Scientific knowledge is a system that has several levels of knowledge, differing in a number of parameters. Depending on the subject, nature, type, method and method of knowledge obtained, empirical and theoretical levels of knowledge are distinguished. Each of them performs specific functions and has specific research methods. The levels correspond to interrelated, but at the same time specific types of cognitive activity: empirical and theoretical research. By distinguishing the empirical and theoretical levels of scientific knowledge, the modern researcher is aware that if in ordinary knowledge it is legitimate to distinguish between the sensory and rational levels, then in scientific research the empirical level of research is never limited to purely sensory knowledge, theoretical knowledge does not represent pure rationality. Even initial empirical knowledge obtained through observation is recorded using scientific terms. Theoretical knowledge is also not pure rationality. When constructing a theory, visual representations are used, which are the basis of sensory perception. Thus, we can say that at the beginning of empirical research, the sensual predominates, and in theoretical research, the rational prevails. At the level of empirical research, it is possible to identify dependencies and connections between phenomena and certain patterns. But if the empirical level can only capture the external manifestation, then the theoretical level comes to explain the essential connections of the object under study.

Empirical knowledge is the result of the researcher’s direct interaction with reality in observation or experiment. At the empirical level, not only the accumulation of facts occurs, but also their primary systematization and classification, which makes it possible to identify empirical rules, principles and laws that are transformed into observable phenomena. At this level, the object under study is reflected primarily in external connections and manifestations. The complexity of scientific knowledge is determined by the presence in it not only of levels and methods of cognition, but also of the forms in which it is recorded and developed. The main forms of scientific knowledge are facts, problems, hypotheses And theories. Their meaning is to reveal the dynamics of the cognition process in the course of research and study of any object. Establishing facts is a necessary condition for the success of natural science research. To build a theory, facts must not only be reliably established, systematized and generalized, but also considered in interconnection. A hypothesis is conjectural knowledge that is probabilistic in nature and requires verification. If during testing the content of the hypothesis does not agree with empirical data, then it is rejected. If the hypothesis is confirmed, then we can talk about it with varying degrees of probability. As a result of testing and proof, some hypotheses become theories, others are clarified and specified, and others are discarded if their testing gives a negative result. The main criterion for the truth of a hypothesis is practice in various forms.

A scientific theory is a generalized system of knowledge that provides a holistic reflection of natural and significant connections in a certain area of ​​objective reality. The main task of the theory is to describe, systematize and explain the entire set of empirical facts. Theories are classified as descriptive, scientific And deductive. In descriptive theories, researchers formulate general patterns based on empirical data. Descriptive theories do not require logical analysis and concrete evidence (the physiological theory of I. Pavlov, the evolutionary theory of Charles Darwin, etc.). In scientific theories, a model is constructed that replaces the real object. The consequences of the theory are verified by experiment (physical theories, etc.). In deductive theories, a special formalized language has been developed, all terms of which are subject to interpretation. The first of them is Euclid’s “Elements” (the main axiom is formulated, then provisions logically deduced from it are added to it, and all proofs are carried out on this basis).

The main elements of a scientific theory are principles and laws. The principles provide general and important confirmations of the theory. In theory, principles play the role of primary prerequisites that form its basis. In turn, the content of each principle is revealed with the help of laws. They specify the principles, reveal the mechanism of their action, the logic of the relationship, and the consequences arising from them. Laws are a form of theoretical statements that reveal the general connections of the phenomena, objects and processes being studied. When formulating principles and laws, it is quite difficult for a researcher to be able to see behind numerous, often completely different externally facts, the essential properties and characteristics of the properties of objects and phenomena under study. The difficulty lies in the fact that it is difficult to record the essential characteristics of the object under study in direct observation. Therefore, it is impossible to directly move from the empirical level of knowledge to the theoretical one. Theory is not built by directly generalizing experience, so the next step is to formulate the problem. It is defined as a form of knowledge, the content of which is a conscious question, to answer which existing knowledge is not enough. Searching, formulating and solving problems are the main features of scientific activity. In turn, the presence of a problem in understanding inexplicable facts entails a preliminary conclusion that requires experimental, theoretical and logical confirmation. The process of cognition of the surrounding world is the solution of various kinds of problems that arise in the course of human practical activity. These problems are solved by using special techniques - methods.

– a set of techniques and operations for practical and theoretical knowledge of reality.

Research methods optimize human activities and equip them with the most rational ways of organizing activities. A.P. Sadokhin, in addition to highlighting the levels of knowledge when classifying scientific methods, takes into account the criterion of applicability of the method and identifies general, special and particular methods of scientific knowledge. The selected methods are often combined and combined during the research process.

General methods knowledge concerns any discipline and makes it possible to connect all stages of the process of knowledge. These methods are used in any field of research and make it possible to identify connections and characteristics of the objects under study. In the history of science, researchers include metaphysical and dialectical methods among such methods. Private Methods scientific knowledge are methods used only in a particular branch of science. Various methods of natural science (physics, chemistry, biology, ecology, etc.) are particular in relation to the general dialectical method of cognition. Sometimes private methods can be used outside the branches of natural science in which they originated. For example, physical and chemical methods are used in astronomy, biology, and ecology. Often researchers apply a complex of interrelated private methods to the study of one subject. For example, ecology simultaneously uses the methods of physics, mathematics, chemistry, and biology. Particular methods of cognition are associated with special methods. Special methods explore certain features of the object being studied. They can manifest themselves at the empirical and theoretical levels of knowledge and be universal.

Among special empirical methods of cognition distinguish between observation, measurement and experiment.

Observation is a purposeful process of perceiving objects of reality, a sensory reflection of objects and phenomena, during which a person receives primary information about the world around him. Therefore, research most often begins with observation, and only then do researchers move on to other methods. Observations are not associated with any theory, but the purpose of observation is always related to some problem situation. Observation presupposes the existence of a specific research plan, an assumption that is subject to analysis and verification. Observations are used where direct experiments cannot be performed (in volcanology, cosmology). The results of the observation are recorded in a description, noting those signs and properties of the object being studied that are the subject of study. The description must be as complete, accurate and objective as possible. It is the descriptions of observation results that constitute the empirical basis of science; on their basis, empirical generalizations, systematization and classification are created.

Measurement– this is the determination of quantitative values ​​(characteristics) of the studied aspects or properties of an object using special technical devices. The units of measurement with which the data obtained are compared play an important role in the study.

Experiment – a more complex method of empirical knowledge compared to observation. It represents a purposeful and strictly controlled influence of the researcher on an object or phenomenon of interest to study its various aspects, connections and relationships. During experimental research, the scientist interferes with the natural course of processes and transforms the object of research. The specificity of the experiment is also that it allows you to see the object or process in its pure form. This occurs due to the maximum exclusion of exposure to extraneous factors. The experimenter separates the essential facts from the unimportant ones and thereby greatly simplifies the situation. Such simplification contributes to a deep understanding of the essence of phenomena and processes and creates the opportunity to control many factors and quantities that are important for a given experiment. The modern experiment is characterized by the following features: an increased role of theory at the preparatory stage of the experiment; complexity of technical means; scale of the experiment. The main objective of the experiment is to test hypotheses and conclusions of theories that have fundamental and applied significance. In experimental work, with active influence on the object under study, certain of its properties are artificially isolated, which are the subject of study in natural or specially created conditions. In the process of natural science experiments, they often resort to physical modeling of the object under study and create various controlled conditions for it. S. X. Karpenkov divides experimental means according to their content into the following systems:

S. Kh. Karpenkov points out that depending on the task at hand, these systems play a different role. For example, when determining the magnetic properties of a substance, the results of an experiment largely depend on the sensitivity of the instruments. At the same time, when studying the properties of a substance that does not occur in nature under ordinary conditions, and even at low temperatures, all systems of experimental means are important.

