow old prematurely. Our brains need regular exercise as much as muscles. How to develop and learn deduction? It's pretty simple.

How to develop deduction

Sherlock Holmes constantly used deduction - slow thinking, the basis of which is the formation of conclusions and assessments. Often people evaluate any people or events that take place in their lives. But at the same time, they use quick thinking, which instantly reacts to what is happening, forcing a person to do wrong things, make wrong decisions.

How to develop deduction? Through regular exercise. For example, reading books that develop deduction.

Solve problems

In the process of any intellectual activity, slow thinking is trained. Solve problems in the exact sciences: physics, mathematics, chemistry. True, for this it will be necessary to restore the forgotten knowledge of the school level.

What if from school days you have been burning with hatred for the general sciences? There is an exit! You can buy several problem books, which include games that develop deduction, puzzles, rebuses, and solve one problem at a time, for example, at lunchtime or before bed. Other ways of developing logic are also possible.

Chess and poker also contribute to the development of logic.

Broaden your horizons

Only a comprehensively developed personality is able to build their own inferences, relying on the knowledge and experience base. Otherwise, it will be just guesswork. Expand your horizons. In-depth knowledge in many areas can be a support in making the right decisions and building logical judgments.

Dictionaries, encyclopedias, reference books, films, books and travel will provide you with invaluable service.

Be meticulous

If you undertake the study of any fact or subject, you should do it as carefully and comprehensively as possible. The object of research should arouse your interest and emotional response, because only in this case you can hope for a good result.

For example, when reading a book or watching a movie, pay attention to the various details of the character's behavior and appearance. Try to predict the further course of events. These experiments are most useful with films and detective books.

Develop flexibility of thinking

Try to solve problems and problems in several ways: look for both the second and third solutions, look at them from different angles, look for a different point of view. This will prove useful in choosing the optimal solution. It is worth listening to the opinions of other people, because their versions are already a different vision of the situation. In this case, your knowledge and experience will be combined with the knowledge and experience of others, and therefore, increase the likelihood of making the right decision.

Be observant

How to develop a deduction method? When communicating with other people, not only listen, but also watch. It is useful to note the facial expressions and gestures of the interlocutor, the timbre of his voice and the intonation with which he speaks about this or that event. Thus, you can reveal a person's intentions, find out how sincere, truthful and friendly he is.

For the development of observation, it is useful to consider strangers: passers-by on the street, customers in a store, and others. Try to mentally guess where a man is working, standing in line for milk, where a long-haired girl with a big bag is going, what is the character of a guy standing at a bus stop, and so on. Observe what a person has a face, hands, shoes, dress, bag ... Try to assume his preferences and habits, what he does, without asking him about it. Of course, try to do this as inconspicuously as possible - no one likes to be looked at closely.

Develop voluntary and involuntary attention

The development of all types of attention is necessary in order not to miss important details, to interpret them correctly, without being distracted by extraneous stimuli.

It is necessary to develop all possible types of attention: both voluntary and involuntary.

Voluntary attention is the ability of the subject to focus on one object and not be distracted by anything else. It is believed that a person is able to keep his attention on an object for a maximum of 20 minutes. For example, the master of deduction Sherlock Holmes, in order to concentrate, played the violin, smoked a pipe, or was alone.

Avoid multitasking: the more factors affect the organs of perception, the harder it is to focus on one thing. By tackling several problems at once, you will make more mistakes, miss a lot of important information.

Involuntary attention is considered a kind of peripheral vision. For its development, it is necessary to regularly observe familiar objects in unusual conditions. For example, with a different sound background or lighting.

To train involuntary attention, one can create conditions unusual for perception, after which one can consciously observe and “catch” what attracted the subject in the “borderline” spectrum, when fixation is still noted, but it is already clear that it is slipping away.

