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

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

Let us analyze induction as a method of empirical knowledge.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Baconian induction is based on the recognition:

material unity of nature;

uniformity of its actions;

universal causation.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The first premise: crucian carp is a fish;

second premise: crucian carp lives in water;

conclusion (inference): fish live in water.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Firstly, creating the most complete classification possible;

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

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

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

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

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

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

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

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

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

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

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

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

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

Inductive method(induction) characterizes the path of knowledge from recording experimental (empirical) data and their analysis to their systematization, generalizations and general conclusions drawn on this basis. This method also consists in the transition from some ideas about certain phenomena and processes to others - more general and often deeper. The basis for the functioning of the inductive method of cognition is experimental data. Thus, the fundamental ideas about modern capitalism, which form the content of the corresponding theories, were obtained as a result of a scientific generalization of the historical experience of the development of capitalist society over the last 100-plus years.

However, inductive generalizations will be completely flawless only if all scientifically established facts on the basis of which these generalizations are made are thoroughly studied. It is called complete induction. Most often, this is very difficult to do, and sometimes impossible.

Therefore in cognitive activity, including in the study of various phenomena and processes public life, the method is more often used incomplete induction – the study of some part of the phenomena and the extension of the conclusion to all phenomena of a given class. Generalizations obtained on the basis of incomplete induction, in some cases can be quite definite and reliable, in others - more probabilistic in nature.

The validity of inductive generalizations can be tested by applying deductive research method, the essence of which is to derive from some general provisions, considered reliable, certain consequences, some of which can be verified experimentally.

If the consequences arising from inductive generalizations are confirmed by the practical experience of people (experiment or real processes of social life), then these generalizations can be considered reliable, i.e. corresponding to reality.

Consequently, induction and deduction are two opposing and at the same time complementary methods of scientific research.

Analogy- this is a certain type of comparison of phenomena and processes, including those occurring in society: having established the similarity of some properties of certain phenomena (processes), a conclusion is drawn about the similarity of their other properties.

An important role in the study of social phenomena is played by the so-called historical analogy. Thus, knowing the history of the development of capitalism in Great Britain (one of the first capitalist countries in Europe), many scientists compared with it the history of the development of capitalism in France, Germany, the USA and other countries. It was recorded that in these countries, as in Great Britain, the economy developed from the free competition of small and medium-sized industrial, commercial and financial enterprises to the dominance of the then formed industrial, commercial and financial monopolies. On this basis, conclusions were drawn that other properties of the economies of France, Germany and the USA are similar to the UK economy. Many Western economists point out that at present, essentially similar models of development of the capitalist economy have formed in the USA and England.

It is clear that it is necessary to take into account the specific features of the development of socio-economic and political processes in different countries. There is no need to reduce the study of these processes only to the search for historical analogies. In addition, the analogy method is most often used along with other general scientific methods for studying social phenomena and processes. At the same time, the scientific effectiveness of using the analogy method is quite high.

Modeling– this is the reproduction in a specially created object (model) of the properties of the phenomenon or process being studied. As a model (from lat. modulus- measure, sample, norm) can be any material system(model of an airplane, power plant, etc.) or mental construct(graph, drawing, mathematical formula), reproducing the properties of the phenomenon or process being studied, including economic, political, etc.

Both the material and the ideal model are built according to the principle analogies, those. the similarity of the properties recorded in them with the properties of the phenomenon or process being studied with their help. The data obtained is used in further research of this phenomenon or process.

Their study using modeling is, as a rule, heuristic character that reveals something new. In particular, when analyzing the model itself, properties are discovered that are absent in its individual parts and their simple sum. This demonstrates the principle: “The whole is greater than the sum of its parts.” It turns out that “the model encodes information that people did not know before,” and therefore the model “contains potential knowledge which a person, by studying it, can acquire, make visual and use for his practical needs. This is precisely what determines the predictive ability of the model description."

When studying the phenomena of social life, the so-called Causal models. They help to identify objective cause-and-effect relationships and interdependencies between social phenomena, the generation of some of them by others, as well as the emergence of new properties in them. However, such models do not always allow us to draw conclusions about the phenomenon under study as a whole, since, while revealing its objective aspects, they do not capture subjective factors relating to the consciousness of people, whose actions determine the content and direction of any social phenomena and processes.

This difficulty is sometimes resolved by sociologists and political scientists in the following way: when analyzing the processes occurring throughout society (in macro level) cause-and-effect models are used that identify objective factors in people’s activities and behavior, and when analyzing processes occurring in individual teams (on micro level) Along with cause-and-effect models, “cognitive models of interactions between individuals” are used, with the help of which the motives, beliefs and goals of subjects of economic, political and other activities are identified.

