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Methods of scientific knowledge

The concept of method and methodology. Classification of methods of scientific knowledge.

The concept method (from the Greek word “method” – the path to something) means a set of techniques and operations of practical and theoretical learning of reality.

The method equips a person with a system of principles, requirements, rules, guided by which he can achieve the intended goal. Mastering a method means for a person knowing how to perform certain actions in order to solve various tasks, and the ability to apply this knowledge in practice.

“Thus, the method (in one form or another) is reduced to a set of specific rules, techniques, methods, norms of cognition and action. It is a system of prescriptions, principles, requirements that orient the subject in solving a specific task, achieving a certain result in a given field of activity. He disciplines the search for truth, allows (if correct) to save time and effort, to move to the goal the shortest way. The main function of the method is the regulation of cognitive and other forms of activity. ”

The doctrine of the method began to develop in the science of modern times. Its representatives considered the correct method a guide in moving to reliable, true knowledge. So, a prominent philosopher of the XVII century. F. Bacon compared the method of knowledge with a lantern illuminating the way for a traveler walking in the dark. And another famous scientist and philosopher of the same period, R. Descartes, set forth his understanding of the method as follows: “By method,” he wrote, “I mean precise and simple rules, strict observance of which … without wasting mental forces, but gradually and continuously increasing knowledge, contributes to the fact that the mind achieves true knowledge of all that is available to him. ”

There is a whole field of knowledge, which is specifically engaged in the study of methods and which is commonly called methodology. The methodology literally means “the doctrine of methods” (for this term derives from two Greek words: “method” – method and “logos” – teaching). Studying the laws of human cognitive activity, the methodology develops on this basis methods for its implementation. The most important task of the methodology is to study the origin, essence, efficiency and other characteristics of the methods of knowledge.

Methods of scientific knowledge can be subdivided according to the degree of their generality, i.e., the breadth of applicability in the process of scientific research.

There are two known general methods in the history of knowledge: diadetic and metaphysical. These are general philosophical methods. From the middle of the 19th century, the metaphysical method began to be more and more displaced from the natural sciences by the dialectical method.

The second group of methods of knowledge consists of general scientific methods that are used in various fields of science, that is, they have a very wide, interdisciplinary spectrum of application.

The classification of general scientific methods is closely related to the concept of levels of scientific knowledge.

There are two levels of scientific knowledge: empirical and theoretical .. “This distinction is based on differences in, firstly, the methods (methods) of the most cognitive activity, and secondly, the nature of the achieved scientific results.” Some general scientific methods are applied only at the empirical level (observation, experiment, measurement), others only at the theoretical (idealization, formalization), and some (for example, modeling) both at the empirical and theoretical levels.

The empirical level of scientific knowledge is characterized by direct research of actually existing, sensually perceived objects. The special role of empiricism in science lies in the fact that only at this level of research we are dealing with the direct interaction of man with the studied natural or social objects. Here, living contemplation (sensory cognition) prevails, the rational moment and its forms (judgments, concepts, etc.) are present here, but they have a subordinate meaning. Therefore, the object under study is reflected mainly from its external relations and manifestations that are accessible to living contemplation and expressing internal relations. At this level, the process of accumulating information about the objects under study, phenomena by observing, performing various measurements, and supplying experiments is carried out. Here is also the primary systematization of the actual data obtained in the form of tables, charts, graphs, etc. In addition, already at the second level of scientific knowledge – as a result of summarizing scientific facts – it is possible to formulate some empirical patterns.

The theoretical level of scientific knowledge is characterized by the predominance of the rational moment – concepts, theories, laws and other forms and “mental operations”. The lack of direct practical interaction with objects determines the peculiarity that an object at a given level of scientific knowledge can be studied only indirectly, in a mental experiment, but not in a real one. However, living contemplation is not eliminated here, but becomes a subordinate (but very important) aspect of the cognitive process.

At this level, the disclosure of the most profound essential aspects, relationships, patterns inherent in the studied objects, phenomena by processing the data of empirical knowledge takes place. This processing is carried out using systems of “higher order” abstractions — such as concepts, conclusions, laws, categories, principles, etc. However, “at the theoretical level, we will not find a fixation or an abbreviated summary of empirical data; theoretical thinking cannot be reduced to the summation of empirically given material. It turns out that the theory does not grow out of empiricism, but, as it were, next to it, or rather, above it and in connection with it. ”

The theoretical level is a higher level in scientific knowledge. “The theoretical level of knowledge is aimed at the formation of theoretical laws that meet the requirements of universality and necessity, i.e. act everywhere and always. ” The results of theoretical knowledge become hypotheses, theories, laws.

Separating in a scientific study these two different levels, one should not, however, separate them from each other and oppose them. After all, the empirical and theoretical levels of knowledge are interrelated. The empirical level acts as a basis, a theoretical foundation. Hypotheses and theories are formed in the process of theoretical understanding of scientific facts, statistical data obtained at the empirical level. Moreover, theoretical thinking inevitably relies on sensually-visual images (including diagrams, graphs, etc.) with which the empirical level of research deals.

In turn, the empirical level of scientific knowledge can not exist without the achievement of the theoretical level. Empirical research usually relies on a certain theoretical structure that determines the direction of this research, determines and justifies the methods used in this process.

According to K. Popper, it is absurd belief that we can begin a scientific study with “pure observations”, not having “something similar to theory”. Therefore, some conceptual point of view is absolutely necessary. Naive attempts to do without it, in his opinion, can only lead to self-deception and uncritical use of some unconscious point of view.

The empirical and theoretical levels of knowledge are interrelated, the boundary between them is conditional and mobile. Empirical research, identifying new observations with the help of observations and experiments, stimulates theoretical knowledge (which summarizes and explains them) and sets new, more complex tasks for it. On the other hand, theoretical knowledge, developing and concretizing new own content on the basis of empiricism, opens new, broader horizons for empirical knowledge, orients and directs it in search of new facts, contributes to the improvement of its methods and means, etc.

The third group of methods of scientific knowledge includes the methods used only in the framework of research of a particular science or a particular phenomenon. Such methods are called tea-science. Each private science (biology, chemistry, geology, etc.) has its own specific research methods.

