Definition of deduction: through the general to the particular. Inductive and deductive teaching methods

Inductive and deductive methods of cognition

Induction is cognition from the particular to the general. For example, by analyzing private knowledge (individual facts), a researcher can come to general knowledge, incl. inference, hypothesis. That. from private knowledge - so-called. generalized knowledge. The more generalized (= more abstract) knowledge, the more useful and powerful it is, in general. Philosophy, for example, is the body of the most generalized knowledge. Science and technology, in relation to philosophy, is knowledge with an average degree of generalization.

It is precisely such (generalized and most generalized) knowledge that gives a person the most power (Force).

Induction, i.e. cognition from the particular to the general (generalized), in fact, is the main content of abstract thinking, i.e. obtaining generalized (= abstract) and more and more generalized knowledge from private ones. In general, this is how they arise and develop: art, science and technology, philosophy. Abstract thinking (induction) - determines the superiority of man over other forms of life on Earth.

Further: If induction is the main content of abstract thought, then what is the opposite method (deduction)? Deduction also refers to abstract thinking, because she, although she does not receive generalized knowledge from private, but operates with generalized (= abstract) knowledge:

Unlike induction, deduction is knowledge from the general to the particular (as well as from the general to the general, and from the particular to the particular). This is the acquisition of new knowledge, with a combination of existing general ones, or the use of general ones (and abstract thinking in general) to obtain new private knowledge from private ones. (Except, perhaps, only the most primitive conclusions from particular to particular, which can be carried out without general knowledge).

Further: Generalized knowledge, by the way, always contains private knowledge, or rather, a lot of private knowledge, combined into one common one. This is the power of general (generalized and most generalized, = abstract) knowledge. For example, the generalized knowledge that all trees are covered with bark contains associated private knowledge about each of the trillions of trees, i.e. trillions of private knowledge! (linked into one laconic and powerful common knowledge of all of them). Having learned that a particular object is a tree, we obtain, using deduction, the knowledge that our particular tree should be covered with bark (i.e., we receive knowledge from the general to the particular). But we already knew that all the trees are covered with bark. In fact, deduction from the general to the particular is the application of existing knowledge, obtaining conclusions (= new knowledge) based on the existing general knowledge ...

By the way, deduction was glorified, at one time, by everyone known, Sherlock Holmes, who had "outstanding deductive abilities."

One of the manifestations of deduction is also the method of cognition - extrapolation. For example, knowing that a new type of grass has been discovered, and knowing that all known types of grass are green, we can conclude that the new type of grass is green. We get thus. - such a new private knowledge: "a new kind of grass is green." Those. we did not check this, and did not see it, but extrapolated (applied) the existing general knowledge - to a new subject that was not included in the generalization. Received so. deductive knowledge taken on faith.

4.1.6. Inductive-deductive method (analysis)

Both mental life as a whole and its constituent elements of content break down into pairs of oppositions. On the other hand, it is the existence of mutually opposed poles that makes it possible to restore the lost ties. Ideas, tendencies, feelings bring their direct opposites to life.

K. Jaspers

Induction - it is the movement of knowledge from particular statements to general ones. Induction underlies any action, any analysis, because a particular criminal action is subject to the influence of inductive inference.

Based on one object and its characteristics, the forensic scientist should:

1. Build a bridge of connections between the particular and the possible general, where this private is included.

For example, a corpse of a man with a slit throat was found ... Subject's version: the killer may be a person for whom cutting the throat is a common occurrence. This is a person who overcomes the fear of profuse bleeding ... This is a person prone to particular cruelty ... This is a native of the village, accustomed to slaughtering livestock ... The alleged object must go through a filter of connections ...

2. Build inductive reasoning, including individuality, reflecting the subjectivity of the performer's personality:

typical characteristics (going back to the pattern of manifestations);
the regularity of relationships between the discovered fact and the investigated set (representative array);
features of the conditions for the appearance of a single fact (phenomenon);
own readiness to perceive a single fact and associate it with a known (established) regular set.

The signs used in inductive inference should:

be significant;
reflect the individuality of the object;
should already be included in the group of previously identified patterns.

Induction should perform in a duet with deduction, it is a paired phenomenon that cannot be alone.

Deduction - it is the movement of knowledge from the general to the particular. It is the discovery of the effect in the cause.

As soon as a person perceives a criminally significant object, inductive activity is immediately turned on, but at the same time, competing with and ahead of the final inference, a deductive process is born. Deduction loads the consciousness of the investigator with knowledge about the general, the known, the classified, from which it is possible to draw counter conclusions about the individual ...

The consciousness of the investigator is picked up by induction and deduction and is confronted with the need to choose behavior with taking into account the current situation and the established patterns of the past. In the field of forensic consciousness, the induction layer mixes with the deduction layer, giving rise to a reaction in which the following stages are distinguished:

indicative;
executive;
control.

Inductive-deductive processes are intellectually rationalized (they are in search of optimal forms), but they are excited by emotional and volitional components. Moreover, emotional components often outstrip rational processes and appear in actions before inductive-deductive mechanisms offer a balanced solution to consciousness.

Iiductive-deductive processes involve:

1. Formulation of the goal.

2. Intellectual and motor actions.

3. Controlling the performed action through feedback channels in accordance with the set goal.

The inductive-deductive method inevitably refutes any procedure performed by the investigator.

The deductive method as applied to investigative practice can be of the following types: genetic and hypothetical-deductive.

When using the genetic method not all initial data are set and not all objects of objective activity are entered. The investigator has the ability to gradually introduce all new initial data for subsequent deduction, i.e. first, private knowledge about the object under investigation (which does not differ in complexity and variety of elements) is deduced, and then the investigator more and more "complicates" the object (for example, the scene of the incident) so that from a larger number of objects combined into a system - the "scene of the incident", to derive new private conclusions-versions about the origin of traces, about the dynamics of the crime, about the identity of the offender or about his personality traits.