When studying socio-economic and political processes, they are also used "models life cycle", with the help of which the peculiarities of the functioning of social phenomena are studied at different stages of their development (for example, models of the life cycle of organizations operating in the field of economic business; the life cycle of ethnic groups, civilizations, etc.). The main phases (stages) of the development of a particular phenomenon are modeled. These models themselves are built based on data on the main parameters of the development of some social phenomenon. The new data obtained from the simulation is used for a more specific analysis of this phenomenon.

In studies of economic processes, the so-called wave dynamics models, reproducing the wave-like nature of the functioning of the economy depending on economic, political and other conditions. The idea of this nature of economic development was scientifically substantiated by the famous Russian scientist N.D. Kondratiev, who revealed, in particular, the presence of “long waves” in its development (“Kondratiev waves”), depending on the mass introduction of new equipment and technology into production, structural changes due to the emergence of new sectors of the economy, as well as various political factors and social upheavals.

Method ascent from abstract to concrete seems to combine the previous ones in a certain ratio general scientific methods research.

Socio-economic and political processes are initially perceived by the subject as a certain set of phenomena that he constantly encounters in Everyday life. The empirical, sensory-concrete ideas about these phenomena that arise in this case reflect the technical or other aspects of them and contain some knowledge about the socio-economic and political processes, however, are rather superficial.

The process of cognition does not stop there and moves further - from sensory-concrete ideas about this or that phenomenon or process to mental-abstract knowledge about its individual aspects, properties, etc. Any scientific abstraction, expressed in the form of a particular concept, more deeply reflects the properties of the phenomenon or process being studied than empirical ideas about them, because it expresses their necessary and essential properties, separating them from everything random and unimportant.

Consequently, there is a deeper knowledge of the content and essence of a particular phenomenon and process. Operations such as analysis and synthesis, corresponding inductive and deductive inferences, analogy, and construction of mental models are performed. As a result, abstract concepts, lining up in a certain system, contribute to the emergence holistic knowledge about the phenomenon or process being studied, reflecting the internal connections and interactions of their constituent elements. This cognitive process is characterized as Ibid. pp. 126-134.

Cm.: Kondratyev N. D. Problems of economic dynamics. M., 1989.

Among the general logical methods of cognition, these two methods cause the most controversy. Conan Doyle played a significant role in this. Therefore, we will once again try to dot the i's in this topic by turning to the very sources of this kind of conclusion.

In the process of scientific knowledge, deduction and induction are almost never used in isolation, apart from each other. However, in the history of philosophy, attempts have been made to contrast induction and deduction, to exaggerate the role of one of them by diminishing the role of the other.

The founder of the deductive method of knowledge 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 the premises according to logical rules and is reliable. This theory is called syllogistic. The theory of proof is built on its basis.

Aristotle's logical works (treatises) were later united under the name “Organon” (instrument, instrument for cognition of reality). Aristotle clearly preferred deduction, which is why the “Organon” is usually identified with the deductive method of knowledge. It should be said that Aristotle also explored inductive reasoning. He called them dialectical and contrasted them with the analytical (deductive) conclusions of syllogistics.

The English philosopher and natural scientist 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 justifying them. According to Bacon, a reliable, effective tool for implementing scientific discoveries are inductive conclusions. 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 has led to a weakening of interest in deductive cognition.

However, 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. revived interest in deduction. This was also facilitated by rationalistic ideas that recognize the priority of reason, which were developed by the French philosopher, mathematician R. Descartes (1596 - 1650) and the German philosopher, mathematician, logician G. W. Leibniz (1646 - 1716).
R. Descartes believed that deduction leads to the discovery of new truths if it derives a consequence from reliable and obvious provisions, such as the axioms of mathematics and mathematical science. In his work “Discourse on a 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 what is known, tested, and proven is true; 2) break down 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 used not only in mathematics, but also in other areas of knowledge. He dreamed of a time when scientists would not empirical research, but by calculation with a pencil in hand. To this end, he sought to invent a universal symbolic language with the help of which any empirical science could be rationalized. New knowledge, in his opinion, will be the result of calculations. Such a program cannot be implemented. However, the very idea of formalizing deductive reasoning laid the foundation for the emergence of symbolic logic, which Conan Doyle apparently picked up when creating Sherlock.

It should be especially emphasized that attempts to separate deduction and induction from each other are not entirely unfounded, although they have the right to occur. In fact, even the definitions of these methods of cognition indicate their interrelation. It is obvious that deduction uses various kinds of general propositions as premises 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 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 interrelated, complement and enrich each other.