At the same time, particular scientific methods, as a rule, contain various general scientific methods of cognition in various combinations. Private science methods may include observations, measurements, inductive or deductive reasoning, etc. The nature of their combination and use depends on the research conditions, the nature of the objects being studied. Thus, private scientific methods are not divorced from general scientific methods. They are closely related to them, include the specific use of general scientific cognitive techniques to study a specific area of ​​the objective world. At the same time, the particular scientific methods are connected with the universal, dialectical method, which is, as it were, refracted through them.

Another group of methods of scientific knowledge are the so-called disciplinary methods, which are systems of techniques used in a particular discipline, which is part of any branch of science or originated at the intersection of sciences. Each fundamental science is a complex of disciplines that have their own specific subject and their own specific research methods.

The latter, the fifth group includes interdisciplinary research methods which are a combination of a number of synthetic, integrative methods (arising as a result of combining elements of different levels of methodology), aimed mainly at joints of scientific disciplines.

Thus, in scientific knowledge, there is a complex, dynamic, integral, subordinated system of diverse methods of different levels, spheres of action, orientation, etc., which are always implemented subject to specific conditions.

It remains to add to this that any method in itself does not predetermine success in the knowledge of one or another aspect of material reality. It is also important to be able to correctly apply the scientific method in the process of knowledge. If we use the figurative comparison of academician P. L. Kapitsa, the scientific method “seems to be the Stradivarius violin, the most perfect of the violins, but in order to play it, you need to be a musician and know music. Without this, it will also be fake, like a normal violin. ”

The universal (dialectical) method of knowledge, the principles of the dialectical method and their application in scientific knowledge.

Dialectics (Greek dialektika – I am talking, arguing) – the doctrine of the most common laws of development of nature, society and knowledge, in which various phenomena are considered in the diversity of their connections, the interaction of opposing forces, trends, in the process of change, development. In its internal structure, the dialectic as a method consists of a number of principles, the purpose of which is to lead knowledge to the unfolding of developmental contradictions. The essence of the dialectic is precisely in the presence of the contradictions of development, in the movement towards these contradictions. Let us consider in brief the basic dialectical principles.

The principle of comprehensive consideration of the objects studied. An integrated approach in knowledge.

One of the important requirements of the dialectical method is to study the object of knowledge from all sides, to strive to identify and study as many as possible (from an infinite set) of its properties, relationships, and relations. Modern research in many fields of science increasingly requires taking into account an increasing number of factual data, parameters, connections, etc. This task is becoming more and more difficult to solve without using the informational power of the latest computer technology.

The world around us is a single whole, a certain system, where each object as a unity of the diverse is inextricably linked with other objects and they all constantly interact with each other. One of the basic principles of materialist dialectics — comprehensiveness of consideration — emerges from the statement about the universal connection and interdependence of all phenomena. The correct understanding of any thing is possible only if the entire set of its internal and external sides, relations, relations to etc. is investigated. To really know a subject deeply and comprehensively, one must embrace, study all its sides, all connections and “ mediation ”in their system, with the isolation of the main, decisive side.

The principle of comprehensiveness in modern scientific research is implemented in the form of an integrated approach to objects of knowledge. The latter allows us to take into account the multiplicity of properties, parties, relationships, etc. of the objects and phenomena under study. This approach underlies the integrated, interdisciplinary research, which allows to “combine into one” multilateral research, to combine the results obtained by different methods. It is this approach that led to the idea of ​​creating research teams consisting of specialists in various fields and fulfilling the requirement of comprehensiveness in solving certain problems.

“Modern integrated scientific and technical disciplines and research are the reality of modern science. However, they do not fit into the traditional organizational forms and methodological standards. It is in the sphere of these studies and disciplines that the practical “internal” interaction of the social, natural and technical sciences is being carried out … Such studies (which, for example, include research in the field of artificial intelligence) require special organizational support and the search for new organizational forms of science. However, unfortunately, their development is hampered precisely because of their non-traditional, lack of a clear idea of ​​their place in the system in the mass (and sometimes professional) consciousness science and technology. ”

Nowadays, complexity (as one of the important aspects of the dialectical methodology) is an integral element of modern global thinking. Based on it, the search for solutions to global problems of our time requires a scientifically based (and politically weighted) integrated approach.

The principle of consideration in the relationship. Systemic cognition.

The problem of taking into account the connections of the investigated thing with other things occupies an important place in the dialectical method of knowledge, distinguishing it from the metaphysical. The metaphysical thinking of many natural scientists, who ignored in their research the real relationships that exist between the objects of the material world, created many difficulties in scientific knowledge at one time. To overcome these difficulties began in the XIX century. the transition from metaphysics to dialectics, “… considering things not in their isolation, but in their interconnection”.

The progress of scientific knowledge already in the 19th century, and even more so in the 20th century, showed that any scientist, in whatever field of knowledge he worked, will inevitably fail in research if he considers the object being studied out of touch with other objects, phenomena or will ignore the nature of the relationship of its elements. In the latter case, it will be impossible to understand and study the material object in its integrity as a system.

A system is always a certain integrity, which is a collection of elements, the functional properties and possible states of which are caused not only by the composition, structure, etc. of its constituent elements, but also by the nature of their interrelationships.

To study an object as a system, a special, systematic approach to its cognition is also required. The latter must take into account the qualitative originality of the system in relation to its elements (that is, that it – as integrity – has properties that the elements that make it up).

It should be borne in mind that “… although the properties of the system as a whole cannot be reduced to the properties of the elements, they can be explained in their origin, in their internal mechanism, in the ways of their functioning based on the properties of the elements of the system and character their interconnections and interdependencies. This is the methodological essence of the system approach.

Otherwise, if there were no connection between the properties of the elements and the nature of their interconnection, on the one hand, and the properties of the whole, on the other hand, there would be no scientific sense in considering the system as a system, that is, as a set of elements with certain properties. Then we would have to consider the system simply as a thing with properties irrespective of the properties of the elements and the structure of the system. ”

“The principle of consistency requires the distinction between the external and internal sides of the material systems, the essence and its manifestations, the discovery of the diverse aspects of the subject, their unity, the disclosure of the form and content, the elements and structure, the random and the necessary, etc. This principle directs thinking to the transition from phenomena to their essence, to the knowledge of the integrity of the system, as well as the necessary connections of the subject under consideration with the processes surrounding it.