In any natural science experiment, the following stages are distinguished:

The preparatory stage represents the theoretical justification of the experiment, its planning, production of a sample of the object under study, selection of conditions and technical means of research. Results obtained on a well-prepared experimental basis, as a rule, are more easily amenable to complex mathematical processing. Analysis of the experimental results allows one to evaluate certain characteristics of the object under study and compare the results obtained with the hypothesis, which is very important in determining the correctness and degree of reliability of the final research results.

To increase the reliability of the experimental results obtained, it is necessary:

Among special theoretical methods of scientific knowledge distinguish procedures of abstraction and idealization. In the processes of abstraction and idealization, concepts and terms used in all theories are formed. Concepts reflect the essential side of phenomena that appears when generalizing the study. In this case, only some aspect of an object or phenomenon is highlighted. Thus, the concept of “temperature” can be given an operational definition (an indicator of the degree of heating of a body on a certain thermometer scale), and from the standpoint of molecular kinetic theory, temperature is a value proportional to the average kinetic energy of motion of the particles that make up the body. Abstraction – mental distraction from all properties, connections and relationships of the object being studied, which are considered unimportant. These are the models of a point, a straight line, a circle, a plane. The result of the abstraction process is called abstraction. Real objects in some problems can be replaced by these abstractions (the Earth can be considered a material point when moving around the Sun, but not when moving along its surface).

Idealization represents the operation of mentally identifying one property or relationship that is important for a given theory, and mentally constructing an object endowed with this property (relationship). As a result, the ideal object has only this property (relation). Science identifies general patterns in reality that are significant and repeated in various subjects, so we have to make abstractions from real objects. This is how such concepts as “atom”, “set”, “absolute black body”, “ideal gas”, “continuous medium” are formed. The ideal objects obtained in this way do not actually exist, since in nature there cannot be objects and phenomena that have only one property or quality. When applying the theory, it is necessary to again compare the obtained and used ideal and abstract models with reality. Therefore, it is important to select abstractions in accordance with their adequacy to a given theory and then exclude them.

Among special universal research methods identify analysis, synthesis, comparison, classification, analogy, modeling. The process of natural scientific knowledge is carried out in such a way that we first observe the general picture of the object being studied, in which the particulars remain in the shadows. With such observation, it is impossible to know the internal structure of the object. To study it, we must separate the objects being studied.

Analysis– one of the initial stages of research, when one moves from a complete description of an object to its structure, composition, characteristics and properties. Analysis is a method of scientific knowledge, which is based on the procedure of mental or real division of an object into its constituent parts and their separate study. It is impossible to know the essence of an object only by highlighting the elements of which it consists. When the particulars of the object under study are studied through analysis, it is supplemented by synthesis.

Synthesis – a method of scientific knowledge, which is based on the combination of elements identified by analysis. Synthesis does not act as a method of constructing the whole, but as a method of representing the whole in the form of the only knowledge obtained through analysis. It shows the place and role of each element in the system, their connection with other components. Analysis mainly captures that specific thing that distinguishes parts from each other, synthesis – generalizes the analytically identified and studied features of an object. Analysis and synthesis originate in the practical activities of man. Man has learned to mentally analyze and synthesize only on the basis of practical separation, gradually comprehending what happens to an object when performing practical actions with it. Analysis and synthesis are components of the analytical-synthetic method of cognition.

When making a quantitative comparison of the studied properties, parameters of objects or phenomena, we speak of a comparison method. Comparison– a method of scientific knowledge that allows one to establish the similarities and differences of the objects being studied. Comparison underlies many natural science measurements that form an integral part of any experiment. By comparing objects with each other, a person gets the opportunity to correctly cognize them and thereby correctly navigate the world around him and purposefully influence it. Comparison matters when objects that are truly homogeneous and similar in essence are compared. The comparison method highlights the differences between the objects under study and forms the basis of any measurements, that is, the basis of experimental research.

Classification– a method of scientific knowledge that combines into one class objects that are as similar as possible to each other in essential characteristics. Classification makes it possible to reduce the accumulated diverse material to a relatively small number of classes, types and forms and identify the initial units of analysis, discover stable characteristics and relationships. Typically, classifications are expressed in the form of natural language texts, diagrams and tables.

Analogy – a method of cognition in which the knowledge gained from examining an object is transferred to another, less studied, but similar to the first in some essential properties. The analogy method is based on the similarity of objects according to a number of characteristics, and the similarity is established as a result of comparing objects with each other. Thus, the basis of the analogy method is the comparison method.

The analogy method is closely related to the method modeling, which is the study of any objects using models with further transfer of the obtained data to the original. This method is based on the significant similarity of the original object and its model. In modern research, various types of modeling are used: subject, mental, symbolic, computer. Subject modeling is the use of models that reproduce certain characteristics of an object. mental Modeling is the use of various mental representations in the form of imaginary models. Symbolic modeling uses drawings, diagrams, and formulas as models. They reflect certain properties of the original in a symbolic form. A type of symbolic modeling is mathematical modeling produced by means of mathematics and logic. It involves the formation of systems of equations that describe the natural phenomenon under study, and their solution under various conditions. Computer modeling has become widespread recently (Sadokhin A.P., 2007).

The variety of methods of scientific knowledge creates difficulties in their application and understanding of their role. These problems are solved by a special field of knowledge - methodology. The main objective of the methodology is to study the origin, essence, effectiveness, and development of methods of cognition.

2) reveal the possibility of using the known laws, forces and substances of nature in practice.

The goal of natural science, ultimately, is an attempt to solve the so-called “world mysteries”, formulated at the end of the 19th century by E. Haeckel and E.G. Dubois-Reymond. Two of these riddles relate to physics, two to biology and three to psychology. These are the riddles:

essence of matter and force

origin of the movement

origin of life

the expediency of nature

the emergence of sensation and consciousness

the emergence of thinking and speech

free will.

The task of natural science is the knowledge of the objective laws of nature and the promotion of their practical use in the interests of man. Natural scientific knowledge is created as a result of generalization of observations obtained and accumulated in the process of practical activity of people, and is itself the theoretical basis of their activity.

All research into nature today can be visually represented as a large network consisting of branches and nodes. This network connects numerous branches of the physical, chemical and biological sciences, including synthetic sciences, which arose at the junction of the main directions (biochemistry, biophysics, etc.).

Even when studying the simplest organism, we must take into account that it is a mechanical unit, a thermodynamic system, and a chemical reactor with multidirectional flows of mass, heat, and electrical impulses; it is, at the same time, a kind of “electric machine” that generates and absorbs electromagnetic radiation. And, at the same time, it is neither one nor the other, it is a single whole.

Natural science methods

The process of scientific knowledge in its most general form is the solution of various kinds of problems that arise in the course of practical activity. The solution to the problems that arise in this case is achieved by using special techniques (methods) that make it possible to move from what is already known to new knowledge. This system of techniques is usually called a method. Method is a set of techniques and operations of practical and theoretical knowledge of reality.

The methods of natural science are based on the unity of its empirical and theoretical sides. They are interconnected and condition each other. Their rupture, or the preferential development of one at the expense of the other, closes the path to correct knowledge of nature - theory becomes pointless, experience becomes blind.

Empirical side presupposes the need to collect facts and information (establishment of facts, their registration, accumulation), as well as their description (statement of facts and their primary systematization).

Theoretical side associated with explanation, generalization, creation of new theories, putting forward hypotheses, discovery of new laws, prediction of new facts within the framework of these theories. With their help, a scientific picture of the world is developed and thereby the ideological function of science is carried out.