Hypothetical-deductive method characterized by the fact that not so much established facts (evidence) are used as initial data, but rather hypothesis-versions built on various grounds. For example, the investigator builds a series of versions:

a) on the objective side of the corpus delicti of the crime being investigated (i.e., on the mechanism of the crime);

b) on his subjective side (i.e. on the subjective attitude of the offender to the crime being committed, on his emotional state before, at the moment and after the commission of the crime), which are reflected in the traces of the crime; by the subject of the crime, i.e. by the identity of the offender.

The set of constructed and tested versions forms a general version, a hypothesis about the crime as a whole. The father of the deductive method is considered R. Descartes, he formulated the following four rules , which can be used in forensic science.

1. It is necessary to carry out the dismemberment of a complex problem into simpler ones, up to those. until further indecomposable are found.

2. Unresolved problems should be reduced to resolved ones. In this way, solutions to simple problems are sought.

3. From solving simple problems, one should proceed to solving more complex ones, until a solution to the problem is obtained, which was the initial in the dissection and is final in this process.

4. After obtaining a solution to the original problem, you need to review all the intermediate ones to make sure that there are no missing links. If the completeness of the solution is established, then the study ends; if a gap is found in the solution, then additional research is required in accordance with the listed rules.

If René Descartes were an investigator, he would surely have been successful in solving complex and intricate crimes. Descartes' proposed rules for dealing with complex problems sound very modern, especially when it comes to deadlock situations. Inductive methods are successfully used to establish and analyze connections (necessary and random, external and internal).

When analyzing causal relationships, five types of inductive methods are used (according to I.S. Ladenko).

1. Method of only similarity. It is used in such conditions when the set of circumstances preceding the phenomenon contains only one similar circumstance and differs in all others. The conclusion is that this is the only similar circumstance that is the cause of the phenomenon under consideration. Analyzing the initial data of the investigative situation, the investigator is able to find one, but the most important circumstance that has a major impact on the behavior of the interrogated. At the same time, similarities are found in similar investigative situations, for which the investigator can view the typical models of crimes or the systems of standard versions set forth in the works of N.A. Selivanova, L.G. Vidonova, G.A. Gustova and others.

2. Single difference method it is used when two cases are considered, in one of which the phenomenon "a" takes place, and in the other it does not; the preceding circumstances differ only in one circumstance - "s". In this case, the investigated phenomenon "a" is possible if the circumstance "c" is present. If these logical constructions are translated into forensic language, then this can be illustrated by the following example.

For example, a collision of a car with a motorcycle occurred on the road, when the driver of the latter, in violation of the rules, changed into the lane of the car. The injured motorcyclist claimed that the accident was due to the driver's speeding and failure to observe the proper distance. Experimental actions of the investigator and expert calculations showed that rearrangement of motorcycle "c" in front of a nearby car in any situation causes collisions "a", regardless of all other circumstances. Accident - "a" - can occur only under the only condition "c" - rebuilding the motorcycle.

3. The combined method of similarity and difference. The bottom line is that conclusions obtained using the method of single similarity are verified by the method of single difference.

4. Method of accompanying changes it is used when it is necessary to establish the cause of changes in the observed phenomenon "a". At the same time, the previous circumstances are reviewed, it is established that only one of them changes, and all the others remain unchanged. On this basis, it is concluded that the cause of the change in the observed phenomenon is the changing previous circumstance "a". With regard to investigative practice, this method can be used when analyzing conditions, for example, a road traffic accident, when among the many factors influencing the dynamics of an accident, those that make up the cause of the accident are identified.

5. Residual method it is used when a complex phenomenon is being investigated, from which a series of components-consequences are distinguished, each of which has its own cause (established). Those consequences that are discovered and do not have established causes, and become the subject of close research. Simply put, from a complex phenomenon, the investigator extracts everything that he understands, that has its own reason, leaving in the remainder that which has no reason, has no logical explanation. It is this unexplored that is the subject of investigation. The method of residuals helps the investigator to narrow the sector of the search for the unknown, to limit the uncertainty, to direct the search exactly where the complex of consequences is grouped, the reasons for which are unclear.

The information base of induction methods can be of a combined nature, i.e. include elements of all five named types of induction (not to mention the fact that induction can be combined with deduction).

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Inductive and deductive teaching methods

Inductive and deductive teaching methods characterize an extremely important feature of the methods - the ability to reveal the logic of the movement of the content of educational material. The use of inductive and deductive methods means the choice of a certain logic of disclosing the content of the studied topic - from the particular to the general and from the general to the particular.

Inductive method

Induction(from Lat. inductio - guidance), the transition from a single knowledge of individual subjects of a given class to a general conclusion about all subjects of a given class; one of the methods of cognition. The basis of induction is the data obtained by observation and experiment. Inductive reasoning occupies an important place in scientific research, which includes, as an obligatory stage, the accumulation of experimental data serving as the basis for subsequent generalization in the form of classifications, scientific hypotheses, etc. inferences and conclusions often turn out to be false after the discovery of new facts. The application of induction is also limited by the fact that the conclusions obtained in the course of inductive inference are not in themselves necessary, therefore the inductive method of cognition must be supplemented by deduction, comparison, etc.

Distinguish between full induction (when a conclusion is made as a result of studying all objects of a given class without exception) and incomplete induction (a general conclusion is made on the basis of considering only a few, often far from all, phenomena of a given kind). Since it is usually almost impossible to exhaust all the concrete variety of facts, incomplete induction is used in the real process of cognition. Conclusion on incomplete induction always has the character of probable knowledge. The reliability of conclusions based on incomplete induction increases with the selection of a sufficiently large number of cases in relation to which an inductive generalization is built, and the facts from which the conclusion is made should be diverse, reflecting not random, but creatures, signs of the phenomenon under study. Compliance with these conditions will allow avoiding such common mistakes in teaching practice as haste to conclusions, mixing a simple sequence of any phenomena with cause-and-effect relationships between them, etc.