The principle of consistency requires the subject to put in the center of knowledge the idea of ​​integrity, which is designed to guide knowledge from the beginning to the end of the study, no matter how it disintegrates into separate possible, at first glance, not related to each other, cycles or moments; the whole way of knowing the idea of ​​integrity will change, enrich, but it must always be a systematic, holistic view of the object. ”

The principle of consistency is aimed at a comprehensive knowledge of the subject, as it exists at one time or another; it aims to reproduce its essence, integrative basis, as well as the diversity of its aspects, manifestations of the essence when it interacts with other material systems. Here it is assumed that this item is separated from its past, from its previous states; This is done for a more directional knowledge of its current state. Distraction from history in this case is a legitimate method of knowledge.

The spread of the systems approach in science was associated with the increasing complexity of research objects and the transition from metaphysical-mechanistic to dialectical methodology. Symptoms of the exhaustion of the cognitive potential of metaphysical-mechanistic methodology, focused on reducing the complex to individual connections and elements, appeared as early as the 19th century, and at the turn of the 19th and 20th centuries. the crisis of such a methodology has already been revealed quite clearly, when common human reason has increasingly begun to come into contact with objects interacting with other material systems, with consequences that can no longer be (without allowing an obvious error) to tear away from the causes that gave rise to them.

The principle of determinism.

Determinism – (from the Latin. Determino – I define) – is a philosophical doctrine about the objective regular relationship and interdependence of the phenomena of the material and spiritual world. The basis of this doctrine is a statement about the existence of causality, that is, such a connection of phenomena in which one phenomenon (cause) under certain conditions necessarily generates another phenomenon (effect). Even in the writings of Galileo, Bacon, Hobbes, Descartes, Spinoza, it was justified that when studying nature one must look for valid causes and that “true knowledge is knowledge by means of causes” (F. Bacon).

Already at the level of phenomena, determinism makes it possible to distinguish the necessary connections from random ones, essential ones from non-essential ones, to establish certain repeatability, correlative dependencies, etc., that is, to carry out the promotion of thinking to the essence, to the causal connections within the essence. Functional objective dependencies, for example, are connections of two or more consequences of the same cause, and the knowledge of regularities at the phenomenological level must be complemented by the knowledge of genetic, causative connections. The cognitive process, going from effects to causes, from accidental to necessary and essential, is aimed at disclosing the law. The law, however, determines phenomena, and therefore knowledge of the law explains phenomena and changes, the movements of the object itself.

Modern determinism presupposes the existence of various objectively existing forms of the interrelation of phenomena. But all these forms ultimately add up on the basis of universal causality, outside of which not a single phenomenon of reality exists.

The principle of study in development. Historical and logical approach in knowledge.

The principle of studying objects in their development is one of the most important principles of the dialectical method of knowledge. This is one of the fundamental differences. dialectical method from the metaphysical. We will not receive true knowledge if we study a thing in a dead, frozen state, if we ignore such an important aspect of its being as development. Only by studying the past of the object of interest to us, the history of its emergence and formation, can we understand its current state and predict its future.

The principle of studying an object in development can be realized in cognition by two approaches: the historical and the logical (or, more precisely, the logical-historical).

In the historical approach, the history of the object is reproduced exactly, in all its versatility, taking into account all the details, events, including all sorts of random deviations, zigzags in development. This approach is used in a detailed, thorough study of human history, in observations, for example, the development of some plants, living organisms (with the corresponding descriptions of these observations in full detail), etc.

The logical approach also reproduces the history of the object, but at the same time it undergoes certain logical transformations: it is processed by theoretical thinking with the release of the general, the essential, and is freed at the same time from everything that is accidental, insignificant, superficial, which hinders the identification of the development pattern of the object being studied.

Such an approach in the natural sciences of the XIX century. It was successfully (albeit spontaneously) implemented by C. Darwin. For the first time, he had a logical process of cognition of the organic world based on the historical process of development of this world, which made it possible to solve scientifically the question of the origin and evolution of plant and animal species.

The choice of a historical or logical approach in cognition is determined by the nature of the object being studied, the objectives of the study and other circumstances. At the same time, in the real process of cognition, both of these approaches are closely interrelated. The historical approach is not complete without some logical understanding of the facts of the history of the object being studied. The logical analysis of the development of an object does not contradict its true history, it proceeds from it.

F. Engels emphasized this interrelation of historical and logical approaches in cognition. “… The logical method,” he wrote, “… is essentially nothing more than the same historical method, only freed from historical form and from interfering accidents. Where the story begins, the same should begin the train of thought, and its further movement will be nothing more than a reflection of the historical process in an abstract and theoretically consistent form; the reflection is amended, but corrected in accordance with the laws, which the actual historical process itself gives … ”

The logical-historical approach, based on the power of theoretical thinking, allows the researcher to achieve a logically reconstructed, generalized reflection of the historical development of the object under study. And this leads to important scientific results.

In addition to the above principles, the dialectical method includes other principles – objectivity, concreteness, “the split of the single” (the principle of contradiction), etc. These principles are formulated on the basis of the relevant laws and categories, which together reflect the unity and integrity of the objective world in its uninterrupted development.

General scientific methods of empirical knowledge.

Scientific observation and description.

Observation is a sensual (mostly visual) reflection of objects and phenomena of the external world. “Observation is a purposeful study of objects, relying mainly on such sensory abilities of a person as sensation, perception, representation; in the course of observation, we gain knowledge of the external aspects, properties, and characteristics of the object in question ”. This is the initial method of empirical knowledge, which allows to obtain some primary information about the objects of the surrounding reality.

Scientific observation (as opposed to routine, everyday observations) is characterized by a number of features:

– focus (observation must be carried out to solve the research problem, and the observer’s attention should be fixed only on the phenomena associated with this task);

– regularity (observation must be carried out strictly according to the plan, drawn up on the basis of the research task);

– activity (the researcher must actively search for, highlight the points he needs in the observed phenomenon, drawing on his knowledge and experience, using various technical means of observation).

Scientific observations are always accompanied by a description of the object of knowledge. An empirical description is the fixation, by means of a natural or artificial language, of information about objects given in observation. With the help of the description, sensual information is translated into the language of concepts, signs, diagrams, drawings, graphs and figures, thus taking the form convenient for further rational processing. The latter is necessary for fixing those properties, the sides of the object being studied, which constitute the subject of study. Descriptions of the results of observations form the empirical basis of science, based on which researchers create empirical generalizations, compare the objects under study according to certain parameters, classify them according to some properties, characteristics, find out the sequence of the stages of their formation and development.