Literature:
1. Demidov I.V. Logics. – M., 2004.
2. Ivanov E.A. Logics. – M., 1996.
3. Ruzavin G.I. Methodology of scientific research. – M., 1999.
4. Ruzavin G.I. Logic and argumentation. – M., 1997.
5. Philosophical encyclopedic dictionary. – M., 1983.

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Moscow State Technical University

named after N. E. Bauman

Faculty of Mechanical Engineering Technologies

Homework

in the course "Methodology of scientific knowledge"

Deduction as a method of science and its functions

Completed by a student

MT groups 4-17

Guskova E.A.

Checked by: Gubanov N.N.

Moscow, 2016

Introduction
1.
2. Deductive method of R. Descartes
3. Verification in modern science
4. Abduction method
List of used literature

Introduction

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 derivation from previously acquired knowledge.

Deduction (from Latin deductio - deduction) is a transition in the process of cognition from general knowledge about a certain class of objects and phenomena to private and individual knowledge. In deduction, general knowledge serves as the starting point of reasoning, and this general knowledge is assumed to be “ready-made,” existing. Note that deduction can also be carried out from particular to particular or from general to 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 enormous persuasive power and is widely used not only to prove theorems in mathematics, but also wherever reliable knowledge is needed.

Induction (from Latin inductio - guidance) is a transition in the process of cognition from particular knowledge to general knowledge; from knowledge of a lesser degree of generality to knowledge of a greater degree of generality. In other words, it is a method of research and cognition associated with generalizing 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, and generalizations. Induction reveals the “mechanism” of the emergence of general knowledge. A special feature of induction is its probabilistic nature, i.e. If the initial premises are true, the conclusion of induction is only probably true and in the final result it can turn out to be either true or false. Thus, induction does not guarantee the achievement of truth, but only “points” to it, i.e. helps to search for the truth.

In the process of scientific knowledge, deduction and induction are not used in isolation, apart from each other. One is impossible without the other.

1. The Birth of the Deductive Method

The foundations of deductive logic were laid in the works of ancient Greek philosophers and mathematicians. Here you can name such names as the names of Pythagoras and Plato, Aristotle and Euclid. It is believed that Pythagoras was one of the first to reason in the style of proving a particular statement, rather than simply proclaiming it. The works of Parmenides, Plato and Aristotle developed ideas about the basic laws correct thinking. Ancient Greek philosopher Parmenides was the first to express the idea that at the basis of truly scientific thinking lies a certain unchangeable principle (“one”), which continues to remain unchanged, no matter how the thinker’s point of view changes. Plato compares the One with the light of thought, which continues to remain unchanged as long as the thought itself exists. In a more strict and concrete form, this idea is expressed in the formulation of the basic laws of logic by Aristotle. In the works of Euclid, the application of these techniques and laws to the mathematical sciences reaches the highest level, which became the ideal of deductive thinking for centuries and millennia in European culture. Later, the formulations of deductive logic were increasingly refined and detailed by the Stoics and medieval scholasticism.

Aristotle is rightfully considered the founder of logic as a deductive science. He was the first to systematize the basic techniques of correct thinking, summarizing the achievements of the ancient Greek mathematicians of his time. Logic, as expounded in the Organon, was seen both as a tool for achieving truth through correct thinking, and as a science that prepared the way for various other sciences.

According to Aristotle, true knowledge can be obtained through logical proof. Considering the inductive method, in which one moves from the particular to the general, Aristotle concluded that such a method is imperfect, believing that the deductive method, in which the particular is derived from the general, provides more reliable knowledge. The fundamental tool of this method is the syllogism. Below is a typical example of a syllogism:

All people are mortal (big premise).

Socrates is a man (minor premise).

Therefore Socrates is mortal (conclusion).

Aristotle believed that the main discoveries in geometry had already been made. It's time to transfer its methods to other sciences: physics and zoology, botany and politics. But the most important tool of geometry is the logical method of reasoning, which leads to correct conclusions from any correct premises. Aristotle outlined this method in his book Organon; now it is called the beginning of mathematical logic. However, logic alone is not enough to substantiate physical science; experiments, measurements and calculations like those carried out by Anaxagoras are needed. Aristotle did not like to conduct experiments. He preferred to guess the truth intuitively - and as a result, he was often mistaken, and there was no one to correct him. Therefore, Greek physics consisted mainly of hypotheses: sometimes ingenious, but sometimes grossly erroneous. There were no proven theorems in this science.

In the Middle Ages, Aristotle's logic attracted much attention as a tool for deductive proof of theological and philosophical propositions. Aristotle's syllogism remained in force for about two thousand years, without undergoing almost any changes during this time.

Thomas Aquinas, combining Christian dogmas with the deductive method of Aristotle, formulated five proofs of the existence of God based on the deductive method.