So, you can monitor familiar objects in low light; to experiment with the power characteristics of stimuli: quiet music - music of medium volume - loud sound of music, rich bright colors - pastel colors; consciously fix your attention when moving between objects: pay attention to what attracted attention when moving from one object to another or when moving to another type of activity; you can "listen" to the work of involuntary attention when changing acoustic perception: sharp sounds - the sound of pleasant music.

Combine deduction and induction

By using both types of logical thinking, you can draw more accurate conclusions about the environment and develop fully. In addition, it is worth critically approaching all emerging situations and looking for the best way out of the situation.

Remember that you must have a wealth of experience and knowledge to successfully use deduction and induction methods.

Deductive thinking is one in which there is a logical conclusion and the particular is reproduced from the general conclusion. Deduction is the main means of logical argument. According to this method, the individual can correctly draw a logical conclusion. Therefore, it is imperative to improve your deductive thinking.

Deductive thinking: what it is

Thinking is an extremely difficult psychological process, according to which people study the outside world. Deduction is a method of thinking in which all reasoning is extracted through logic from a generally recognized whole.

For example, all metals conduct current, or there is always the sun in the sky. In the case of applying the described method, a person's thinking becomes more reliable. It is based on the particular, which follows from general assumptions. Thanks to deductive thinking, an individual can make correct reasoning, based on indisputable facts.

Almost every individual uses this method and tries to improve it. With its help, you can think through all your actions to the smallest detail several steps ahead.

Important! Deduction cannot be obtained if exercises are performed irregularly. There is a list of effective exercises for developing this method.

These include:

1. Solving problems in physics, chemistry and mathematics... The process of solving such problems improves intellectual activity and contributes to the development of this type of thinking.
2. Broadening your horizons... Each person should understand several areas at once. Therefore, it is necessary to receive as much information as possible from the scientific, historical, cultural spheres every day. This will help not only improve the personality from all sides, but also help preserve the experience. In this case, the person will not refer to assumptions. Encyclopedias and educational films will come to the rescue.
3. Observation... At the moment of conducting a dialogue with a person, it is necessary to be able not only to listen to him, but also to observe facial expressions and behavior, intonation and voice. Thus, you can find out how the person relates to the interlocutor - sincerely or lying.
4. Flexibility of mind... In case of problems, you must try to resolve them in several ways. In order to stay on the right approach, you need to listen to others and consider all versions. The most optimal and correct conclusion can be chosen only in the aggregate of personal experience with information from outside.
5. Pedantry... Full understanding can be obtained if a person can fully study the object of interest. It is important that this object is emotionally delighted.
6. Dig deeper... If there is a desire to study any material, then you need to be quite enthusiastic to study it fully. When reading a work, you need not just to grasp its essence. It is important to carefully study the character of each hero, to experience his emotions. Thanks to this, you can predict the ending of the work. This is especially true for detectives. This also applies to cinema.
7. Connect deduction and induction... For example, a patient is admitted to a hospital with a stomach ulcer. To make a diagnosis, the doctor pays attention to the symptoms. Whether all signs appear or only part of them. Only after that does it confirm or deny the diagnosis. Or a patient comes to the hospital with abdominal pain, heartburn, lack of appetite. The doctor summarizes all the symptoms and makes a diagnosis.
8. See not only what you want... Often the brain looks through all the problems and difficult situations. He lacks objectivity, and this is an indicator of such a method of thinking. You don't need to take everything that your brain gives out as fact. People tend to make mistakes, so the whole situation must be soberly assessed again. You don't need to jump to conclusions. The situation must be carefully investigated and only after that a conclusion must be drawn. The first conclusion may be wrong.
9. Solve puzzles... The goal of each person is to learn how to find a way out of any situation. A fun puzzle game is a good way to prepare yourself for global challenges. Repeat such sessions regularly. Solving puzzles should become a habit.

Developing deductive thinking is not as difficult as it sounds. But it is important to engage in self-development on an ongoing basis. One-time sessions won't do any good. There are many methods for its development, so each person can choose the most suitable option for him.