Almost every science goes through the specified initial, “descriptive” stage of development. At the same time, as emphasized in one of the papers dealing with this issue, “the main requirements that are imposed on a scientific description are aimed at making it as complete, accurate and objective as possible. The description should give a reliable and adequate picture of the object itself, accurately reflect the phenomena under study. It is important that the concepts used for the description always have a clear and unambiguous meaning. With the development of science, changes in its fundamentals, means of description are transformed, and a new system of concepts is often created. ”

When observing there is no activity aimed at the transformation, change of objects of knowledge. This is due to a number of circumstances: the inaccessibility of these objects for practical impact (for example, observation of remote space objects), undesirability, based on research objectives, interference with the observed process (phenological, psychological, etc.), lack of technical, energy, financial and other capabilities. experimental studies of objects of knowledge.

According to the method of observation can be direct and indirect.

With mediocre observations, certain properties of the object are reflected, perceived by the human senses. This kind of observation has given much useful in the history of science. It is known, for example, that the observations of the position of planets and stars in the sky, carried out for more than twenty years by Tycho Brahe with unparalleled accuracy for the naked eye, were the empirical basis for Kepler’s discovery of his famous laws.

Although direct observation continues to play an important role in modern science, more often than not scientific observation is indirect, that is, it is carried out using certain technical means. The emergence and development of such means has largely determined the enormous expansion of the capabilities of the method of observation that has occurred over the past four centuries.

If, for example, before the beginning of the XVII century. astronomers observed the celestial bodies with the naked eye, then the invention of the optical telescope by Galileo in 1608 raised astronomical observations to a new, much higher level. Nowadays, the creation of X-ray telescopes and their output into outer space aboard the orbital station (X-ray telescopes can work only outside the earth’s atmosphere) made it possible to observe such objects of the Universe (pulsars, quasars) that could not be studied in any other way.

The development of modern science is associated with the increasing role of the so-called indirect observations. Thus, objects and phenomena studied by nuclear physics cannot be directly observed either with the help of the human sense organs, nor with the help of the most advanced instruments. For example, when studying the properties of charged particles with the help of the Wilson camera, these particles are perceived by the researcher indirectly – according to their visible manifestations, such as the formation of tracks consisting of many droplets of liquid.

At the same time, any scientific observations, although they rely primarily on the work of the sense organs, require at the same time participation and theoretical thinking. The researcher, relying on his knowledge and experience, should be aware of sensory perceptions and express them (describe) either in terms of ordinary language, or – more strictly and abbreviatedly – in certain scientific terms, in some graphs, tables, figures, etc. For example, emphasizing the role of theory in the process of indirect observations, A. Einstein, speaking to V. Heisenberg, noted: “Whether this phenomenon can be observed or not depends on your theory. It is the theory that must establish what can be observed and what cannot. ”

Observations can often play an important heuristic role in scientific knowledge. In the process of observation, completely new phenomena can be discovered that allow one or another scientific hypothesis to be substantiated.

From the foregoing it follows that observation is a very important method of empirical knowledge, providing for the collection of extensive information about the world around it. As the history of science shows, with the correct use of this method, it turns out to be very fruitful.


Experiment is a more complex method of empirical knowledge than observation. It involves the active, purposeful and strictly controlled influence of the researcher on the object being studied in order to identify and study various aspects, properties, connections. In this case, the experimenter can transform the object under study, create artificial conditions for its study, interfere with the natural course of the processes.

“Experiment holds a special place in the general structure of scientific research. On the one hand, it is the experiment that is the link between the theoretical and empirical stages and levels of scientific research. According to its design, an experiment is always mediated by preliminary theoretical knowledge: it is conceived on the basis of relevant theoretical knowledge, and its goal is often to confirm or refute a scientific theory or hypothesis. The results of the experiment themselves need a certain theoretical interpretation. At the same time, the method of experiment according to the nature of the cognitive means used belongs to the empirical stage of cognition. The result of experimental research is, first of all, the achievement of factual knowledge and the establishment of empirical patterns. ”

Experimentally oriented scientists argue that a cleverly thought out and “cunning” expertly staged experiment is above theory: theory can be completely refuted, and reliably gained experience is not!

The experiment includes other methods of empirical research (observation, measurement). At the same time, it has a number of important, unique features.

First, the experiment allows us to study the object in a “purified” form, i.e., to eliminate all kinds of side factors, stratifications that impede the process of research.

Secondly, in the course of the experiment, an object can be placed in some artificial, in particular, extreme conditions, that is, it can be studied at ultralow temperatures, at extremely high pressures or, conversely, in vacuum, at enormous electromagnetic field strengths, etc. In such artificially created conditions, it is possible to detect surprising at times unexpected properties of objects and, thus, to comprehend their essence more deeply.

Third, by studying a process, the experimenter can intervene in it, actively influence its course. As academician I.P.Pavlov noted, “experience seems to take phenomena into its own hands and sets in motion one or the other, and thus, in artificial, simplified combinations, determines the true connection between phenomena. In other words, observation collects what nature offers it, while experience takes from nature what it wants. ”

Fourth, an important advantage of many experiments is their reproducibility. This means that the experimental conditions, and accordingly the observations made at the same time, can be repeated as many times as necessary to obtain reliable results.

Preparation and conduct of the experiment require compliance with a number of conditions.

So, the scientific experiment:

  • it is never put at random, it assumes the existence of a clearly defined research goal;
  • it is not done “blindly”, it is always based on some initial theoretical positions. Without an idea in his head, said I.P.Pavlov, one cannot see the fact at all;
  • not carried out unplanned, randomly, the researcher preliminarily outlines the ways of its implementation
  • requires a certain level of development of technical means of knowledge necessary for its implementation;
  • should be conducted by people with sufficiently high qualifications.

Only the totality of all these conditions determines the success in experimental research.

Depending on the nature of the problems solved during the experiments, the latter are usually divided into research and verification.

Research experiments make it possible to discover new, unknown properties of an object. The result of such an experiment can be conclusions that do not follow from the available knowledge about the object of study. An example is the experiments put in the laboratory of E. Rutherford, which led to the discovery of the atomic nucleus, and thus to the birth of nuclear physics.

Verification experiments are used to verify, confirm those or other theoretical constructs. Thus, the existence of a number of elementary particles (positron, neutrinos, etc.) was initially predicted theoretically, and only later they were discovered experimentally.