Induction is widely used in school teaching. Many of the teaching texts and explanations of the teacher are built on an inductive basis. For example, when explaining the concept of specific gravity, different substances are taken in equal volumes and weighed. The different weights of these substances make it possible to put forward a general position on the relationship between the weight of a substance and its volume, that is, the concept of specific gravity. This is an example of incomplete induction (not all are taken, but only some substances). As in science, it is incomplete induction that is most often used in school teaching. Most widely, induction is used in the so-called. experienced sciences and corresponding academic subjects. In the lower grades, when children still have a small amount of knowledge about the world, acquaintance with various facts from the life of nature and society is useful, since it enriches the child's experience, contributes to the development of the ability to observe and analyze the studied phenomena. This factual knowledge serves as the basis for the assimilation of generalizing provisions. In high school, induction is used in cases where it is necessary to show a general pattern for all the phenomena of a group, but the proof of this position cannot be offered to students yet. The use of induction in teaching makes it possible to draw a generalizing conclusion that is obvious, convincing, arising from the facts considered and therefore evidence-based for students. This important feature of induction has been emphasized by many educators. So, N.F.Bunakov wrote about the study of grammar: "The inductive method ... comes from concrete facts, that is, from the language itself as an object of study, from its various natural phenomena, first of all, using the observation of students, turning it to the phenomena of language , to the knowledge of its forms, to the disclosure of their meaning, then they direct their thought to comparison, classification and generalization "(Izbr. ped. soch. 1953, pp. 173-74).

So, when using the inductive teaching method, the activities of the teacher and students proceed as follows:

Teacher	Student
Option 1	Option 2
First, he expounds facts, demonstrates experiments, visual aids, organizes the exercises, gradually leading students to generalizations, definition of concepts, formulation of laws.	First, they assimilate particular facts, then draw conclusions and generalizations of a particular nature.
2 options	Option 2
It puts before the students problematic tasks that require independent reasoning from particular provisions to more general ones, to conclusions and generalizations.	They independently reflect on the facts and make accessible conclusions and generalizations.

The weakness of inductive teaching methods is that they take more time to learn new material than deductive ones. They contribute to the development of abstract thinking to a lesser extent, since they rely on concrete facts, experiences and other data.

Induction cannot be turned into a universal teaching method. In accordance with modern trends towards an increase in theoretical information in curricula and with the introduction into practice of the corresponding problem-type teaching methods, the role of other logical forms of presentation of educational material, primarily deduction, as well as analogy, hypothesis, etc., increases.

An inductive study of a topic is especially useful in cases where the material is predominantly factual or associated with the formation of concepts, the meaning of which can only become clear in the course of inductive reasoning. Inductive methods are widely used for studying technical devices and performing practical tasks.

Deductive method

inductive deductive schooling

Deduction(from Lat. deductio - deduction), the transition from general knowledge about the subjects of a given class to a single (private) knowledge about a separate subject of the class; one of the methods of cognition. Deductive inferences can be used for foresight on the basis of general patterns of facts that have not yet occurred, in substantiating, proving certain provisions, as well as in testing outlined assumptions and hypotheses. Important discoveries have been made in science through deduction.

Deduction is widely used in teaching as one of the main forms of presentation of educational material. In a physics course, for example, the presence of gravity on Earth, and hence the law of falling bodies, is explained by the law of universal gravitation, i.e. in a deductive way. In deductive reasoning, new knowledge is obtained indirectly, without resorting to direct experience. The deductive approach to the construction of a school subject allows, instead of describing a multitude of individual single facts, to outline general principles, concepts and skills in relation to the relevant field of knowledge, the assimilation of which will then allow students to analyze all particular options as their manifestations. The application of the deductive method is especially useful in the study of theoretical material, in solving problems requiring the identification of consequences from some of the more general provisions. It allows students to assimilate knowledge of a general and abstract nature earlier and derive more specific and specific knowledge from them. This opens up great opportunities for reducing the volume of educational material and the time required for its assimilation.

Deduction plays an important role in the formation of logical thinking, contributing to the development of students' ability to use already known knowledge when assimilating new ones, to logically substantiate certain specific provisions, proving the correctness of their thoughts. Deduction fosters an approach to each specific case as a link in a chain of phenomena, teaches them to consider them in conjunction with each other. As a result of deductive reasoning, the student obtains data that go beyond the initial conditions, and, using them, comes to new conclusions. By including the objects of the initial positions in ever new connections, he opens up new properties in them. This contributes to the development of activity and "productivity" of thinking. Deduction occupies a prominent place in the formation of the causal thinking of students. Mastering deduction reveals to students the objective connections and relationships between the studied facts and phenomena. Deduction helps to apply the students' knowledge in practice, to use general theoretical propositions, which are often abstract in nature, to specific phenomena that students have to face in life, in educational activities. Deduction is one of the main ways that condition the connection between school knowledge and life.

So, when using the deductive method, the activities of the teacher and students are of the following nature:

When acquiring knowledge deductively, it is very important to monitor the correctness of the premises: a formally correct deductive inference made from false premises will be incorrect. It is necessary to be able to correctly relate particular cases to the category of phenomena to which this general provision applies. This is what presents the greatest difficulties for students: they cannot always understand a given specific case as a manifestation of a general rule already known to them. The full mastery of the intended content by students, including those built according to the deductive principle, depends on the observance of the general psychological and pedagogical requirements for the assimilation process.

But this does not mean that it is necessary to move on to the deductive study of all the material. Its rational combination with the inductive approach must be found, since without the inductive approach, it is impossible to successfully prepare students for solving more complex problems.

It is necessary to use the inductive-deductive method, when a transition is made from particular cases to a general position, and then other particular facts are comprehended. For example, the concept of the type of problems is formed inductively (students solve a number of problems of this type, highlighting the typical, essential for them). Then, meeting any task, the student, analyzing its content, finds those essential features that are characteristic of tasks of this type and determine the type of task. Thus, the general law obtained by inductive means becomes the basis for obtaining new conclusions by deductive means.

As can be seen from the characteristics of the activities of the teacher and students, when using deductive or inductive teaching methods, visual and practical methods are used. But at the same time, the content of the educational material is revealed in a certain logical way - inductively or deductively. Therefore, we can talk about an inductively or deductively constructed conversation, about a deductive and problem-based story, about a reproductively or search-based practical work. In the system of teaching methods actually used at the moment, several methods conditionally distinguished in the classification are combined. And what I say about the application of the deductive or inductive method in a given situation is determined by the leading didactic task set by the teacher at this stage of training. If, for example, the teacher decided to focus on the development of generalized deductive thinking, then he uses the deductive method, combining it with the problem-search method, implemented through a specially constructed conversation.