1. Proof one: Prime mover

Proof by motion means that any moving object was once set in motion by some other object, which in turn was set in motion by a third, and so on. In this way, a sequence of “engines” is built, which cannot be infinite. As a result, we will always find an “engine” that moves everything else, but is itself not driven by anything else and is motionless. It is God who turns out to be the root cause of all movement.

2. Proof two: First Cause

Proof through productive cause. Proof similar to the previous one. Only in this case it is not the cause of movement, but the cause that produces something. Since nothing can produce itself, there is something that is the first cause of everything - this is God.

3. Proof three: Necessity

Each thing has the possibility of both its potential and real existence. If we assume that all things are in potency, then nothing would come into being. There must be something that contributed to the transfer of a thing from a potential to an actual state. This something is God.

4. Proof four: The highest degree of being

Proof from degrees of being - the fourth proof says that people talk about different degrees of perfection of an object only through comparisons with the most perfect. This means that there is the most beautiful, the most noble, the best - this is God.

5. Proof five: Goal-setter

Proof through the target reason. In the world of rational and irrational beings, there is a purposefulness of activity, which means there is a rational being who posits a goal for everything. After all, nothing we know looks like it was intentionally created unless it was created. Accordingly, there is a creator, and his name is God.

The deductive method is always present in the concepts of mystical and religious theories. It is characterized by the presence of concepts that are not disclosed, in fact, in the necessary details, and therefore different people causes different ideas. This is the reason that everyone understands religious ideas in their own way, everyone has their own god in their soul.

2. Deductiveth methodR. Decamouth

In modern times, the credit for transforming deduction belongs to Rene Descartes (1596-1650). He criticized medieval scholasticism for its method of deduction and considered this method not scientific, but related to the field of rhetoric. Descartes dreamed of connecting all sciences into one whole, into a system of knowledge about the world, growing from one single principle, an axiom. Then science would turn from a collection of disparate facts and quite often contradictory theories into a logically coherent and integral picture of the world. Instead of medieval deduction, he proposed a precise, mathematized way of moving from the self-evident and simple to the derivative and complex.

“By method,” writes Descartes, “I mean precise and simple rules, strict observance of which always prevents the acceptance of false as true - and, without unnecessary waste mental powers, - but gradually and continuously increasing knowledge, it helps the mind achieve true knowledge of everything that is available to it.” R. Descartes outlined his ideas about the method in his work “Discourse on Method”, “Rules for Guiding the Mind”. They are given four rules.

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

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

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

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

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

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

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

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

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

· firstly, the creation of as complete a classification as possible;

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

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

deduction aristotle logic

3. Hypothetico-deductive method

Currently, in modern science, the hypothetico-deductive method most often operates. This is a method of reasoning based on the derivation (deduction) of conclusions from hypotheses and other premises, the true meaning of which is unknown. Therefore, the hypothetico-deductive method obtains only probabilistic knowledge.

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

According to the nature of the premises, all hypothetical conclusions can be divided into three groups.

First group make problematic inferences, the premises of which are hypotheses or generalizations of empirical data. Therefore, they can also be called hypothetical conclusions proper, since the truth value of their premises remains unknown.

Second group consists of inferences, the premises of which are assumptions that contradict any statements. By putting forward such an assumption, a consequence is deduced from it, which turns out to be clearly inconsistent obvious facts or firmly established provisions. Well-known methods of such inferences are the method of reasoning by contradiction, often used in mathematical proofs, as well as the method of refutation known in ancient logic - reduction to absurdity (reductio ad absurdum).

ThirdI'm a group is not much different from the second, but in it the assumptions contradict any opinions and statements taken on faith. Such reasoning was widely used in ancient debates, and it formed the basis of the Socratic method discussed at the beginning of this chapter.

Hypothetical reasoning is usually resorted to when there are no other ways of establishing the truth or falsity of certain generalizations, most often of an inductive nature, that can be linked into a deductive system. Traditional logic was limited to the study of the most general principles of hypothetical inferences and did not delve almost at all into the logical structure of the systems used in the developed empirical sciences.

A new trend that has emerged in the modern methodology of empirical sciences is that it considers any system of experimental knowledge as a hypothetico-deductive system. One can hardly completely agree with this because there are sciences that have not reached the necessary theoretical maturity and which are still limited to individual, unrelated generalizations or hypotheses, or even simple descriptions the phenomena described. Advanced hypothetico-deductive systems often use mathematical methods.