Natural science methods can be divided into groups:

a) general methods relating to all natural science, any subject of nature, any science. These are various forms of a method that makes it possible to connect together all aspects of the process of cognition, all its stages, for example, the method of ascent from the abstract to the concrete, the unity of the logical and historical. These are, rather, general philosophical methods of cognition.

b) special methods- special methods that relate not to the subject of natural science as a whole, but only to one of its aspects or to a specific method of research: analysis, synthesis, induction, deduction;

Special methods also include observation, measurement, comparison and experiment.

In natural science, special methods of science are given extremely important importance, therefore, within the framework of our course, it is necessary to consider their essence in more detail.

Observation - This is a purposeful, strict process of perceiving objects of reality that should not be changed. Historically, the observation method develops as an integral part of a labor operation, which includes establishing the conformity of the product of labor with its planned model.

Observation as a method presupposes the existence of a research program formed on the basis of past beliefs, established facts, and accepted concepts. Special cases of the observation method are measurement and comparison.

Experiment - a method of cognition with the help of which phenomena of reality are studied under controlled and controlled conditions. It differs from observation by intervention in the object under study, that is, activity in relation to it. When conducting an experiment, the researcher is not limited to passive observation of phenomena, but consciously intervenes in the natural course of their occurrence by directly influencing the process under study or changing the conditions in which this process takes place.

The development of natural science raises the problem of the rigor of observation and experiment. The fact is that they need special tools and devices, which have recently become so complex that they themselves begin to influence the object of observation and experiment, which, according to the conditions, should not be the case. This primarily applies to research in the field of microworld physics (quantum mechanics, quantum electrodynamics, etc.).

Analogy - a method of cognition in which the transfer of knowledge obtained during the consideration of any one object occurs to another, less studied and currently being studied. The analogy method is based on the similarity of objects according to a number of characteristics, which allows one to obtain completely reliable knowledge about the subject being studied.

The use of the analogy method in scientific knowledge requires some caution. Here it is extremely important to clearly identify the conditions under which it works most effectively. However, in cases where it is possible to develop a system of clearly formulated rules for transferring knowledge from a model to a prototype, the results and conclusions using the analogy method acquire evidentiary force.

Analysis - a method of scientific knowledge, which is based on the procedure of mental or real division of an object into its constituent parts. Dismemberment aims to move from the study of the whole to the study of its parts and is carried out by abstracting from the connection of the parts with each other.

Synthesis - This is a method of scientific knowledge, which is based on the procedure for combining various elements of a subject into a single whole, a system, without which truly scientific knowledge of this subject is impossible. Synthesis acts not as a method of constructing the whole, but as a method of representing the whole in the form of a unity of knowledge obtained through analysis. In synthesis, there is not just a unification, but a generalization of the analytically identified and studied features of the object. The provisions obtained as a result of synthesis are included in the theory of the object, which, enriched and refined, determines the path of new scientific research.

Induction - a method of scientific knowledge, which is the formulation of a logical conclusion by summarizing observational and experimental data.

Deduction - a method of scientific knowledge, which consists in the transition from certain general premises to particular results and consequences.

The solution to any scientific problem involves putting forward various guesses, assumptions, and most often more or less substantiated hypotheses, with the help of which the researcher tries to explain facts that do not fit into old theories. Hypotheses arise in uncertain situations, the explanation of which becomes relevant for science. In addition, at the level of empirical knowledge (as well as at the level of its explanation), there are often contradictory judgments. To resolve these problems, hypotheses are required.

Hypothesis is any assumption, guess or prediction put forward to eliminate a situation of uncertainty in scientific research. Therefore, a hypothesis is not reliable knowledge, but probable knowledge, the truth or falsity of which has not yet been established.

Any hypothesis must be justified either by the achieved knowledge of a given science or by new facts (uncertain knowledge is not used to substantiate the hypothesis). It must have the property of explaining all facts that relate to a given field of knowledge, systematizing them, as well as facts outside this field, predicting the emergence of new facts (for example, the quantum hypothesis of M. Planck, put forward at the beginning of the 20th century, led to the creation of a quantum mechanics, quantum electrodynamics and other theories). Moreover, the hypothesis should not contradict existing facts. A hypothesis must either be confirmed or refuted.

c) private methods- these are methods that operate either only within a particular branch of natural science, or outside the branch of natural science where they arose. This is the method of bird ringing used in zoology. And the methods of physics used in other branches of natural science led to the creation of astrophysics, geophysics, crystal physics, etc. A complex of interrelated private methods is often used to study one subject. For example, molecular biology simultaneously uses the methods of physics, mathematics, chemistry, and cybernetics.

Modeling is a method of scientific knowledge based on the study of real objects through the study of models of these objects, i.e. by studying substitute objects of natural or artificial origin that are more accessible to research and (or) intervention and have the properties of real objects.

The properties of any model should not, and cannot, accurately and completely correspond to absolutely all the properties of the corresponding real object in all situations. In mathematical models, any additional parameter can lead to a significant complication of solving the corresponding system of equations, to the need to apply additional assumptions, discard small terms, etc., with numerical modeling, the processing time of the problem by a computer disproportionately increases, and the calculation error increases.

Conclusion

Natural science appeared more than 3000 years ago. Then there was no division into physics, biology, geography. Philosophers studied science. With the development of trade and navigation, the development of geography began, and with the development of technology - the development of physics and chemistry.

Natural science is a very ramified field of scientific knowledge, touching on a wide range of issues about various aspects of the life of nature. Nature as an object of study of natural science is complex and diverse in its manifestations: it is constantly changing and in constant motion. Accordingly, this diversity is reflected in a large number of concepts devoted to almost all natural processes and phenomena. A careful study of them shows that the Universe is regular and predictable; matter consists of atoms and elementary particles; the properties of material objects depend on which atoms are included in their composition and how they are located there; atoms consist of quarks and leptons; stars are born and die, like everything else in the world; The universe arose in the distant past and has been expanding ever since; all living things consist of cells, and all organisms appeared as a result of natural selection; natural processes on Earth occur in cycles; changes are constantly taking place on its surface and there is nothing eternal, etc. In general, the world is both united and surprisingly diverse, it is eternal and endless in the constant process of mutual transformation of some systems into others, while each part of it is relatively independent, being inevitably dependent on the general laws of existence .

List of used literature

Novosibirsk State University

Faculty of Mechanics and Mathematics

Subject: Concepts of Modern Natural Science

On the topic: “Methods of scientific knowledge”

Panov L.V.

Course 3, group 4123

Science is the main reason for the transition to a post-industrial society, the widespread introduction of information technology, and the emergence of a “new economy”. Science has a developed system of methods, principles and imperatives of knowledge. It is the correctly chosen method, along with the scientist’s talent, that helps him to understand the deep connection of phenomena, reveal their essence, discover laws and regularities. The number of scientific methods is constantly increasing. After all, there are a large number of sciences in the world and each of them has its own specific methods and subject of research.

The purpose of this work is to examine in detail the methods of scientific experimental and theoretical knowledge. Namely, what is the method, the main features of the method, classification, scope, etc. The criteria of scientific knowledge will also be considered.

Observation.

Knowledge begins with observation. Observation is a sensory reflection of objects and phenomena of the external world. Observation is a purposeful study of objects, based mainly on such human sensory abilities as sensation, perception, and representation. This is the initial method of empirical cognition, which allows us to obtain some primary information about the objects of the surrounding reality.

Scientific observation is characterized by a number of features. Firstly, by purposefulness, observation should be carried out to solve the stated research problem, and the observer’s attention should be fixed only on phenomena related to this task. Secondly, systematically, since the observation must be carried out strictly according to plan. Thirdly, by activity - the researcher must actively search, highlight the moments he needs in the observed phenomenon, drawing on his knowledge and experience for this.