Literature

1. Shardakov M. H., Essays on the psychology of teaching, M., 1951.

2. Babansky Yu. K., Teaching methods in modern. general education. school. M., 1985.

3. Kaiberg G., Probability and inductive logic, trans. from English, M., 1978.

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Introduction

Knowledge plays an important role in our life and scientific methods of acquiring knowledge are very diverse, but closely related to each other.

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 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 substantiating hypotheses, the establishment of the complete reliability of which is often impossible, require more and more sophisticated research methods.

The relevance of this topic is due to the fact that induction-deduction plays an important role both in philosophical and in any other knowledge, and is understood as a synonym for any scientific research.

induction deduction theory cognition

1. Theory as a special form of scientific knowledge

Theory (Greek θεωρία - consideration, research) is a set of inferences reflecting objectively existing relations and connections between the phenomena of objective reality. Thus, theory is an intellectual reflection of reality. In theory, each inference is deduced from other inferences based on some rules of inference. The ability to predict is a consequence of theoretical constructions. Theories are formulated, developed and tested according to the scientific method.

A theory is a teaching, a system of ideas or principles. It is a set of generalized provisions that form a science or its section. Theory acts as a form of synthetic knowledge, within the boundaries of which individual concepts, hypotheses and laws lose their former autonomy and become elements of an integral system.

Other definitions

There are other definitions of "theory", in which any inference is called such, regardless of the objectivity of this inference. As a result, various hypothetical constructions are often called theory, for example, "the theory of geosynclines", etc. This can be regarded as an attempt to give weight to this hypothetical construct, i.e. an attempt to mislead.

In the "pure" sciences, a theory is an arbitrary collection of sentences of some artificial language, characterized by precise rules for constructing expressions and understanding them.

Functions of theory

Any theory has a number of functions. Let's designate the most significant functions of the theory:

theory provides the user with conceptual structures;

in theory, terminology is being developed;

theory allows you to understand, explain or predict various manifestations of the object of the theory.

Testing the theory

It is generally believed that the standard method of testing theories is direct experimental testing ("experiment is the criterion of truth"). However, often a theory cannot be verified by direct experiment (for example, the theory of the origin of life on Earth), or such verification is too complicated or costly (macroeconomic and social theories), and therefore theories are often tested not by direct experiment, but by the presence of predictive power - that is, if unknown / previously unnoticed events follow from it, and with close observation these events are detected, then the predictive power is present.

In fact, the theory-experiment relationship is more complex. Since the theory already reflects objective phenomena previously verified by experiment, it is impossible to draw such conclusions. At the same time, since the theory is built on the basis of the laws of logic, then conclusions are possible about the phenomena not established by early experiments, which are verified by practice. However, these conclusions must already be called a hypothesis, the objectivity of which, that is, the transfer of this hypothesis to the rank of theory, is proved by experiment. In this case, the experiment does not test the theory, but clarifies or expands the provisions of this theory.

To summarize, the applied goal of science is to predict the future both in an observational sense - to describe the course of events that we cannot influence, and in a synthetic way - to create the desired future through technology. Figuratively speaking, the essence of the theory is to tie together "circumstantial evidence", to pass a verdict on past events and to indicate what will happen in the future if certain conditions are met.

2. The main forms of inference

Consider the main forms of inference characteristic of logical thinking. There are not so many such forms: these are induction, deduction and analogy. They can be briefly characterized as follows. Induction is a conclusion about a set, based on the consideration of the individual elements of this set. Deduction is, on the contrary, a conclusion about an element based on knowledge of certain qualities of the set of which it is included. An analogy is a conclusion about an element (set), transferring to it the properties of another element (set). Let's analyze each method separately.

3. Induction

Induction (Latin inductio - guidance) is a process of logical inference based on the transition from a particular position to a general one. Inductive inference connects particular premises with inference not so much through the laws of logic, but rather through some factual, psychological or mathematical representations.

Distinguish between complete induction - a method of proof, in which a statement is proved for a finite number of special cases that exhaust all the possibilities, and incomplete induction - observation of individual special cases leads to a hypothesis that, of course, needs proof. The method of mathematical induction is also used for proofs. Contents [remove]

The term is first encountered by Socrates (other - Greek ἐπαγωγή). But Socrates' induction has little to do with modern induction. Socrates by induction means finding a general definition of a concept by comparing particular cases and eliminating false, too narrow definitions.

Aristotle pointed out the features of inductive inference (Analyt. I, Book 2 § 23, Anal. II, Book 1 § 23; Book 2 § 19 etc.). He defines it as an ascent from the particular to the general. He distinguished complete induction from incomplete induction, pointed out the role of induction in the formation of first principles, but did not clarify the basis of incomplete induction and its rights. He viewed it as a way of inference, the opposite of syllogism. The syllogism, according to Aristotle, indicates through the middle concept that the higher concept belongs to the third, and induction with the third concept shows the belonging of the higher to the middle.

During the Renaissance, the struggle against Aristotle and the syllogistic method began, and at the same time they began to recommend the inductive method as the only fruitful one in natural science and the opposite of the syllogistic one. Bacon is usually seen as the ancestor of modern I., although justice requires mentioning his predecessors, for example Leonardo da Vinci and others. Praising I., Bacon denies the meaning of syllogism (“syllogism consists of sentences, sentences consist of words, words are signs of concepts; if therefore the concepts that form the basis of the case are indistinct and hastily abstracted from things, then what is built on them cannot have any strength "). This denial did not follow from the theory of I. Bekonovskaya I. (see his "Novum Organon") not only does not contradict the syllogism, but even requires it. The essence of Bacon's doctrine boils down to the fact that in gradual generalization, one must adhere to known rules, that is, three reviews of all known cases of manifestation of a known property in different objects must be made: a review of positive cases, a review of negative ones (that , however, the investigated property is absent) and an overview of the cases in which the investigated property is manifested in various degrees, and from here to make a generalization ("Nov.org." LI, aph.13). According to Bacon's method, it is impossible to draw a new conclusion without bringing the subject under study under general judgments, that is, without resorting to syllogism. So, Bacon did not succeed in establishing I. as a special method opposite to the deductive one.