Often in logic, hypothetico-deductive systems are considered as meaningful axiomatic systems that allow only one possible interpretation. However, such a formal analogy does not take into account the specific features of the deductive organization of experimental knowledge, which are abstracted from during the axiomatic construction of theories in mathematics. To illustrate this thesis, consider, for example, the difference between the familiar geometry of Euclid as a formal mathematical system, on the one hand, and geometry as an interpreted or physical system, on the other. It is known that before the discovery of non-Euclidean geometries, Euclidean geometry was considered the only correct doctrine about the properties of the space around us, and I. Kant even raised such a belief to the rank of an a priori principle. The situation after the discovery of new geometries by Lobachevsky, Bolyai and Riemann, although gradually, changed radically. From a purely logical and mathematical point of view, all these geometric systems are equally valid and valid, because they are consistent. But as soon as they are given a certain interpretation, they turn into some specific hypotheses, for example, physical ones. Check which one better reflects reality, say, physical properties and the relationship of the surrounding space, only a physical experiment can. From here it becomes clear that experimental sciences, in order to systematize and organize all the material accumulated in them, strive to build interpreted systems, where concepts and judgments have a certain meaning associated with the study of a specific empirical area of objects and phenomena of the real world. In mathematical research, one abstracts from the concrete meaning and significance of objects and builds abstract systems, which can subsequently receive a completely different interpretation. No matter how strange it may seem, the axioms of Euclid’s geometry can describe not only the properties and relationships between the geometric points, lines and planes that are familiar to us, but also many relationships between various other objects, for example, the relationships between color sensations. It follows that the difference between the axiomatic systems of pure mathematics and the hypothetico-deductive systems of applied mathematics, natural science and the empirical sciences in general arises at the level of interpretation. If for a mathematician a point, a straight line and a plane simply mean initial concepts that are not defined within the framework of a geometric system, then for a physicist they have a certain empirical content.

Sometimes it is possible to give an empirical interpretation of the initial concepts and axioms of the system under consideration. Then the whole theory can be considered as a system of deductively related empirical hypotheses. However, most often it turns out to be possible to empirically interpret only some of the hypotheses obtained from the axioms as a consequence. It is precisely this kind of hypothesis that turns out to be associated with the results of experiment. So, for example, Galileo already built a whole system of hypotheses in his experiments in order to, with the help of lower-level hypotheses, verify the truth of higher-level hypotheses.

The hypothetico-deductive system can thus be considered as a hierarchy of hypotheses, the degree of abstraction of which increases with distance from the empirical basis. At the very top are hypotheses, the formulation of which uses very abstract theoretical concepts. That is why they cannot be directly compared with experimental data. On the contrary, at the bottom of the hierarchical ladder there are hypotheses, the connection of which with experience is quite obvious. But the less abstract and general the hypotheses are, the smaller the range of empirical phenomena they can explain. A characteristic feature of hypothetico-deductive systems is precisely that in them the logical power of hypotheses increases with the level at which the hypothesis is located. The greater the logical power of a hypothesis, the greater the number of consequences that can be deduced from it, which means that the greater the range of phenomena it can explain.

And from the above, we can conclude that the hypothetico-deductive method is most widely used in those branches of natural science that use a developed conceptual apparatus and mathematical research methods. In descriptive sciences, where isolated generalizations and hypotheses predominate, establishing a logical connection between them encounters serious difficulties: firstly, because they do not single out the most important generalizations and facts from a huge number of other, secondary ones; secondly, the main hypotheses are not separated from the derivative ones; thirdly, logical relationships between individual groups of hypotheses have not been identified; fourthly, the sheer number of hypotheses is usually large. Therefore, the efforts of researchers in such sciences are aimed not so much at unifying all existing empirical generalizations and hypotheses by establishing deductive relationships between them, but at searching for the most general fundamental hypotheses that could become the basis for building a unified system of knowledge.

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

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

4. Abduction method

The methods of induction and traditional forms of deductive reasoning analyzed above cannot be considered as the optimal means of discovering new ideas, although F. Bacon and R. Descartes were convinced of this. Due to this circumstance at the end of the 19th century. drew the attention of the American logician and philosopher Charles S. Peirce, the founder of pragmatism, who stated that logic and philosophy of science should engage in conceptual analysis of the emergence of new ideas and hypotheses in science. For this purpose, he proposed to supplement the general logical methods of induction and deduction with the method of abduction as a specific way of searching for explanatory hypotheses. The terms “deduction”, “induction” and “abduction” come from the root “to lead” and are translated respectively as “removal”, “guidance”, “bringing”. C. Pierce wrote: “Induction examines theories and measures the degree of their agreement with facts. She can never create any idea at all. Deduction can do no more than that. All ideas of science arise through abduction. Abduction consists of examining facts and constructing a theory to explain them.” In other words, according to Peirce, abduction is a method of searching for hypotheses, while induction, being a probabilistic inference, according to the philosopher, is a method of testing existing hypotheses and theories.