During observation, there is no activity aimed at transforming or changing the objects of knowledge. This is due to a number of circumstances: the inaccessibility of these objects for practical influence (for example, observation of distant space objects), the undesirability, based on the purposes of the study, of interference in the observed process (phenological, psychological and other observations), the lack of technical, energy, financial and other capabilities setting up experimental studies of objects of knowledge.

Scientific observations are always accompanied by a description of the object of knowledge. With the help of description, sensory information is translated into the language of concepts, signs, diagrams, drawings, graphs and numbers, thereby taking a form convenient for further rational processing. It is important that the concepts used for description always have a clear and unambiguous meaning. With the development of science and changes in its foundations, the means of description are transformed, and a new system of concepts is often created.

According to the method of conducting observations, they can be direct or indirect. During direct observations, certain properties and aspects of an object are reflected and perceived by human senses. It is known that observations of the positions of planets and stars in the sky, carried out for more than twenty years by Tycho Brahe, were the empirical basis for Kepler’s discovery of his famous laws. Most often, scientific observation is indirect, i.e., carried out using certain technical means. If before the beginning of the 17th century. As astronomers observed celestial bodies with the naked eye, Galileo's invention of the optical telescope in 1608 raised astronomical observations to a new, much higher level. And the creation today of X-ray telescopes and their launch into outer space on board an orbital station has made it possible to observe such objects of the Universe as pulsars and quasars.

The development of modern natural science is associated with the increasing role of so-called indirect observations. Thus, objects and phenomena studied by nuclear physics cannot be directly observed either with the help of human senses or with the help of the most advanced instruments. For example, when studying the properties of charged particles using a cloud chamber, these particles are perceived by the researcher indirectly - through visible tracks consisting of many droplets of liquid.

Experiment

Experiment - a more complex method of empirical knowledge compared to observation. It involves the active, purposeful and strictly controlled influence of the researcher on the object being studied in order to identify and study certain aspects, properties, and connections. In this case, the experimenter can transform the object under study, create artificial conditions for its study, and interfere with the natural course of processes. In the general structure of scientific research, experiment occupies a special place. It is the experiment that is the connecting link between the theoretical and empirical stages and levels of scientific research.

Some scientists argue that a cleverly thought out and skillfully executed experiment is superior to theory, because theory, unlike experience, can be completely refuted.

An experiment includes, on the one hand, observation and measurement, and on the other, it has a number of important features. Firstly, an experiment allows you to study an object in a “purified” form, that is, eliminate all kinds of side factors and layers that complicate the research process. Secondly, during the experiment, the object can be placed in some artificial, in particular, extreme conditions, i.e., studied at ultra-low temperatures, at extremely high pressures or, conversely, in a vacuum, at enormous electromagnetic field strengths, etc. Thirdly, when studying a process, an experimenter can intervene in it and actively influence its course. Fourth, an important advantage of many experiments is their reproducibility. This means that the experimental conditions can be repeated as many times as necessary to obtain reliable results.

Preparing and conducting an experiment requires compliance with a number of conditions. Thus, a scientific experiment presupposes the presence of a clearly formulated research goal. The experiment is based on some initial theoretical principles. An experiment requires a certain level of development of technical means of cognition necessary for its implementation. And finally, it must be carried out by people who are sufficiently qualified.

Based on the nature of the problems being solved, experiments are divided into research and testing. Research experiments make it possible to discover new, unknown properties in an object. The result of such an experiment may be conclusions that do not follow from existing knowledge about the object of study. An example is the experiments carried out in the laboratory of E. Rutherford, which led to the discovery of the atomic nucleus. Verification experiments serve to test and confirm certain theoretical constructs. For example, the existence of a number of elementary particles (positron, neutrino, etc.) was first predicted theoretically, and only later were they discovered experimentally. Experiments can be divided into qualitative and quantitative. Qualitative experiments only allow us to identify the effect of certain factors on the phenomenon being studied. Quantitative experiments establish precise quantitative relationships. 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 (having placed a magnetic compass needle next to a conductor through which an electric current was passed, he discovered that the needle deviates from its original position). This was followed by quantitative experiments by the French scientists Biot and Savart, as well as Ampere's experiments, on the basis of which a mathematical formula was derived. According to the field of scientific knowledge in which the experiment is carried out, natural science, applied and socio-economic experiments are distinguished.

Measurement and comparison.

Scientific experiments and observations usually involve making a variety of measurements. Measurement is a process that involves determining the quantitative values ​​of certain properties, aspects of the object or phenomenon under study using special technical devices.

The measurement operation is based on comparison. To make a comparison, you need to determine the units of measurement. In science, comparison also acts as a comparative or comparative-historical method. Originally arose in philology and literary criticism, it then began to be successfully applied in law, sociology, history, biology, psychology, history of religion, ethnography and other fields of knowledge. Entire branches of knowledge have emerged that use this method: comparative anatomy, comparative physiology, comparative psychology, etc. Thus, in comparative psychology, the study of the psyche is carried out on the basis of comparing the psyche of an adult with the development of the psyche of a child, as well as animals.

An important aspect of the measurement process is the methodology for carrying it out. It is a set of techniques that use certain principles and means of measurement. By measurement principles we mean the phenomena that form the basis of measurements.

Measurements are divided into static and dynamic. Static measurements include the measurement of body sizes, constant pressure, etc. Examples of dynamic measurements are the measurement of vibration, pulsating pressure, etc. Based on the method of obtaining results, direct and indirect measurements are distinguished. In direct measurements, the desired value of the measured quantity is obtained by directly comparing it with a standard or is issued by a measuring device. In indirect measurement, the desired value is determined on the basis of a known mathematical relationship between this value and other values ​​obtained by direct measurements. For example, finding the electrical resistivity of a conductor by its resistance, length and cross-sectional area. Indirect measurements are widely used in cases where the desired quantity is impossible or too difficult to measure directly.

Over time, on the one hand, existing measuring instruments are improved, on the other, new measuring devices are introduced. Thus, the development of quantum physics has significantly increased the possibilities of measurements with a high degree of accuracy. Using the Mössbauer effect makes it possible to create a device with a resolution of about 10 -13 percent of the measured value. Well-developed measuring instrumentation, a variety of methods and high characteristics of measuring instruments contribute to progress in scientific research.

General characteristics of theoretical methods

Theory is a system of concepts of laws and principles that makes it possible to describe and explain a certain group of phenomena and outline a program of action for their transformation. Consequently, theoretical knowledge is carried out with the help of various concepts, laws and principles. Facts and theories do not oppose each other, but form a single whole. The difference between them is that facts express something individual, while theory deals with the general. In facts and theories, three levels can be distinguished: eventual, psychological and linguistic. These levels of unity can be represented as follows:

Linguistic level: theories include universal statements, facts include individual statements.

Psychological level: thoughts (t) and feelings (f).

Event level - total single events (t) and single events (f)

The theory, as a rule, is constructed in such a way that it describes not the surrounding reality, but ideal objects, such as a material point, an ideal gas, an absolutely black body, etc. This scientific concept is called idealization. Idealization is a mentally constructed concept of objects, processes and phenomena that do not seem to exist, but have images or prototypes. For example, a small body can serve as a prototype of a material point. Ideal objects, unlike real ones, are characterized not by an infinite, but by a well-defined number of properties. For example, the properties of a material point are mass and the ability to be in space and time.

In addition, the theory specifies the relationships between ideal objects, described by laws. Derived objects can also be constructed from primary ideal objects. As a result, a theory that describes the properties of ideal objects, the relationships between them and the properties of structures formed from primary ideal objects is able to describe the entire variety of data that a scientist encounters at the empirical level.

Let us consider the main methods by which theoretical knowledge is realized. These methods are: axiomatic, constructivist, hypothetic-inductive and pragmatic.