The next step was taken by J. St. Mill. Every syllogism, according to Mill, contains a petitio principii; any syllogistic conclusion actually goes from the particular to the particular, and not from the general to the particular. This criticism of Mill is unfair, because we cannot conclude from particular to particular without introducing an additional general provision on the similarity of particular cases to each other [source not specified 574 days]. Considering I., Mill, first, asks the question about the basis or the right to an inductive conclusion and sees this right in the idea of a uniform order of phenomena, and, secondly, reduces all methods of inference in I. to four main ones: the method of agreement (if two or more cases of the phenomenon under study converge in only one circumstance, then this circumstance is the cause or part of the cause of the phenomenon under study, the method of difference (if the case in which the phenomenon under study occurs and the case in which it does not occur are completely similar in all details , with the exception of the investigated one, then the circumstance that occurs in the first case and is absent in the second is the reason or part of the reason for the investigated phenomenon); the method of residuals (if in the investigated phenomenon part of the circumstances can be explained by certain reasons, then the remaining part of the phenomenon is explained from the remaining preceding facts) and the method of corresponding changes (if, after a change in one phenomenon, a change the other, then we can conclude about a causal relationship between them). It is characteristic that these methods, upon closer examination, turn out to be deductive methods; ex. the method of residuals is nothing more than a determination by elimination. Aristotle, Bacon and Mill represent the main moments in the development of the theory of I.; just for the sake of a detailed elaboration of some questions, one has to pay attention to Claude Bernard ("Introduction to Experimental Medicine"), to Esterlen ("Medicinische Logik"), Herschel, Liebig, Wavel, Apelt and others.

Inductive method

There are two types of induction: complete (induction complete) and incomplete (inductio incomplete or per enumerationem simplicem). In the first, we conclude from the complete enumeration of species of a known genus to the entire genus; it is obvious that with such a method of reasoning, we get a completely reliable conclusion, which at the same time, in a certain respect, expands our knowledge; this mode of reasoning is beyond doubt. Having identified the subject of a logical group with the subjects of private judgments, we will have the right to transfer the definition to the entire group. On the contrary, an incomplete I., going from the particular to the general (a method of inference prohibited by formal logic), should raise the question of law. Incomplete I. by construction resembles the third figure of the syllogism, differing from it, however, in that I. tends to general conclusions, while the third figure allows only particulars.

Inference based on incomplete I. (per enumerationem simplicem, ubi non reperitur instantia contradictoria) is apparently based on habit and gives the right only to a probable conclusion in the entire part of the statement that goes beyond the number of cases already investigated. Mill, in explaining the logical right to a conclusion on incomplete I., pointed to the idea of a uniform order in nature, by virtue of which our belief in inductive inference should increase, but the idea of a uniform order of things is itself the result of incomplete induction and, therefore, cannot serve as a basis for I. ... In fact, the basis of incomplete I. is the same as that of complete, as well as of the third figure of the syllogism, that is, the identity of private judgments about an object with the entire group of objects. "In incomplete I., we conclude on the basis of the real identity not just of some objects with some members of the group, but of such objects, the appearance of which before our consciousness depends on the logical characteristics of the group and which appear before us with the powers of representatives of the group." The task of logic is to indicate the boundaries beyond which the inductive inference ceases to be legitimate, as well as auxiliary methods that the researcher uses in the formation of empirical generalizations and laws. There is no doubt that experience (in the sense of experiment) and observation serve as powerful tools in the investigation of facts, providing the material through which the researcher can make a hypothetical assumption that should explain the facts.

Any comparison and analogy, which point to common features in phenomena, serves as the same tool, while the commonality of phenomena compels us to assume that we are dealing with common causes; thus, the coexistence of phenomena, to which the analogy indicates, does not in itself yet contain an explanation of the phenomenon, but provides an indication of where the explanation should be sought. The main relation of phenomena, which I. has in mind, is the relation of a causal relation, which, like the inductive inference itself, rests on identity, for the sum of conditions, called a cause, if it is given in its entirety, is nothing more than a consequence caused by a cause. ... The validity of the inductive inference is beyond question; however, logic must rigorously establish the conditions under which an inductive inference can be considered correct; the absence of negative instances does not yet prove the correctness of the conclusion. It is necessary that the inductive inference be based on as many cases as possible, that these cases be as varied as possible, that they serve as typical representatives of the entire group of phenomena to which the conclusion concerns, etc.

For all that, inductive inferences easily lead to errors, of which the most common arise from a plurality of causes and from the confusion of the temporal order with the causal one. In inductive research we are always dealing with consequences for which reasons must be sought; finding them is called an explanation of the phenomenon, but a certain effect can be caused by a number of different reasons; the talent of an inductive researcher lies in the fact that he gradually chooses from a multitude of logical possibilities only the one that is actually possible. For human limited knowledge, of course, different causes can produce the same phenomenon; but complete adequate knowledge in this phenomenon is able to discern signs that indicate its origin from only one possible cause. The temporal alternation of phenomena always serves as an indication of a possible causal connection, but not every alternation of phenomena, even if correctly repeated, must certainly be understood as a causal connection. Quite often we conclude post hoc - ergo propter hoc, in this way all superstitions arose, but here is also the correct indication for the inductive inference.

4. Deduction

Deduction (from Lat. Deductio - deduction) - deduction of the particular from the general; the way of thinking that leads from the general to the particular, from the general to the particular; the general form of deduction is a syllogism, the premises of which form the indicated general position, and the conclusions form the corresponding private judgment; is used only in the natural sciences, especially in mathematics: for example, from Hilbert's axiom ("two distinct points A and B always define the straight line a") deductively we can conclude that the shortest line between two points is the straight line connecting these two points ; the opposite of deduction is induction; Kant calls transcendental deduction the explanation of how a priori concepts can relate to objects, i.e. how pre-conceptual perception can be formed into conceptual experience; transcendental deduction differs from empirical deduction, which indicates only the way a concept is formed through experience and reflection.