Based on the methodology and results obtained, the experiments can be divided into qualitative and quantitative. Qualitative experiments are exploratory in nature and do not lead to any quantitative relationships. They only allow to identify the effect of certain factors on the phenomenon under study. Quantitative experiments are aimed at establishing accurate quantitative dependencies in the phenomenon under study. In actual practice, experimental studies of both of these types of experiments are implemented, as a rule, in the form of successive stages in the development of knowledge.

As is known, the connection between electrical and magnetic phenomena was first discovered by the Danish physicist Oersted as a result of a purely qualitative experiment (by placing a magnetic compass needle next to a conductor through which electric current was passed, he found that the arrow was deviating from the initial position). After Oersted published his discovery, quantitative experiments of the French scientists Biot and Savard followed, as well as Ampere’s experiments, on the basis of which the corresponding mathematical formula was derived.

All these qualitative and quantitative empirical studies laid the foundation for the study of electromagnetism.

Depending on the field of scientific knowledge, in which the experimental research method is used, there are natural science, applied (in technical sciences, agricultural science, etc.) and socio-economic experiments.

Measurement and comparison.

Most scientific experiments and observations involve a variety of measurements. Measurement is the process of determining the quantitative values ​​of certain properties, the sides of the object being studied, a phenomenon with the help of special technical devices.

The great importance of measurement for science was noted by many prominent scientists. For example, D. I. Mendeleev emphasized that “science begins with the beginning of measurement.” A well-known English physicist V. Thomson (Kelvin) pointed out that “every thing is known only to the extent that it can be measured”.

The measurement operation is based on the comparison of objects for some similar properties or sides. To make such a comparison, it is necessary to have certain units of measurement, the presence of which makes it possible to express the studied properties from the side of their quantitative characteristics. In turn, this allows the wide use of mathematical tools in science and creates prerequisites for the mathematical expression of empirical dependencies. The comparison is used not only in connection with the measurement. In science, comparison acts as a comparative or comparative historical method. Originally established in philology, literary criticism, it was then successfully applied in jurisprudence, sociology, history, biology, psychology, history of religion, ethnography, and other areas of knowledge. Whole branches of knowledge using this method appeared: comparative anatomy, comparative physiology, comparative psychology, etc. Thus, in comparative psychology, the study of the psyche is based on a comparison of the psyche of an adult with the development of the psyche in a child, as well as animals. In the course of scientific comparison, not arbitrarily chosen properties and relations are compared, but significant ones.

An important aspect of the measurement process is the method of its conduct. It is a set of techniques that use certain principles and measurement tools. The principles of measurement in this case refer to some phenomena that form the basis of measurements (for example, temperature measurement using the thermoelectric effect).

There are several types of measurements. Based on the nature of the dependence of the measured value on time, the measurements are divided into static and dynamic. In static measurements, the value that we measure remains constant in time (measurement of the size of bodies, constant pressure, etc.). Dynamic includes such measurements, during which the measured value changes over time (measurement of vibration, pulsating pressures, etc.).

According to the method of obtaining results, direct and indirect measurements are distinguished. In direct measurements, the desired value of the measured value is obtained by directly comparing it with a standard or issued by a measuring instrument. In indirect measurement, the quantity sought is determined on the basis of a known mathematical relationship between this quantity and other quantities obtained by direct measurements (for example, finding the specific electrical resistance of a conductor by its resistance, length and cross-sectional area). Indirect measurements are widely used in cases where the desired value is impossible or too difficult to measure directly or when direct measurement gives a less accurate result.

With the progress of science, the measuring technique is moving forward. Along with the improvement of the existing measuring instruments, working on the basis of traditional established principles (replacement of the materials from which the device parts were made, the introduction of individual changes in the design, etc.), there is a transition to fundamentally new, measuring device designs caused by new theoretical prerequisites. In the latter case, devices are created in which new scientific ones are implemented. progress. For example, the development of quantum physics significantly increased the possibilities of measurements with a high degree of accuracy. Using the Mössbauer effect allows you to create a device with a resolution of about 10 -13% of the measured value.

Well-developed instrumentation, a variety of methods and high characteristics of measuring instruments contribute to the progress in scientific research. In turn, the solution of scientific problems, as noted above, often opens up new ways to improve the measurements themselves.

General scientific methods of theoretical knowledge.

Abstraction The ascent from the abstract to the concrete.

The process of cognition always begins with the consideration of specific, sensually perceived objects and phenomena, their external features, properties, relationships. Only as a result of the study of the sensually-concrete, does a person arrive at some generalized notions, concepts, or other theoretical propositions, that is, scientific abstractions. Obtaining these abstractions is associated with a complex abstracting activity of thinking.

In the process of abstraction, there is a departure (ascent) from sensually perceived concrete objects (with all their properties, sides, etc.) to the abstract ideas about them that are reproduced in thought. At the same time, a sensually concrete perception is, as it were, “… evaporates to a degree of abstract definition.” Abstraction, thus, consists in mental abstraction from some – less significant – properties, sides, signs of the object being studied with simultaneous release, formation of one or several essential sides, properties, signs of this object. The result obtained in the process of abstraction, called abstraction (or use the term “abstract” – as opposed to concrete).

In scientific knowledge, for example, identification abstractions and isolating abstractions are widely used. Identification abstraction is a concept that results from the identification of a certain set of objects (at the same time they are diverted from a number of individual properties, characteristics of these objects) and their uniting into a special group. An example is the grouping of the whole variety of plants and animals living on our planet into special species, genera, orders, etc. Isolating abstractions are obtained by highlighting certain properties, relationships that are inseparably connected with objects of the material world, into independent entities (“stability “,” Solubility “,” electrical conductivity “, etc.).

The transition from the sensible-concrete to the abstract is always associated with a certain simplification of reality. At the same time, ascending from the sensually concrete to the abstract, theoretical, the researcher gets an opportunity to understand the object under study more deeply, to reveal its essence. At the same time, the researcher first finds the main connection (relation) of the object being studied, and then, step by step, tracing how it changes in different conditions, opens new connections, establishes their interactions and in this way reflects in its entirety the essence of the object being studied.

The process of transition from sensual-empirical, visual representations about the phenomena under study to the formation of certain abstract, theoretical constructions reflecting the essence of these phenomena is the basis of the development of any science.