When using the axiomatic method, a scientific theory is constructed in the form of a system of axioms (propositions accepted without logical proof) and rules of inference that allow, through logical deduction, to obtain statements of a given theory (theorems). The axioms should not contradict each other; it is also desirable that they should not depend on each other. The axiomatic method will be discussed in more detail below.

The constructivist method, along with the axiomatic one, is used in mathematical sciences and computer science. In this method, the development of a theory begins not with axioms, but with concepts, the legitimacy of the use of which is considered intuitively justified. In addition, rules for constructing new theoretical structures are set. Only those structures that were actually built are considered scientific. This method is considered the best remedy against the emergence of logical contradictions: the concept is constructed, therefore, the very way of its construction is consistent.

In natural science, the hypothetico-deductive method or the method of hypotheses is widely used. The basis of this method is hypotheses of generalizing power, from which all other knowledge is derived. Until a hypothesis is rejected, it acts as a scientific law. Hypotheses, unlike axioms, require experimental confirmation. This method will be described in detail below.

In the technical and human sciences, the pragmatic method is widely used, the essence of which is the logic of the so-called. practical conclusion. For example, subject L wants to carry out A, but he believes that he will not be able to carry out A if he does not carry out c. Therefore, A is taken to have done c. The logical constructions look like this: A-> p-> c. With the constructivist method, the constructions would have the following form: A-> c-> r. Unlike hypothetico-deductive inference, in which information about a fact is brought under the law, in practical inference information about a means c must correspond to the goal p, which is consistent with certain values.

In addition to the methods discussed, there are also so-called. descriptive methods. They are addressed if the methods discussed above are unacceptable. The description of the phenomena being studied can be verbal, graphic, schematic, formal-symbolic. Descriptive methods are often the stage of scientific research that leads to the ideals of more developed scientific methods. Often this method is the most adequate, since modern science often deals with phenomena that do not obey too stringent requirements.

Abstraction.

In the process of abstraction, there is a departure from sensually perceived concrete objects to abstract ideas about them. Abstraction consists of mental abstraction from some less significant properties, aspects, features of the object being studied while simultaneously highlighting and forming one or more essential aspects, properties, features of this object. The result obtained during the abstraction process is called abstraction.

The transition from the sensory-concrete to the abstract is always associated with a certain simplification of reality. At the same time, ascending from the sensory-concrete to the abstract, theoretical, the researcher gets the opportunity to better understand the object being studied and reveal its essence. The process of transition from sensory-empirical, visual ideas about the phenomena being studied to the formation of certain abstract, theoretical structures that reflect the essence of these phenomena lies at the basis of the development of any science.

Since the concrete is a collection of many properties, aspects, internal and external connections and relationships, it is impossible to know it in all its diversity, remaining at the stage of sensory cognition and limiting ourselves to it. Therefore, there is a need for a theoretical understanding of the concrete, which is usually called the ascent from the sensory-concrete to the abstract. However, the formation of scientific abstractions and general theoretical positions is not the ultimate goal of knowledge, but is only a means of deeper, more versatile knowledge of the concrete. Therefore, it is necessary to further move knowledge from the achieved abstract back to the concrete. The logical-concrete obtained at this stage of the study will be qualitatively different in comparison with the sensory-concrete. The logical-concrete is the concrete, theoretically reproduced in the researcher’s thinking, in all the richness of its content. It contains not only something sensually perceived, but also something hidden, inaccessible to sensory perception, something essential, natural, comprehended only with the help of theoretical thinking, with the help of certain abstractions.

The method of ascent from the abstract to the concrete is used in the construction of various scientific theories and can be used in both social and natural sciences. For example, in the theory of gases, having identified the basic laws of an ideal gas - Clapeyron's equations, Avogadro's law, etc., the researcher goes to the specific interactions and properties of real gases, characterizing their essential aspects and properties. As we delve deeper into the concrete, new abstractions are introduced, which act as a deeper reflection of the essence of the object. Thus, in the process of developing the theory of gases, it was found that the ideal gas laws characterize the behavior of real gases only at low pressures. Taking these forces into account led to the formulation of Van der Waals' law.

Idealization. Thought experiment.

Idealization is the mental introduction of certain changes to the object being studied in accordance with the goals of the research. As a result of such changes, for example, some properties, aspects, or features of objects may be excluded from consideration. Thus, the widespread idealization in mechanics - a material point implies a body devoid of any dimensions. 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. When idealized, an object can be endowed with some special properties that are not realizable in reality. An example is the abstraction introduced into physics through idealization, known as the absolutely black body. This body is endowed with the property, which does not exist in nature, of absorbing absolutely all radiant energy falling on it, without reflecting anything and without letting anything pass through it.

Idealization is appropriate when the real objects to be studied are sufficiently complex for the available means of theoretical, in particular mathematical, analysis. It is advisable to use idealization in cases where it is necessary to exclude certain properties of an object that obscure the essence of the processes occurring in it. A complex object is presented in a “purified” form, which makes it easier to study.

As an example, we can point to three different concepts of “ideal gas”, formed under the influence of different theoretical and physical concepts: Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac. However, all three idealization options obtained in this case turned out to be fruitful in the study of gas states of various natures: the Maxwell-Boltzmann ideal gas became the basis for studies of ordinary rarefied molecular gases located at fairly high temperatures; The Bose-Einstein ideal gas was used to study photonic gas, and the Fermi-Dirac ideal gas helped solve a number of electron gas problems.

A thought experiment involves operating with an idealized object, which consists in the mental selection of certain positions and situations that make it possible to detect some important features of the object under study. Any real experiment, before being carried out in practice, is first carried out by the researcher mentally in the process of thinking and planning. In scientific knowledge, there may be cases when, when studying certain phenomena and situations, conducting real experiments turns out to be completely impossible. This gap in knowledge can only be filled by a thought experiment.

The scientific activity of Galileo, Newton, Maxwell, Carnot, Einstein and other scientists who laid the foundations of modern natural science testifies to the significant role of thought experiments in the formation of theoretical ideas. The history of the development of physics is rich in facts about the use of thought experiments. An example is Galileo's thought experiments, which led to the discovery of the law of inertia.

The main advantage of idealization as a method of scientific knowledge is that the theoretical constructions obtained on its basis then make it possible to effectively study real objects and phenomena. Simplifications achieved through idealization facilitate the creation of a theory that reveals the laws of the studied area of ​​​​phenomena of the material world. If the theory as a whole correctly describes real phenomena, then the idealizations underlying it are also legitimate.

Formalization. Axioms.

Formalization is a special approach in scientific knowledge, which consists in the use of special symbols, which allows one to escape from the study of real objects, from the content of the theoretical provisions describing them, and to operate instead with a certain set of symbols (signs).

This method of cognition consists in constructing abstract mathematical models that reveal the essence of the processes of reality being studied. When formalizing, reasoning about objects is transferred to the plane of operating with signs (formulas). Relationships of signs replace statements about the properties and relationships of objects. In this way, a generalized sign model of a certain subject area is created, which makes it possible to detect the structure of various phenomena and processes while abstracting from the qualitative characteristics of the latter. The derivation of some formulas from others according to the strict rules of logic represents a formal study of the main characteristics of the structure of various, sometimes very distant in nature, phenomena.

An example of formalization is the mathematical descriptions of various objects and phenomena widely used in science, based on relevant substantive theories. At the same time, the mathematical symbolism used not only helps to consolidate existing knowledge about the objects and phenomena being studied, but also acts as a kind of tool in the process of further knowledge of them.

From the course of mathematical logic it is known that in order to build a formal system it is necessary to set the alphabet, set the rules for the formation of formulas, set the rules for deriving some formulas from others. An important advantage of a formal system is the possibility of conducting within its framework the study of any object in a purely formal way, using signs. Another advantage of formalization is to ensure that scientific information is recorded concisely and clearly.