The study of Deduction is the main task of logic; sometimes logic - at least formal logic - is even defined as the "theory of deduction", although logic is far from the only science that studies the methods of deduction: psychology studies the implementation of deduction in the process of real individual thinking and its formation, and epistemology as one of the main methods of scientific knowledge of the world.

Although the term "deduction" itself was first used, apparently, by Boethius, the concept of deduction - as a proof of a sentence by means of a syllogism - appears already in Aristotle. In the philosophy and logic of the Middle Ages and modern times, there were significant differences in views on the role of Deduction in a number of other methods of cognition. So, R. Descartes opposed deduction to intuition, through which, in his opinion, the human mind "directly perceives" the truth, while deduction delivers to the mind only "mediated" knowledge. F. Bacon, and later other English "inductivist" logicians, rightly noting that the conclusion obtained by means of Deduction does not contain any "information" that would not be contained in the premises, and on this basis considered Deduction as a "secondary" method, in while true knowledge, in their opinion, is given only by induction. Finally, representatives of the direction that comes primarily from German philosophy, also 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 through deduction is "true in all possible worlds "(or, as I. Kant later said," analytically true "), which determines their" enduring "value [in contrast to the" factual "truths obtained by inductive generalization of observation data and experience, true by coincidence "].

From the modern point of view, the question of the mutual "advantages" of deduction or induction has largely lost its meaning. Already F. Engels wrote that “induction and deduction are interconnected in the same necessary way as synthesis and analysis. can be achieved only if you do not lose sight of their relationship with each other, their mutual complement to each other. " However, regardless of the dialectical relationship between deduction and induction noted here and their applications, the study of the principles of deduction has enormous independent significance. It was the study of these principles as such that essentially constituted the main content of all formal logic - from Aristotle to the present day. Moreover, at present, more and more actively work is underway to create various systems of "inductive logic", and the creation of "deductive-like" systems seems to be a kind of ideal here, i.e. sets of such rules, following which it would be possible to obtain conclusions that have, if not 100% certainty, then at least a sufficiently large "degree of likelihood" or "probability".

As for formal logic in a narrower sense of this term, both the system of logical rules in itself and any of their applications in any field fully applies the provision that everything that is contained in any one obtained by means of deductive inference "analytical truth" is already contained in the premises from which it is derived: each application of the rule consists in the fact that the general position refers to some specific situation. Some rules of inference fall under this characteristic and in a very explicit way; for example, various modifications of the so-called substitution rule state that the provability property is preserved for any replacement of the elements of an arbitrary formula of a given formal theory by "concrete" expressions of the "same kind". The same applies to the widespread way of defining axiomatic systems by means of the so-called axiom schemes, i.e. expressions that turn into "concrete" axioms after the substitution of specific formulas of the given theory instead of the "generic" designations included in them.

But no matter what specific form a given rule may have, any of its application always bears the character of deduction. The "immutability", obligatoryness, "formality" of the rules of logic, knowing no exceptions, conceals the richest possibilities of automating the process of logical inference using a computer.

Deduction is often understood as the very process of logical following. This determines the close connection between the concept of deduction and the concepts of inference and consequence, which is reflected in logical terminology; thus, it is customary to call one of the important relations between the logical connective of implication and the relation of logical consequence "the deduction theorem": if corollary B is derived from premise A, then implication A É B is provable. Other logical terms associated with the concept of deduction are of a similar nature; thus, sentences derived from each other are called deductively equivalent; the deductive completeness of a system consists in the fact that all expressions of a given system possessing this property are provable in it.

The properties of deduction are, in essence, the properties of the deducibility relation. Therefore, they were revealed mainly in the course of constructing specific logical formal systems and the general theory of such systems. A great contribution to this study was made by: the creator of formal logic Aristotle and other ancient scientists; who put forward the idea of a formal logical calculus G.V. Leibniz; the creators of the first algebraological systems J. Boole, W. Jevons, P.S. Poretsky, Ch. Pierce; the creators of the first logical-mathematical axiomatic systems J. Peano, G. Frege, B. Russell; finally, the school of modern researchers, which comes from Hilbert's deduction, including the creators of the theory of deduction in the form of the so-called calculi of natural inference of the German logician G. Gentzen, the Polish logician S. Jaskowski and the Dutch logician E. Bet. The theory of deduction is being actively developed at the present time, including in the USSR (P.S. Novikov, A.A. Markov, N.A. Shanin, A.S. Yesenin-Volpin, etc.).

Bibliography

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7. Ilyin V.V. Theory of knowledge. Introduction. Common problems. - M., 2004.

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10. Pechenkin AA, Substantiation of scientific theory. Classics and modernity. - M., Science, 1991.

11. Philosophy: Textbook // Ed. V.D. Gubina, T.Yu. Sidorina. - 3rd ed., Rev. and add. - M .: Gardariki, 2003.

Deduction as a research method, opposite to induction, is used where the researcher extends general knowledge (rule, law) to a separate, particular, concrete case, to a single phenomenon.

Deduction theory

This is a form of knowledge in which there is a transition from knowledge of a greater community to new knowledge, of a lesser community. The transition from general knowledge to private, therefore, is carried out through special knowledge (knowledge of laws, theories, hypotheses).

Deduction is a special case of inference. In a broad sense, inference is a logical operation, as a result of which a new statement is obtained from one or several accepted statements (premises) - a conclusion (conclusion, consequence).

In deductive inference, the conclusion with logical necessity follows from the accepted premises. A distinctive feature of this inference is that it always leads from true premises to a true conclusion.

Examples of deductive reasoning:

1. All liquids are elastic; water liquid; means the water is resilient.

2. If it rains, the ground becomes wet; it is raining, therefore the ground is wet.

In all deductive inferences, the truth of the premises guarantees the truth of the conclusion. They allow you to obtain new truths from existing knowledge, and moreover with the help of pure reasoning, without resorting to experience, intuition, etc. Deduction provides a 100% guarantee of success, not just one or another - perhaps a high - probability of a true conclusion.

General scheme of deductive inference:

a) if A, then B; A; hence B, where A and B are statements.

b) if A, then B; wrong B; means wrong A.