Induction in traditional logic is considered as an inference from the particular to the general, from individual facts to their generalization. The result of induction can be the establishment of simple empirical hypotheses. Peirce is looking for a means by which hypotheses are created that make it possible to reveal the internal mechanism underlying the observed facts and phenomena. Thus, abduction, like induction, refers to facts, but not in order to compare or generalize them, but in order to formulate a hypothesis based on them.

At first glance, it seems that abduction is no different from the hypothetico-deductive method, since it also includes the statement of a hypothesis. However, it is not. The hypothetico-deductive method begins with a predetermined hypothesis, and then consequences are derived from it, which are tested for truth. Abduction begins with an analysis and accurate assessment of established facts, after which a hypothesis is selected to explain them. Peirce formulates methodological requirements for abductive hypotheses.

They must explain not only empirically observed facts, but also facts that are directly unobservable and verifiable indirectly.

They must be confirmed, not only by observed facts, but also by newly identified facts.

List of usedliterature

1. Alekseev P.V., Panin A.V. Philosophy. M.: TEIS, 1996.

2. Novikov A.M., Novikov D.A. Methodology. M.: SIN-TEG, 2007.

3. Novikov A.M., Novikov D.A. Methodology. Dictionary of the system of basic concepts. M.: SIN-TEG, 2013.

4. Philosophy and methodology of science. Under. ed. IN AND. Kuptsova. M.: ASPECT PRESS, 1996.

5. Dictionary of philosophical terms. Scientific edition of Professor V.G. Kuznetsova. M., INFRA-M, 2007, p. 74-75.

6. Ababilova L.S., Shlekin S.I. The problem of the scientific method. - M., 2007.

7. Ruzavin G.I. Methodology of scientific research: Textbook. manual for universities. - M.: UNITY-DANA, 1999. - 317 p.

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Introduction

Knowledge plays an important role in our lives 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 knowledge has been discussed throughout the history of philosophy. In contrast to analysis and synthesis, these methods were often opposed to each other and considered in isolation from each other and from other means of cognition.

In 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, in modern inductive logic, probabilistic methods play a huge role. Assessing the likelihood of generalizations, searching for criteria for substantiating hypotheses, the establishment of complete reliability of which is often impossible, requires increasingly sophisticated research methods.

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 of knowledge

1. Theory as a special form of scientific knowledge

Theory (Greek θεωρία - consideration, research) is a set of conclusions that reflects objectively existing relationships and connections between the phenomena of objective reality. Thus, theory is an intellectual reflection of reality. In theory, each conclusion is derived from other conclusions based on certain rules of logical inference. The ability to predict is a consequence of theoretical constructs. Theories are formulated, developed and tested according to the scientific method.

Theory is a doctrine, 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 conclusion is called such, regardless of the objectivity of this conclusion. As a result, various hypothetical constructions are often called a theory, for example, “the theory of geosynclines,” etc. This can be considered as an attempt to give weight to this hypothetical construction, i.e. an attempt to mislead.

In the “pure” sciences, a theory is an arbitrary set of propositions of some artificial language, characterized by precise rules for the construction of expressions and their understanding.

Functions of the theory

Any theories have a number of functions. Let us denote the most significant functions of the theory:

theory provides its user with conceptual structures;

in theory, terminology is developed;

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

Testing the theory

It is usually believed that the standard method of testing theories is direct experimental verification (“experiment is the criterion of truth”). However, often a theory cannot be tested by direct experiment (for example, the theory about the origin of life on Earth), or such testing is too complex or expensive (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 relationship between theory and experiment is more complex. Since the theory already reflects objective phenomena previously verified by experiment, such conclusions cannot be drawn. At the same time, since the theory is built on the basis of the laws of logic, conclusions are possible about 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 translation of this hypothesis into the rank of a theory, is proven 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 the observational sense - to describe the course of events that we cannot influence, and in the synthetic sense - to create the desired future through technology. Figuratively speaking, the essence of theory is to connect together “circumstantial evidence”, to render a verdict on past events and to indicate what will happen in the future if certain conditions are met.

2. Basic forms of inferences

Let us consider the basic forms of inferences characteristic of logical thinking. There are not so many such forms: these are induction, deduction and analogy. Briefly they can be characterized as follows. Induction is a conclusion about a set based on consideration of 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. Analogy is a conclusion about an element (set) that transfers the properties of another element (set) to it. 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 situation to a general one. Inductive reasoning connects particular premises with a conclusion not so much through the laws of logic, but rather through some factual, psychological or mathematical ideas.