It should be noted that formalized artificial languages ​​do not have the flexibility and richness of natural language. But they lack the polysemy of terms characteristic of natural languages. They are characterized by precisely constructed syntax and unambiguous semantics.

Analysis and synthesis. Induction and deduction. Analogy

Empirical analysis is simply the decomposition of a whole into its constituent, simpler elementary parts. . Such parts can be the material elements of an object or its properties, characteristics, relationships.

Synthesis, on the contrary, is the combination of components of a complex phenomenon. Theoretical analysis involves highlighting the basic and essential in an object, imperceptible to empirical vision. The analytical method includes the results of abstraction, simplification, and formalization. Theoretical synthesis is an expanding knowledge that constructs something new that goes beyond the existing framework.

In the process of synthesis, the components (sides, properties, characteristics, etc.) of the object under study, dissected as a result of analysis, are brought together. On this basis, further study of the object takes place, but as a single whole. At the same time, synthesis does not mean a simple mechanical connection of disconnected elements into a single system. Analysis mainly captures what is specific that distinguishes parts from each other. Synthesis reveals that essential commonality that connects the parts into a single whole.

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

Induction can be defined as a method of moving from knowledge of individual facts to knowledge of general facts. Deduction is a method of moving from knowledge of general laws to their particular manifestation.

Induction is widely used in scientific knowledge. By discovering similar signs and properties in many objects of a certain class, the researcher concludes that these signs and properties are inherent in all objects of a given class. The inductive method played an important role in the discovery of some laws of nature - universal gravitation, atmospheric pressure, thermal expansion of bodies.

The induction method can be implemented in the form of the following methods. The method of single similarity, in which in all cases of observation of a phenomenon only one common factor is found, all others are different. This single similar factor is the cause of this phenomenon. The method of single difference, in which the causes of the occurrence of a phenomenon and the circumstances under which it does not occur are similar in almost all respects and differ only in one factor, present only in the first case. It is concluded that this factor is the cause of this phenomenon. The combined similarity and difference method is a combination of the above two methods. The method of accompanying changes, in which if certain changes in one phenomenon each time entail certain changes in another phenomenon, then a conclusion is drawn about the causal relationship of these phenomena. The method of residuals, in which if a complex phenomenon is caused by a multifactorial cause, and some of these factors are known as the cause of some part of this phenomenon, then the conclusion follows: the cause of another part of the phenomenon is the remaining factors included in the general cause of this phenomenon. In fact, the above methods of scientific induction serve mainly to find empirical relationships between the experimentally observed properties of objects and phenomena.

F. Bacon. interpreted induction extremely broadly, considering it the most important method of discovering new truths in science, the main means of scientific knowledge of nature.

Deduction, on the contrary, is obtaining specific conclusions based on knowledge of some general provisions. In other words, this is the movement of our thinking from the general to the specific. But the especially great cognitive significance of deduction is manifested in the case when the general premise is not just an inductive generalization, but some kind of hypothetical assumption, for example, a new scientific idea. In this case, deduction is the starting point for the emergence 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.

Obtaining new knowledge through deduction exists in all natural sciences, but the deductive method is especially important in mathematics. Mathematicians are forced to use deduction most often. And mathematics is, perhaps, the only truly deductive science.

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

Induction and deduction are not used as isolated, separate from each other. Each of these methods is used at the appropriate stage of the cognitive process. Moreover, in the process of using the inductive method, deduction is often present “in a hidden form.”

Analogy is understood as similarity, similarity of some properties, characteristics or relationships of generally different objects. Establishing similarities (or differences) between objects is carried out as a result of their comparison. Thus, comparison is the basis of the analogy method.

Obtaining a correct conclusion by analogy depends on the following factors. Firstly, on the number of common properties of the compared objects. Secondly, from the ease of discovering common properties. Thirdly, on the depth of understanding of the connections between these similar properties. At the same time, it must be borne in mind that if an object in respect of which an inference is made by analogy with another object has some property that is incompatible with the property the existence of which should be concluded, then the general similarity of these objects loses all meaning .

There are different types of inferences by analogy. But what they have in common is that in all cases one object is directly examined, and a conclusion is drawn about another object. Therefore, inference by analogy in the most general sense can be defined as the transfer of information from one object to another. In this case, the first object, which is actually subject to research, is called a model, and the other object, to which the information obtained as a result of studying the first object (model) is transferred, is called the original or prototype. 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).

The analogy method is used in a variety of fields of science: mathematics, physics, chemistry, cybernetics, humanities, etc.

Modeling

The modeling method is based on creating a model that is a substitute for a real object due to a certain similarity with it. The main function of modeling, if we take it in the broadest sense, is to materialize, to objectify the ideal. Building and studying a model is equivalent to researching and constructing a modeled object, with the only difference being that the second is done materially, and the first is done ideally, without affecting the modeled object itself.

The use of modeling is dictated by the need to reveal aspects of objects that either cannot be comprehended through direct study, or are unprofitable to study them in this way for purely economic reasons. A person, for example, cannot directly observe the process of natural formation of diamonds, the origin and development of life on Earth, a number of phenomena of the microworld and macrocosm. Therefore, we have to resort to artificial reproduction of such phenomena in a form convenient for observation and study. In some cases, it is much more profitable and economical to build and study its model instead of directly experimenting with an object.

Depending on the nature of the model, several types of modeling are distinguished. Mental 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 sensory-perceptible physical models. Physical modeling is characterized by physical similarity between the model and the original and aims to reproduce in the model the processes inherent in the original. Based on the results of studying certain physical properties of the model, phenomena occurring in real conditions are judged.

Currently, 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.

Symbolic modeling is associated with a conventionally symbolic representation of some properties, relationships of the original object. Symbolic (sign) models include various topological and graph representations 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 type of symbolic (sign) modeling is mathematical modeling. The symbolic language of mathematics makes it possible to express the properties, aspects, relationships of objects and phenomena of a very different nature. The relationships between various quantities that describe the functioning of such an object or phenomenon can be represented by the corresponding equations (differential, integral, algebraic) and their systems. Numerical modeling is based on a previously created mathematical model of the object or phenomenon being studied and is used in cases of large volumes of calculations required to study this model.

Numerical modeling is especially important where the physical picture of the phenomenon being studied is not entirely clear and the internal mechanism of interaction is not known. By calculating various options on a computer, facts are accumulated, which makes it possible, ultimately, to select the most realistic and probable situations. The active use of numerical modeling methods can dramatically reduce the time required for scientific and design development.

The modeling method is constantly evolving: some types of models are being replaced by others as science progresses. At the same time, one thing remains unchanged: the importance, relevance, and sometimes irreplaceability of modeling as a method of scientific knowledge.

To determine the criteria of natural scientific knowledge, several principles have been formulated in the methodology of science - the principle of verification and the principle of falsification. Formulation of the verification principle: any concept or judgment has meaning if it is reducible to direct experience or statements about it, i.e. empirically verifiable. If it is not possible to find something empirically fixed for such a judgment, then it either represents a tautology or is meaningless. Since the concepts of a developed theory, as a rule, are not reducible to experimental data, a relaxation has been made for them: indirect verification is also possible. For example, it is impossible to indicate an experimental analogue to the concept of “quark”. But the quark theory predicts a number of phenomena that can already be detected experimentally. And thereby indirectly verify the theory itself.

The principle of verification makes it possible, to a first approximation, to distinguish scientific knowledge from clearly unscientific knowledge. However, it cannot help where the system of ideas is tailored in such a way that it can interpret absolutely all possible empirical facts in its favor - ideology, religion, astrology, etc.

In such cases, it is useful to resort to another principle of differentiation between science and non-science, proposed by the greatest philosopher of the 20th century. K. Popper, - the principle of falsification. It states: the criterion for the scientific status of a theory is its falsifiability or falsifiability. In other words, only that knowledge can claim the title of “scientific” that is, in principle, refutable.