Since the concrete (i.e., real objects, processes of the material world) is a combination of a set of properties, sides, internal and external relations and relations, it cannot be known in all its diversity, remaining at the stage of sensory cognition, being limited to them. Therefore, there is a need for a theoretical understanding of the concrete, that is, the ascent from the sensually concrete to the abstract.

But the formation of scientific abstractions, general theoretical principles is not the ultimate goal of knowledge, but is only a means of a deeper, more diverse knowledge of the concrete. Therefore, the further movement (ascent) of knowledge from the achieved abstract again to the concrete is necessary. The knowledge of the concrete obtained at this stage of the research will be qualitatively different compared to that which was at the stage of sensory cognition. In other words, the concrete at the beginning of the process of cognition (sensually-concrete, which is its initial moment) and the concrete that is comprehended at the end of the cognitive process (it is called logical-concrete, emphasizing the role of abstract thinking in its comprehension) are radically different from each other.

The logical-concrete is theoretically reproduced in the mind of the researcher concrete in all the richness of its content.

It contains in itself not only sense-perceptible, but also something hidden, inaccessible to sensory perception, something essential, regular, comprehended only with the help of theoretical thinking, with the help of certain abstractions.

Idealization. Thought experiment.

The mental activity of a researcher in the process of scientific knowledge includes a special kind of abstraction, which is called idealization. Idealization is the mental introduction of certain changes in the object under study in accordance with the objectives of research.

As a result of such changes, for example, some properties, parties, attributes of objects can be excluded from consideration. Thus, idealization widespread in mechanics, called the material point, implies a body devoid of any size. Such an abstract object, the dimensions of which are neglected, is convenient when describing the movement of a wide variety of material objects from atoms and molecules to the planets of the solar system.

Changes to the object, achieved in the process of idealization, can also be made by giving it some special properties, which are in reality impracticable. An example is the abstraction introduced by idealizing into physics, known as an absolutely black body (such a body is endowed with a property that does not exist in nature absorb absolutely all radiant energy falling on it, not reflecting anything and not passing through itself).

The expediency of using idealization is determined by the following circumstances:

First, “idealization is expedient when real objects to be investigated are rather complicated for the available means of theoretical, in particular mathematical, analysis, and in relation to an idealized case, by attaching these means, a theory can be constructed and developed under certain conditions and goals , to describe the properties and behavior of these real objects. The latter, in essence, certifies the fruitfulness of idealization, distinguishes it from barren fantasy. ”

Secondly, it is advisable to use idealization in those cases when it is necessary to exclude certain properties, the connections of the object under study, without which it cannot exist, but which obscure the essence of the processes occurring in it. A complex object appears as if in a “purified” form, which facilitates its study.

Thirdly, the use of idealization is advisable when the properties, parties, relations of the object being studied are excluded from consideration in the framework of this study on its essence. In this case, the correct choice of the admissibility of such an idealization plays a very large role.

It should be noted that the nature of idealization can be quite different if there are different theoretical approaches to the study of a phenomenon. As an example, we can point out three different notions of the “ideal gas”, which were formed under the influence of various theoretical-physical concepts: Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac. However, all three variants of idealization obtained in this case turned out to be fruitful in the study of gas states of various nature: the ideal Maxwell-Boltzmann gas became the basis for the study of ordinary molecular rarefied gases at rather high temperatures; The ideal Bose-Einstein gas was used to study the photon gas, and the ideal Fermi-Dirac gas helped solve a number of electron gas problems.

Being a kind of abstraction, idealization allows an element of sensual visibility (the usual process of abstraction leads to the formation of mental abstractions that do not have any visibility). This feature of idealization is very important for the implementation of such a specific method of theoretical knowledge, which is a mental experiment (it is also called mental, subjective, imaginary, idealized).

A mental experiment involves operating with an idealized object (replacing a real object in abstraction), which consists in the mental selection of certain provisions, situations that allow to detect some important features of the object under study. This shows a certain similarity of the mental (idealized) experiment with the real. Moreover, any real experiment, before being carried out in practice, is first “played” by the researcher mentally in the process of reflection and planning. In this case, the mental experiment acts as a preliminary ideal plan for a real experiment.

A mental experiment can be of great heuristic value, helping to interpret new knowledge obtained in a purely mathematical way. This is confirmed by many examples from the history of science.

The idealization method, which is very fruitful in many cases, has at the same time certain limitations. In addition, any idealization is limited to a specific area of ​​phenomena and serves to solve only certain problems. This can be clearly seen at least by the example of the above idealization “an absolutely black body”.

The main positive value of idealization as a method of scientific knowledge lies in the fact that the theoretical constructions obtained on its basis allow then to effectively explore real objects and phenomena. The simplifications achieved with the help of idealization facilitate the creation of a theory that reveals the laws of the studied area of ​​the phenomena of the material world. If the theory as a whole correctly describes real phenomena, then the idealisations put in its basis are legitimate.


Formalization is understood as a special approach to scientific knowledge, which consists in using special symbolism, which allows to distract from the study of real objects, from the content of theoretical positions describing them and operate instead with a certain set of symbols (signs).

This technique is to build abstract mathematical models that reveal the essence of the studied processes of reality. When formalizing, the arguments about objects are transferred to the plane of operation with signs (formulas). Relationships of signs replace statements about the properties and relationships of objects. In this way, a generalized symbolic model of a certain subject area is created, which makes it possible to detect the structure of various phenomena and processes when diverting from the qualitative characteristics of the latter. The derivation of some formulas from others according to strict rules of logic and mathematics represents a formal study of the basic characteristics of the structure of various, sometimes very distant in nature phenomena.

A vivid example of formalization is the mathematical descriptions of various objects and phenomena that are widely used in science and are based on relevant substantial theories. At the same time, the mathematical symbolism used not only helps to consolidate the already existing knowledge about the objects and phenomena under study, but also acts as a tool in the process of their further cognition.

To construct any formal system, it is necessary: ​​a) to assign an alphabet, that is, a specific set of characters; b) setting rules by which “words”, “formulas” can be obtained from the initial characters of this alphabet; c) setting rules by which from some words, formulas of this system, you can move on to other words and formulas (the so-called inference rules).

As a result, a formal sign system is created in the form of a specific artificial language. An important advantage of this system is the possibility of conducting an object in its framework in a purely formal way (operating with signs) without directly referring to this object.