There is a distinction between complete induction - a method of proof in which a statement is proven for a finite number of special cases that exhaust all possibilities, and incomplete induction - observations of individual special cases lead to a hypothesis, which, of course, needs proof. The method of mathematical induction is also used for proof. Contents [remove]

The term first appears in Socrates (ancient Greek: ἐπαγωγή). But Socrates' induction has little in common 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 (Anal. 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 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 method of inference opposite to syllogism. A syllogism, according to Aristotle, indicates through the middle concept that the highest concept belongs to the third, and induction by the third concept shows the belonging of the highest to the middle.

During the Renaissance, a struggle began against Aristotle and the syllogistic method, 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 founder of modern I., although fairness requires mention of his predecessors, for example Leonardo da Vinci and others. Praising I., Bacon denies the significance of the syllogism (“a syllogism consists of sentences, sentences consist of words, words are signs of concepts; If, therefore, the concepts that form the basis of the matter are unclear and hastily abstracted from things, then what is built on them cannot have any strength." This negation did not follow from I. Bacon’s theory (see his “Novum Organon”) not only does not contradict the syllogism, but even requires it. The essence of Bacon's teaching boils down to the fact that with gradual generalization one must adhere to known rules, that is, one must make three reviews of all known cases of manifestation of a known property in various items: a review of positive cases, a review of negative ones (that is, a review of objects similar to the first ones, in which, however, the property being studied is absent) and a review of cases in which the property being studied is manifested in varying degrees, and from here make a generalization ("Nov.org. "LI, aph.13). According to Bacon's method, it is impossible to draw a new conclusion without subsuming the subject under study under general judgments, that is, without resorting to a syllogism. So, Bacon failed to establish I. as a special method opposite to deductive.

A further step was taken by J. St. Millem. Every syllogism, according to Mill, contains a petitio principii; every syllogistic conclusion actually proceeds from particular to particular, and not from general to particular. This criticism of Mill is unfair, because we cannot conclude from particular to particular without introducing an additional general proposition about the similarity of particular cases among themselves [source not specified 574 days]. Considering I., Mill, firstly, asks the question of the basis or 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 one under study, the circumstance that occurs in the first case and is absent in the second is the cause or part of the cause of the phenomenon under study); the method of residuals (if in the phenomenon under study some of the circumstances can be explained by certain causes, then the remaining part of the phenomenon is explained from the remaining previous ones facts) and the method of corresponding changes (if, following a change in one phenomenon, a change in another is noticed, then we can conclude a causal relationship between them). It is characteristic that these methods, upon closer examination, turn out to be deductive methods; eg The residual method is nothing more than determination by elimination. Aristotle, Bacon and Mill represent the main moments in the development of the doctrine of history; only for the sake of a detailed development of some issues one has to pay attention to Claude Bernard ("Introduction to Experimental Medicine"), to Oesterlen ("Medicinische Logik"), Herschel, Liebig, Wevel, 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 a complete enumeration of the species of a certain genus to the entire genus; It is obvious that with such a method of inference we obtain a completely reliable conclusion, which at the same time in a certain respect expands our knowledge; this method of inference cannot raise any doubts. 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, incomplete I., going from the particular to the general (a method of inference prohibited formal logic), should raise a question of law. In its construction, incomplete I. resembles the third figure of a syllogism, differing from it, however, in that I. strives for general conclusions, while the third figure allows only specific ones.

The inference from 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 studied. Mill, in explaining the logical right to conclude from incomplete induction, pointed to the idea of a uniform order in nature, due to which our faith in inductive conclusion should increase, but the idea of a uniform order of things is itself the result of incomplete induction and, therefore, cannot serve as the basis of induction . In fact, the basis of incomplete I. is the same as the complete one, as well as the third figure of the syllogism, that is, the identity of particular judgments about an object with the entire group of objects. “In incomplete I. we conclude, on the basis of 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 features 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 inductive inference ceases to be legitimate, as well as the auxiliary techniques used by the researcher 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 study of facts, providing material with which the researcher can make a hypothetical assumption that should explain the facts.

The same tool is used by any comparison and analogy that points to common features in phenomena, but the commonality of phenomena forces us to assume that we are also dealing with general causes; Thus, the coexistence of phenomena, which the analogy points to, does not in itself yet contain an explanation of the phenomenon, but provides an indication of where the explanation should be sought. The main relationship of phenomena that I. has in mind is the relationship of causality, which, like the inductive inference itself, rests on identity, for the sum of conditions called the cause, if given in its entirety, is nothing more than the effect caused by the cause . The validity of the inductive conclusion is not in doubt; however, logic must strictly establish the conditions under which an inductive conclusion can be considered correct; the absence of negative instances does not yet prove the correctness of the conclusion. It is necessary that the inductive conclusion be based on the largest possible number of cases, that these cases be as diverse as possible, that they serve as typical representatives of the entire group of phenomena that the conclusion concerns, etc.