Despite its seemingly paradoxical form, this principle has a simple and deep meaning. K. Popper drew attention to the significant asymmetry in the procedures of confirmation and refutation in cognition. No number of falling apples is sufficient to definitively confirm the truth of the law of universal gravitation. However, just one apple flying away from the Earth is enough for this law to be recognized as false. Therefore, it is precisely attempts to falsify, i.e. to refute a theory should be most effective in terms of confirming its truth and scientific character.

A theory that is irrefutable in principle cannot be scientific. The idea of ​​the divine creation of the world is in principle irrefutable. For any attempt to refute it can be presented as the result of the same divine plan, all the complexity and unpredictability of which is simply too much for us to handle. But since this idea is irrefutable, it means that it is outside of science.

It can, however, be noted that the consistently applied principle of falsification makes any knowledge hypothetical, i.e. deprives it of completeness, absoluteness, immutability. But this is probably not a bad thing: it is the constant threat of falsification that keeps science “on its toes” and prevents it from stagnating and resting on its laurels.

Thus, the main methods of the empirical and theoretical level of scientific knowledge were considered. Empirical knowledge includes making observations and experiments. Knowledge begins with observation. To confirm a hypothesis or to study the properties of an object, a scientist places it under certain conditions - conducts an experiment. The block of experimental and observation procedures includes description, measurement, and comparison. At the level of theoretical knowledge, abstraction, idealization, and formalization are widely used. Modeling is of great importance, and with the development of computer technology - numerical modeling, since the complexity and cost of conducting an experiment are increasing.

The work describes two main criteria of natural scientific knowledge – the principle of verification and falsification.

1. Alekseev P.V., Panin A.V. “Philosophy” M.: Prospekt, 2000

2. Leshkevich T.G. “Philosophy of Science: Traditions and Innovations” M.: PRIOR, 2001

3. Ruzavin G.I. “Methodology of scientific research” M.: UNITY-DANA, 1999.

4. Gorelov A.A. “Concepts of modern natural science” - M.: Center, 2003.

5. http://istina.rin.ru/philosofy/text/3763.html

6. http://vsvcorp.chat.ru/mguie/teor.htm

Send your good work in the knowledge base is simple. Use the form below

Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

METHODOLOGY OF SCIENTIFIC RESEARCH IN NATURAL SCIENCE

• Chapter 1. The role of the dialectical method in scientific creativity 3
• Chapter 2. Psychology of scientific creativity 8
• Chapter 3. General scientific research methods 12
• Chapter 4. Main stages of implementation and forecasting of scientific research 20
• Chapter 5. Application of mathematical research methods 23
• in natural science 23
• History of mathematics 23
• Mathematics - the language of science 26
• Using a mathematical method and mathematical result 28
• Mathematics and Environment 30
• Bibliography 35

Chapter 1. The role of the dialectical method in scientific creativity

The concept of “method” (from the Greek “methodos” - the path to something) means a set of techniques and operations for the practical and theoretical development of reality. The method equips a person with a system of principles, requirements, rules, guided by which he can achieve the intended goal. Mastery of a method means for a person knowledge of how, in what sequence to perform certain actions to solve certain problems, and the ability to apply this knowledge in practice. The doctrine of method began to develop in modern science. Its representatives considered the correct method to be a guide in the movement towards reliable, true knowledge. Thus, a prominent philosopher of the 17th century. F. Bacon compared the method of cognition to a lantern illuminating the way for a traveler walking in the dark. And another famous scientist and philosopher of the same period, R. Descartes, outlined his understanding of the method as follows: “By method I mean precise and simple rules, strict adherence to which, without unnecessary waste of mental strength, but gradually and continuously increasing knowledge, contributes to the fact that the mind achieves true knowledge of everything that is available to him." There is a whole field of knowledge that specifically deals with the study of methods and which is usually called methodology. Methodology literally means “the study of methods” (this term comes from two Greek words: “methodos” - method and “logos” - doctrine). By studying the patterns 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, effectiveness and other characteristics of methods of cognition.

The development of science at the present stage is a revolutionary process. Old scientific concepts are being broken down, new concepts are being formed that most fully reflect the properties and connections of phenomena. The role of synthesis and a systematic approach is increasing.

The concept of science covers all areas of scientific knowledge taken in their organic unity. Technical creativity is different from scientific creativity. A feature of technical knowledge is the practical application of objective laws of nature, the invention of artificial systems. Technical solutions are: ship and plane, steam engine and nuclear reactor, modern cybernetic devices and spaceships. Such decisions are based on the laws of hydro-, aero- and thermodynamics, nuclear physics and many others discovered as a result of scientific research.

Science in its theoretical part is the sphere of spiritual (ideal) activity, which arises from material conditions, from production. But science also has the opposite effect on production - the known laws of nature are embodied in various technical solutions.

At all stages of scientific work, the method of dialectical materialism is used, which provides the main direction of research. All other methods are divided into general methods of scientific knowledge (observation and experiment, analogy and hypothesis, analysis and synthesis, etc.) and private scientific (specific) methods used in a narrow field of knowledge or in a separate science. Dialectical and particular scientific methods are interconnected in various techniques and logical operations.

The laws of dialectics reveal the process of development, its nature and direction. In scientific creativity, the methodological function of the laws of dialectics is manifested in the justification and interpretation of scientific research. It ensures comprehensiveness, consistency and clarity of the analysis of the entire situation under consideration. The laws of dialectics allow the researcher to develop new methods and means of cognition and facilitate orientation in a previously unknown phenomenon.

The categories of dialectics (essence and phenomenon, form and content, cause and effect, necessity and chance, possibility and reality) capture important aspects of the real world. They show that cognition is characterized by the expression of the universal, constant, stable, and natural. Through philosophical categories in specific sciences, the world appears unified, all phenomena are interconnected. For example, the relationship between the categories of cause and effect helps the researcher to correctly navigate the tasks of constructing mathematical models based on given descriptions of input and output processes, and the relationship between the categories of necessity and chance - in the mass of events and facts using statistical methods. In scientific creativity, the categories of dialectics never appear in isolation. They are interconnected and interdependent. Thus, the category of essence is important when identifying patterns in a limited number of observations obtained in an expensive experiment. When processing the results of an experiment, it is of particular interest to find out the reasons for the existing patterns and establish the necessary connections.

Knowledge of cause-and-effect relationships allows you to reduce funds and labor costs when conducting experiments.

When designing an experimental setup, the researcher provides for the operation of various contingencies.

The role of dialectics in scientific knowledge is revealed not only through laws and categories, but also through methodological principles (objectivity, knowability, determinism). These principles, guiding researchers towards the most complete and comprehensive reflection of objective properties, connections, trends and laws of knowledge in the scientific problems being developed, are of exceptional importance for shaping the worldview of researchers.

The manifestation of the dialectical method in the process of development of science and scientific creativity can be traced to the connection of new statistical methods with the principle of determinism. Having emerged as one of the essential aspects of materialistic philosophy, determinism was further developed in the concepts of I. Newton and P. Laplace. On the basis of new scientific achievements, this system was improved, and instead of an unambiguous connection between objects and phenomena, statistical determinism was established, allowing for the random nature of connections. The idea of ​​statistical determinism is widely used in various fields of scientific knowledge, marking a new stage in the development of science. It is thanks to the principle of determinism that scientific thought has, in the words of I. P. Pavlov, “prediction and power,” explaining many events in the logic of scientific research.