Another advantage of formalization is to ensure the brevity and clarity of recording scientific information, which opens up great opportunities for operating it.

Axiomatic method.

In the axiomatic construction of theoretical knowledge, first a set of starting points is specified that do not require proof (at least within the framework of this knowledge system). These provisions are called axioms, or postulates. Then, from them, according to certain rules, a system of conclusion sentences is built. The set of initial axioms and sentences derived from them forms an axiomatically constructed theory.

Axioms are statements whose proof of truth is not required. The number of axioms varies widely: from two to three to several dozen. The logical conclusion allows to transfer the truth of axioms to the consequences derived from them. At the same time, axioms and conclusions from them are subject to the requirements of consistency, independence and completeness. Following certain well-defined rules of inference allows us to streamline the process of reasoning when deploying an axiomatic system, to make this reasoning more strict and correct.

To define an axiomatic system, some language is required. In this connection, symbols (icons) are widely used, rather than bulky verbal expressions. Replacing a spoken language with logical and mathematical symbols, as mentioned above, is called formalization. If formalization takes place, then the axiomatic system is formal, and the positions of the system acquire the character of formulas. The formulas obtained as a result of the derivation are called theorems, and the arguments used in this case are called proofs of theorems. Such is the almost well-known structure of the axiomatic method.

Method hypothesis.

In methodology, the term “hypothesis” is used in two senses: as a form of the existence of knowledge, characterized by problematic, unreliability, need for proof, and as a method of forming and substantiating explanatory sentences, leading to the establishment of laws, principles, theories. The hypothesis in the first sense of the word is included in the method of the hypothesis, but it can also be used outside of it.

The best idea of ​​the method of the hypothesis is an introduction to its structure. The first stage of the hypothesis method is familiarization with the empirical material that is subject to theoretical explanation. Initially, this material is tried to be explained with the help of laws and theories already existing in science. If there are none, the scientist proceeds to the second stage – the suggestion of assumptions or assumptions about the causes and patterns of these phenomena. At the same time, he tries to use various methods of research: inductive guidance, analogy, modeling, etc. It is quite possible that at this stage several explanatory assumptions are made that are incompatible with each other.

The third stage is the stage of assessing the severity of the assumption and selection from the set of most guesswork. The hypothesis is tested primarily for logical consistency, especially if it has a complex shape and turns into a system of assumptions. Further, the hypothesis is tested for compatibility with the fundamental inter-theoretical principles of this science.

At the fourth stage, the assumption is unfolded and a deductive derivation of empirically verifiable consequences from it takes place. At this stage, a partial reworking of the hypothesis is possible, an introduction to it using mental experiments of specifying details.

At the fifth stage, experimental verification of the consequences derived from the hypothesis is carried out. The hypothesis either receives empirical confirmation, or is refuted as a result of experimental verification. However, the empirical confirmation of the consequences of the hypothesis does not guarantee its truth, and the refutation of one of the consequences does not unambiguously indicate its falsity as a whole. All attempts to build an effective logic for confirming and refuting theoretical explanatory hypotheses have so far failed. The status of an explanatory law, principle, or theory is best obtained by testing the proposed hypotheses. From such a hypothesis, as a rule, maximum explanatory and predictive power is required.

Familiarity with the general structure of the hypothesis method allows you to define it as a complex, complex method of cognition, which includes all its diversity and forms and is aimed at establishing laws, principles and theories.

Sometimes the hypothesis method is also called the hypothetical-deductive method, bearing in mind the fact that the hypothesis is always accompanied by deductive derivation of empirically verifiable consequences from it. But deductive reasoning is not the only logical device used in the framework of the hypothesis method. When establishing the degree of empirical validity of the hypothesis, elements of inductive logic are used. Induction is also used at the stage of guessing. A significant place in the hypothesis is the conclusion by analogy. As already noted, at the stage of development of a theoretical hypothesis, a mental experiment can also be used.

The explanatory hypothesis as the assumption of the law is not the only kind of hypotheses in science. There are also “existential” hypotheses — assumptions about the existence of elementary particles unknown to science, units of heredity, chemical elements, new biological species, etc. The ways of proposing and substantiating such hypotheses differ from explanatory hypotheses. Along with the main theoretical hypotheses, there may be auxiliary ones that allow the main hypothesis to be brought into better agreement with experience. As a rule, such auxiliary hypotheses are later eliminated. There are also so-called working hypotheses, which make it possible to better organize the collection of empirical material, but do not pretend to explain it.

The most important kind of hypothesis method is the method of mathematical hypothesis, which is characteristic of sciences with a high degree of mathematization. The hypothesis method described above is a meaningful hypothesis method. Within its framework, meaningful assumptions about laws are first formulated, and then they receive the corresponding mathematical expression. In the method of the mathematical hypothesis, thinking follows a different path. First, to explain quantitative dependencies, a suitable equation is selected from adjacent fields of science, which often implies its modification, and then a meaningful interpretation is attempted to give this equation.

General scientific methods applied at the empirical and theoretical levels of knowledge.

Analysis and synthesis.

Under the analysis understand the division of the object (mentally or realistically) into its component parts for the purpose of their separate study. As such parts there may be some real elements of the object or its properties, signs, relations, etc.

Analysis – a necessary stage in the knowledge of the object. Since ancient times, the analysis has been used, for example, to decompose into components of certain substances. Note that the method of analysis played an important role in the breakdown of the phlogiston theory.

Undoubtedly, analysis occupies an important place in the study of objects of the material world. But it is only the first stage of the process of knowledge.

To comprehend an object as a whole, one cannot limit oneself to studying only its constituent parts. In the process of cognition, it is necessary to reveal the objectively existing connections between them, to consider them as a whole, in unity. To carry out this second stage in the process of cognition – it is possible to move from studying the individual constituent parts of an object to studying it as a single connected whole if the method of analysis is supplemented by another method – synthesis.

In the process of synthesis, a combination of the constituent parts (sides, properties, features, etc.) of the object under study, dissected as a result of the analysis, is made. On this basis, further study of the object takes place, but as a whole. At the same time, synthesis does not mean simple mechanical connection of separated elements into a single system. He reveals the place and role of each element in the system of the whole, establishes their interrelation and interdependence, that is, it allows one to understand the true dialectical unity of the object under study.