With all this, inductive conclusions easily lead to errors, the most common of which stem from the multiplicity of causes and from confusing the temporal order with the causal. In inductive research we are always dealing with effects for which causes must be found; their discovery is called an explanation of the phenomenon, but a known consequence can be caused by a number of different reasons; The talent of an inductive researcher lies in the fact that he gradually selects from a variety of logical possibilities only the one that is actually possible. To human limited knowledge, of course, different causes can produce the same phenomenon; but complete adequate knowledge in this phenomenon is able to discern signs indicating its origin from only one possible cause. Temporary alternation of phenomena always serves as an indication of a possible causal connection, but not every alternation of phenomena, even if correctly repeated, must necessarily be understood as a causal connection. Quite often we conclude post hoc - ergo propter hoc, this is how all superstitions arose, but here is also the correct indication for an inductive conclusion.

4. Deduction

Deduction (from Latin deductio - deduction) - deducing the particular from the general; the path 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 are the corresponding private judgment; is used only in the natural sciences, especially in mathematics: for example, from Hilbert’s axiom (“two points A and B distinct from each other always determine a straight line a”), we can deductively 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 take shape 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 apparently first used by Boethius, the concept of Deduction - as proof of a proposition through 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 knowledge. Thus, R. Descartes contrasted Deduction with intuition, through which, in his opinion, the human mind “directly perceives” the truth, while Deduction provides the mind with only “indirect” knowledge. F. Bacon, and later other English “inductivist” logicians, rightly noting that the conclusion obtained through Deduction does not contain any “information” that would not be contained in the premises, considered on this basis Deduction a “minor” method, in while true knowledge, in their opinion, is provided only by induction. Finally, representatives of the direction coming primarily from German philosophy, also, essentially proceeding from the fact that Deduction does not provide “new” facts, it was on this basis that they came to the exact opposite conclusion: the 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 observational and experience data, which are true, so to speak, "only due to a combination of circumstances"].

From a 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 related to each other in the same necessary way as synthesis and analysis. Instead of unilaterally extolling one of them to the skies at the expense of the other, we must try to apply each of them in its place, and this can only be achieved if one does not lose sight of their connection with each other, their mutual complementarity." However, regardless of the dialectical relationship between deduction and induction and their applications noted here, the study of the principles of deduction is of enormous independent importance. 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, work is increasingly being carried out 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% reliability, then at least a sufficiently large “degree of likelihood” or “probability”.

As for formal logic in the narrower sense of the term, both the system of logical rules in itself and any of their applications in any field fully apply to the proposition that everything contained in any system of logical rules obtained through deductive inference "analytic truth" is already contained in the premises from which it is derived: each application of a rule consists in the fact that the general proposition applies to some specific situation. Some rules of logical inference fall under this characterization quite explicitly; for example, various modifications of the so-called substitution rule state that the property of provability is preserved whenever elements of an arbitrary formula of a given formal theory are replaced by “concrete” expressions of the “same kind”. The same applies to the common way of specifying axiomatic systems using so-called axiom schemes, i.e. expressions that turn into “concrete” axioms after substituting the “generic” designations included in them for the specific formulas of a given theory.

But no matter what specific form this rule has, any application of it always has the character of a deduction. “Immutability,” obligatoryness, “formality” of the rules of logic, which does not know any exceptions, is fraught with the richest possibilities for automating the process of logical inference itself using a computer.

Deduction is often understood as the process of logical consequence itself. This determines the close connection of the concept of deduction with the concepts of inference and consequence, which is also reflected in logical terminology; Thus, the “deduction theorem” is usually called one of the important relationships between the logical connective of implication and the relation of logical implication: if a consequence B is derived from premise A, then the 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 is that all expressions of a given system that have this property are provable in it.

The properties of deduction are essentially properties of the relation of deducibility. Therefore, they were revealed primarily in the course of constructing specific logical formal systems and general theory 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 formal logical calculus G.V. Leibniz; creators of the first algebrological systems J. Boole, W. Jevons, P.S. Poretsky, C. Pierce; the creators of the first logical-mathematical axiomatic systems J. Peano, G. Frege, B. Russell; finally, the school of modern researchers coming from Hilbert’s deduction, including the creators of the theory of Deduction in the form of the so-called calculus of natural deduction of the German logician G. Gentzen, the Polish logician S. Jaskovsky and the Dutch logician E. Beta. 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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5. http://problema-talanta.ru/page/logika_cheloveka_indukciya_dedukciya - article from the Internet.

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Inductive method of cognition. Deduction as a method of science and its functions

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