The deductive method of cognition allows, through various logical and mathematical transformations, to obtain a large number of consequences from a relatively small number of basic provisions and laws of this theory.

The value of deduction consists, firstly, in the fact that it always gives reliable, necessary conclusions in all its forms. Secondly, in a deductive way it is possible to operate with information of any kind, to express all the richness of the content of our thinking. All other methods of logical reasoning can be reduced to deduction. The ability to reason in a deductive way is a fundamental property of logical thinking. Thirdly, deduction is the main way of building evidence, arguing, debating.

The essence of deduction and induction. Foundations of deductive logic, a study by Aristotle. Description and formation of evidence of the existence of God based on the deductive method. Characteristics of the hypothetical-deductive method, the specificity of the method of R. Descartes and abduction.

1. Views of Rene Descartes

Characteristics of the rationalistic method of cognition. The rules of the deductive method. The principle of doubt. Cogito, ergo sum. Significance of the Cartesian heritage. Deduction and "universal mathematics". The rules of the method of R. Descartes. Moral attitudes of Cartesianism.

abstract added on 05/21/2013

2. Deduction as a form of thought

The concept of the term "deduction". Deduction as a transition from the general to the particular.

Deduction as a research method

The role of the deductive method in mathematics. Deduction theory. Induction and deduction as two inseparable sides of a single cognitive process. Deductive reasoning and deductive reasoning.

abstract, added 06/06/2011

3. The concept of deductive inferences, their role in cognition

The concept of such a special case of inference as deduction. Conventional deductions and their cognitive role. Features of deductive argumentation. Characterization of inference as a form of thinking. The value of deductive thinking (syllogisms) for the development of logic.

test, added 05/24/2015

4. The role of F. Bacon, R. Descartes and G. Galileo in the formation of the empirical and theoretical foundations of scientific rationality

The philosophy of rationalism, the impact on its emergence of the scientific revolution of the XVI-XVII centuries. Features of the philosophical doctrine of R. Descartes. Basic rules of the deductive method, the relationship between intuition and deduction. F. Bacon's contribution to the development of scientific rationality.

abstract added 12/25/2013

5. Theoretical research methods, their characteristics

Abstraction and concretization. Exploring the cognitive role of induction and deduction. Investigation of the procedure for the mental division of an object. Types of analysis as a method of scientific knowledge. Faceted classification method. Form of synthesis as a method of scientific research.

report added on 01/20/2016

6. Inductive inference

Characterization of induction as a method of scientific knowledge. Types of inductive inference. Methods for establishing causal relationships between phenomena. The combined method of similarity and difference. The cognitive role of eliminative induction. The relationship between induction and deduction.

abstract added on 05/20/2018

7. Philosophical system of R. Descartes

Life path and sphere of activity of the representative of materialist philosophers and the ancestor of rational knowledge, Rene Descartes. Basic rules of the deductive method of Descartes' rationalism. Characteristics and structure of the doctrine of doubt and its overcoming.

abstract added on 04/18/2013

8. Rene Descartes's method of doubt

The concept, essence and history of the formation of rationalism as a philosophical and worldview setting. The essence of the rationalistic method and the characteristics of Descartes's original doubt principles. Basic rules of the scientific method. Analysis of the problems of philosophy of R. Descartes.

abstract added on 01/30/2018

9. Deductive inference and its role in cognition

Consideration of logical approaches in the definition of deduction. Disclosure of the content of deductive and direct inference, their features, due to the quantitative and qualitative characteristics of the judgment. Description of an example of a deductive conclusion.

abstract added on 12/01/2015

10. Cognition, its capabilities and boundaries

Study of the structure and dynamics of the cognition process. Study of the types of human cognition: sensory and rational. Characteristics of the main types of the method of cognition: comparative-historical, analysis, synthesis, abstraction, induction and deduction.

abstract, added 11/15/2010

K. f. n. Tyagnibedina O.S.

Luhansk National Pedagogical University

named after Taras Shevchenko, Ukraine

DEDUCTIVE AND INDUCTIVE METHODS OF RECOGNITION

Among the general logical methods of cognition, the most common are deductive and inductive methods. It is known that deduction and induction are the most important types of inferences that play a huge role in the process of obtaining new knowledge based on inference from previously obtained ones. However, it is customary to consider these forms of thinking as special methods, methods of cognition.

The purpose of our work - on the basis of the essence of deduction and induction, substantiate their unity, inextricable connection and thereby show the inconsistency of attempts to oppose deduction and induction, exaggerating the role of one of these methods by belittling the role of the other.

Let's reveal the essence of these methods of cognition.

Deduction (from Lat.deductio - withdrawal) - transition in the process of cognition from common knowledge of a certain class of objects and phenomena to knowledge private and single... In deduction, general knowledge serves as the starting point of reasoning, and this general knowledge is assumed to be “ready”, existing. Note that deduction can also be carried out from the particular to the particular or from the general to the general. The peculiarity of deduction as a method of cognition is that the truth of its premises guarantees the truth of the conclusion. Therefore, deduction has a tremendous power of persuasion and is widely used not only for proving theorems in mathematics, but also wherever reliable knowledge is needed.

Induction (from Latin inductio - guidance) is a transition in the process of cognition from private knowledge to common; from knowledge of a lesser degree of community to knowledge of a greater degree of community. In other words, it is a method of research, cognition, associated with the generalization of the results of observations and experiments. The main function of induction in the process of cognition is to obtain general judgments, which can be empirical and theoretical laws, hypotheses, generalizations. In induction, the "mechanism" of the emergence of common knowledge is revealed. A feature of induction is its probabilistic nature, i.e. if the initial premises are true, the induction conclusion is only likely true and in the final result it may turn out to be both true and false. Thus, induction does not guarantee the attainment of the truth, but only "leads" to it, i.e. helps to seek the truth.

In the process of scientific knowledge, deduction and induction are not applied in isolation, apart from each other. However, in the history of philosophy, attempts were made to oppose induction and deduction, to exaggerate the role of one of them at the expense of belittling the role of the other.

Let's take a short excursion into the history of philosophy.