The analysis fixes mainly the specific, which distinguishes the parts from each other. Synthesis, on the other hand, reveals what is essentially common, which binds the parts together. The analysis involving the implementation of the synthesis, its central core has a significant selection. Then the whole does not look the same as at the “first acquaintance” of the mind with it, but much deeper, more meaningful.

Analysis and synthesis are successfully used in the field of human mental activity, that is, in theoretical knowledge. But here, as well as at the empirical level of knowledge, analysis and synthesis are not two operations separated from each other. In essence, they are like two sides of a single analytical-synthetic method of knowledge.

These two interrelated methods of research receive their own specification in each branch of science. From general reception, they can turn into a special method: for example, there are specific methods of mathematical, chemical and social analysis. The analytical method was developed in some philosophical schools and directions. The same can be said about synthesis.

Induction and deduction.

Induction (from the Latin. Inductio – guidance, inducement) is a formalological conclusion, which leads to a general conclusion on the basis of private premises. In other words, this is the movement of our thinking from the particular to the general.

Induction is widely used in scientific knowledge. Finding similar signs, properties of many objects of a certain class, the researcher makes a conclusion about the inherentness of these signs, properties of all objects of this class. Along with other methods of cognition, the inductive method has played an important role in the discovery of some laws of nature (world wideness, atmospheric pressure, thermal expansion of bodies, etc.).

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

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

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

3. The combined method of similarity and differences (is a combination of the above two methods).

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

5. Method of residues (if a complex phenomenon is caused by a multifactorial cause, some of these factors are known as the cause of some part of this phenomenon, then the conclusion follows: the cause of the other part of the phenomenon is the other factors that are part of the common cause of this phenomenon).

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

Deduction (from the Latin. Deductio – elimination) is to obtain private conclusions based on the knowledge of some general provisions. In other words, this is the movement of our thinking from the general to the particular, the individual.

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

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

In the science of New Age, the prominent mathematician and philosopher R. Descartes was a promoter of the deductive method of knowledge.

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

Moreover, in the process of using the inductive method, deduction is also often “hidden”. “Summarizing the facts in accordance with some ideas, we thereby indirectly deduce the generalizations we receive from these ideas, and we are not always aware of this. It seems that our thought moves directly from facts to generalizations, that is, that there is pure induction. In fact, in line with some ideas, in other words, implicitly guided by them in the process of summarizing the facts, our thought indirectly goes from ideas to these generalizations, and, therefore, there is a deduction here … in all cases when we generalize, in accordance with any philosophical propositions, our conclusions are not only induction, but also hidden deduction. ”

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

Analogy and modeling.

An analogy is understood as the similarity, similarity of some properties, signs or relations among various objects in general. The establishment of similarities (or differences) between objects is carried out as a result of their comparison. Thus, the comparison underlies the method of analogy.

If a logical conclusion is made about the presence of any property, attribute, relationship of the object being studied on the basis of establishing its similarity with other objects, then this conclusion is called inference by analogy.

The degree of probability of obtaining the correct inference by analogy will be the higher: 1) the more well known are the general properties of the compared objects; 2) the more significant the common properties found in them, and 3) the deeper the mutual regular relationship of these similar properties is known. It should be borne in mind that if an object in relation to which an inference is made by analogy with another object has some property that is incompatible with the property about the existence of which a conclusion should be drawn, then the general similarity of these objects loses any meaning .

The method of analogy is used in various fields of science: in mathematics, physics, chemistry, cybernetics, in the humanities, etc. Well-known energy scientist V. A. Venikov well said about the cognitive value of the method of analogy: “Sometimes they say:“ The analogy is not proof ”… But after all, if you look it out, you can easily understand that scientists do not seek to prove anything in this way. Is it not enough that the true resemblance gives a powerful impulse to creativity? .. The analogy can jump out the idea into new, unknown orbits, and, of course, the correct idea is that the analogy, if treated with due care, is the simplest and clear path from old to new. ”

There are different types of conclusions by analogy. But it is common for them that in all cases one object is directly examined, and a conclusion is drawn about another object. Therefore, the conclusion by analogy in the most general sense can be defined as the transfer of information from one object to another. At the same time, the first object, which is actually being investigated, is called a model, and another object, to which information received as a result of research of the first object (model) is transferred, is called the original (sometimes a prototype, sample, etc.). Thus, the model always acts as an analogy, that is, the model and the object (original) displayed with its help are in a certain similarity (similarity).

Depending on the nature of the models used in scientific research, there are several types of modeling.

  1. Mental (perfect) modeling. This type of modeling includes various mental representations in the form of certain imaginary models. It should be noted that mental (ideal) models can often be realized materially in the form of sensually perceived physical models.
  2. Physical modeling. It is characterized by a physical similarity between the model and the original and aims at reproducing in the model the processes peculiar to the original. According to the results of the study of certain physical properties of the model, they judge the phenomena that occur (or may occur) in the so-called “natural conditions”. Nowadays, physical modeling is widely used for the development and experimental study of various structures, machines, for a better understanding of some natural phenomena, for studying effective and safe methods of mining, etc.
  3. Symbolic (sign) modeling. It is associated with the conditional-sign representation of some properties, relations of the original object. Symbolic (sign) models include a variety of topological and graph representations (in the form of graphs, nomograms, diagrams, etc.) of the objects under study or, for example, models presented in the form of chemical symbols and reflecting the state or ratio of elements during chemical reactions. A special and very important kind of symbolic (sign) modeling is mathematical modeling. The symbolic language of mathematics makes it possible to express the properties, sides, relations of objects and phenomena of the most diverse nature. The relationships between various quantities describing the functioning of such an object or phenomenon can be represented by the corresponding equations (differential, integral, integro-differential, algebraic) and their systems.
  4. Numerical simulation on a computer. This type of modeling is based on the previously created mathematical model of the object or phenomenon under study and is used in cases of large amounts of computation required for the study of this model. Numerical modeling is especially important where the physical picture of the phenomenon being studied is not completely clear, the internal mechanism of interaction is not known. By means of calculations on the computer of various options, an accumulation of facts is carried out, which makes it possible, in the end, to make a selection of the most real and probable situations. The active use of numerical simulation methods makes it possible to drastically reduce the time required for scientific and design developments.

The modeling method is constantly evolving: one type of model replaces another as science advances. At the same time, one thing remains unchanged: the importance, relevance, and sometimes the indispensability of modeling as a method of scientific knowledge.

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