The founder of the deductive method of cognition is the ancient Greek philosopher Aristotle (364 - 322 BC). He developed the first theory of deductive inferences (categorical syllogisms), in which the conclusion (consequence) is obtained from premises according to logical rules and has a reliable character. This theory is called syllogistic. The theory of proof is based on it.

Aristotle's logical works (treatises) were later combined under the name "Organon" (an instrument, a tool for cognizing reality). Aristotle clearly preferred deduction, so the Organon is usually identified with the deductive method of cognition. It should be said that Aristotle also explored inductive reasoning. He called them dialectical and opposed the analytical (deductive) conclusions of syllogistics.

The English philosopher and naturalist F. Bacon (1561 - 1626) developed the foundations of inductive logic in his work "New Organon", which was directed against Aristotle's "Organon". Syllogistics, according to Bacon, is useless for discovering new truths; at best, it can be used as a means of testing and substantiating them.

4 Methods of theoretical research

According to Bacon, inductive inference is a reliable, effective tool for making scientific discoveries. He developed inductive methods for establishing causal relationships between phenomena: similarities, differences, concomitant changes, residues. The absolutization of the role of induction in the process of cognition led to a weakening of interest in deductive cognition.

However, the growing advances in the development of mathematics and the penetration of mathematical methods into other sciences were already in the second half of the 17th century. revived interest in deduction. This was also facilitated by rationalistic ideas recognizing the priority of reason, which were developed by the French philosopher, mathematician R. Descartes (1596 - 1650) and the German philosopher, mathematician, logician G.V. Leibniz (1646 - 1716).

R. Descartes believed that deduction leads to the discovery of new truths if it deduces a consequence from the positions of reliable and obvious, which are the axioms of mathematics and mathematical natural science. In his work "Discourse on the method for the good direction of the mind and the search for truth in the sciences," he formulated four basic rules of any scientific research: 1) only that which is known, verified, proven is true; 2) dismember the complex into the simple; 3) ascend from simple to complex; 4) explore the subject comprehensively, in all details.

G.V. Leibniz argued that deduction should be applied not only in mathematics, but also in other areas of knowledge. He dreamed of a time when scientists would not do empirical research, but calculations with a pencil in their hands. To this end, he strove to invent a universal symbolic language with which it would be possible to rationalize any empirical science. New knowledge, in his opinion, will be the result of calculations. Such a program cannot be realized. However, the very idea of formalizing deductive reasoning laid the foundation for the emergence of symbolic logic.

It should be emphasized that attempts to separate deduction and induction from each other are unfounded. In fact, even the definitions of these methods of cognition testify to their interconnection. Obviously, deduction uses as premises various kinds of general judgments that cannot be obtained through deduction. And if there were no general knowledge obtained through induction, then deductive reasoning would be impossible. In turn, deductive knowledge about the individual and the particular creates the basis for further inductive research of individual objects and obtaining new generalizations. Thus, in the process of scientific knowledge, induction and deduction are closely interconnected, complement and enrich each other.

Literature:

1. Demidov I.V. Logics. - M., 2004.

2. Ivanov E.A. Logics. - M., 1996.

3. Ruzavin G.I. Research methodology. - M., 1999.

4. Ruzavin G.I. Logic and argumentation. - M., 1997.

5. Philosophical Encyclopedic Dictionary. - M., 1983.

Who developed the deductive method of knowledge

Download file - Who developed the deductive method of cognition

Luhansk National Pedagogical University. However, it is customary to consider these forms of thinking as special methods, methods of cognition. The purpose of our work is to substantiate their unity, inextricable connection on the basis of the essence of deduction and induction, and thereby show the inconsistency of attempts to oppose deduction and induction, exaggerating the role of one of these methods at the expense of belittling the role of the other. Let's reveal the essence of these methods of cognition. The peculiarity of deduction as a method of cognition is that the truth of its premises guarantees the truth of the conclusion. In other words, it is a method of research, cognition, associated with the generalization of the results of observations and experiments. The main function of induction in the process of cognition is to obtain general judgments, which can be empirical and theoretical laws, hypotheses, generalizations. A feature of induction is its probabilistic nature, that is, if the initial premises are true, the conclusion of induction is only likely true and in the final result it may turn out to be both true and false. In the process of scientific knowledge, deduction and induction are not applied in isolation, apart from each other. However, in the history of philosophy, attempts were made to oppose induction and deduction, to exaggerate the role of one of them at the expense of belittling the role of the other. Let's take a short excursion into the history of philosophy. The founder of the deductive method of knowledge is the ancient Greek philosopher Aristotle - gg. This theory is called syllogistic. It should be said that Aristotle also explored inductive reasoning. The English philosopher and naturalist F. Syllogistics, according to Bacon, is useless for discovering new truths, at best it can be used as a means of testing and substantiating them. According to Bacon, inductive inference is a reliable, effective tool for making scientific discoveries. He developed inductive methods for establishing causal relationships between phenomena: However, the growing successes in the development of mathematics and the penetration of mathematical methods into other sciences already in the second half of the 17th century.

7.2. Induction and deduction

This was also facilitated by rationalistic ideas recognizing the priority of reason, which were developed by the French philosopher, mathematician R. Descartes - and the German philosopher, mathematician, logician G. Leibniz - Leibniz argued that deduction should be applied not only in mathematics, but also in other areas of knowledge. He dreamed of a time when scientists would not do empirical research, but calculations with a pencil in their hands. New knowledge, in his opinion, will be the result of calculations. Such a program cannot be realized. However, the very idea of formalizing deductive reasoning laid the foundation for the emergence of symbolic logic. It should be emphasized that attempts to separate deduction and induction from each other are unfounded. In fact, even the definitions of these methods of cognition testify to their interconnection. Obviously, deduction uses as premises various kinds of general judgments that cannot be obtained through deduction. And if there were no general knowledge obtained through induction, then deductive reasoning would be impossible. In turn, deductive knowledge about the individual and the particular creates the basis for further inductive research of individual objects and obtaining new generalizations. Thus, in the process of scientific knowledge, induction and deduction are closely interconnected, complement and enrich each other.

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