An important aspect of the dialectics of scientific creativity is foresight, which is the creative development of the theory of reflection. As a result of foresight, a new system of actions is created or previously unknown patterns are discovered. Foresight allows you to form, on the basis of accumulated information, a model of a new situation that does not yet exist in reality. The correctness of foresight is verified by practice. At this stage of the development of science, it is not possible to present a rigorous scheme modeling possible ways of thinking in scientific foresight. However, when carrying out scientific work, one must strive to build a model of at least individual, most labor-intensive fragments of the research, in order to transfer some of the functions to the machine.

The choice of a specific form of theoretical description of physical phenomena in scientific research is determined by certain initial provisions. Thus, when the units of measurement change, the numerical values ​​of the quantities being determined also change. Changing the units of measurement used leads to the appearance of other numerical coefficients

in expressions of physical laws connecting various quantities. The invariance (independence) of these forms of description is obvious. The mathematical relationships that describe the observed phenomenon are independent of the specific reference system. Using the property of invariance, a researcher can conduct experiments not only with really existing objects, but also with systems that do not yet exist in nature and that are created by the imagination of the designer.

The dialectical method pays special attention to the principle of the unity of theory and practice. Being a motivator and source of knowledge, practice simultaneously serves as a criterion for the reliability of truth.

The requirements of the practice criterion should not be taken literally. This is not only a direct experiment that allows you to test a hypothesis, a model of a phenomenon. The results of the study must meet the requirements of practice, i.e. help achieve the goals a person strives for.

Discovering his first law, I. Newton understood the difficulties associated with the interpretation of this law: in the Universe there are no conditions so that forces do not act on a material body. Many years of practical testing of the law have confirmed its impeccability.

Thus, the dialectical method underlying the methodology of scientific research manifests itself not only in interaction with other private scientific methods, but also in the process of cognition. Lighting the way for scientific research, the dialectical method indicates the direction of the experiment, determines the strategy of science, contributing in the theoretical aspect to the formulation of hypotheses and theories, and in the practical aspect - ways to realize the goals of knowledge. By directing science to use the entire wealth of cognitive techniques, the dialectical method allows for the analysis and synthesis of problems being solved and making reasonable predictions for the future.

In conclusion, we cite the words of P. L. Kapitsa, in which the combination of the dialectical method and the nature of scientific research is perfectly expressed: “... the application of dialectics in the field of natural sciences requires an exceptionally deep knowledge of experimental facts and their theoretical generalization. Without this, dialectics in itself cannot "can give a solution to the problem. It is like a Stradivarius violin, the most perfect of violins, but in order to play it, you need to be a musician and know music. Without this, it will be just as out of tune as an ordinary violin." Chapter 2. Psychology of scientific creativity

Considering science as a complex system, dialectics is not limited to the study of the interaction of its elements, but reveals the foundations of this interaction. Scientific activity as a branch of spiritual production includes three main structural elements: work, an object of knowledge and cognitive means. In their mutual dependence, these components form a single system and do not exist outside of this system. Analysis of the connections between components allows us to reveal the structure of scientific activity, the central point of which is the researcher, i.e. subject of scientific knowledge.

Of undoubted interest when studying the research process is the question of the psychology of scientific creativity. The cognitive process is carried out by specific people, and between these people there are certain social connections that manifest themselves in different ways. The work of a scientist is inseparable from the work of his predecessors and contemporaries. In the works of an individual scientist, like in a drop of water, the peculiarities of the science of his time are refracted. The specificity of scientific creativity requires certain qualities of a scientist characteristic of this particular type of cognitive activity.

The force that motivates one to know must be a disinterested thirst for knowledge, enjoyment of the research process, and the desire to be useful to society. The main thing in scientific work is not to strive for discovery, but to deeply and comprehensively explore the chosen field of knowledge. Discovery arises as a side element of research.

The scientist’s plan of action, the uniqueness of the decisions he makes, the reasons for successes and failures depend largely on factors such as observation, intuition, hard work, creative imagination, etc. But the main thing is to have the courage to believe in your results, no matter how much they diverge from the generally accepted ones. A striking example of a scientist who knew how to break any “psychological barriers” is the creator of the first space technology, S.P. Korolev.

The driving force of scientific creativity should not be the desire to make a revolution, but curiosity and the ability to be surprised. There are many cases where surprise, formulated in the form of a paradox, led to discoveries. This is what happened, for example, when A. Einstein created the theory of gravity. A. Einstein’s statement about how discoveries are made is also interesting: everyone knows that something cannot be done, but one person accidentally does not know this, so he makes a discovery.

Of exceptional importance for scientific creativity is the ability to rejoice at every small success, as well as a sense of the beauty of science, which lies in the logical harmony and richness of connections in the phenomenon being studied. The concept of beauty plays an important role in checking the correctness of results and in finding new laws. It represents a reflection in our consciousness of the harmony that exists in nature.

The scientific process is a manifestation of the totality of the listed factors, a function of the researcher’s personality.

The task of science is to find objective laws of nature, and therefore the final result does not depend on the personal qualities of the scientist. However, the methods of cognition may be different; each scientist comes to a solution in his own way. It is known that M.V. Lomonosov, without using mathematical apparatus, without a single formula, was able to discover the fundamental law of conservation of matter, and his contemporary L. Euler thought in mathematical categories. A. Einstein preferred the harmony of logical constructions, and N. Bohr used precise calculations.

A modern scientist needs such qualities as the ability to move from one type of problem to another, the ability to predict the future state of the object being studied or the significance of any methods, and most importantly, the ability to dialectically deny (while preserving everything positive) old systems that interfere with a qualitative change in knowledge, because Without breaking down outdated ideas, it is impossible to create more perfect ones. In cognition, doubt performs two directly opposite functions: on the one hand, it is an objective basis for agnosticism, on the other, it is a powerful stimulus for cognition.

Success in scientific research often accompanies those who look to old knowledge as a condition for moving forward. As the development of science in recent years shows, each new generation of scientists creates most of the knowledge accumulated by humanity. Scientific competition with teachers, and not blind imitation of them, contributes to the progress of science. For a student, the ideal should be not so much the content of knowledge received from the supervisor, but rather his qualities as a person whom one wants to imitate.

Special requirements are placed on a scientist, so he should strive to make the knowledge he has acquired available to his colleagues as quickly as possible, but not allow hasty publications; be sensitive, receptive to new things and defend your ideas, no matter how great the opposition. He must make use of the work of his predecessors and contemporaries, paying meticulous attention to detail; perceive as its first responsibility the education of a new generation of scientists. Young scientists consider it lucky if they manage to undergo an apprenticeship with masters of science, but at the same time they must become independent, achieve independence and not remain in the shadow of their teachers.

The progress of science, characteristic of our time, has led to a new style of work. The romance of collective work has emerged, and the main principle of organizing modern scientific research is its complexity. A new type of scientist is a scientist-organizer, a leader of a large scientific team, capable of managing the process of solving complex scientific problems.

Indicators of the purity of the moral character of outstanding scientists have always been: exceptional conscientiousness, a principled attitude to the choice of direction of research and the results obtained. Therefore, the final authority in science is social practice, the results of which are higher than the opinions of the greatest authorities.

Chapter 3. General scientific research methods

The process of cognition as the basis of any scientific research is a complex dialectical process of gradual reproduction in the human mind of the essence of the processes and phenomena of the surrounding reality. In the process of cognition, a person masters the world, transforms it to improve his life. The driving force and ultimate goal of knowledge is practice that transforms the world on the basis of its own laws.

The theory of knowledge is a doctrine about the laws of the process of cognition of the surrounding world, the methods and forms of this process, about truth, the criteria and conditions of its reliability. The theory of knowledge is the philosophical and methodological basis of any scientific research and therefore every novice researcher should know the basics of this theory. The methodology of scientific research is the doctrine of the principles of construction, forms and methods of scientific knowledge.

Direct contemplation is the first stage of the process of cognition, its sensory (living) stage and is aimed at establishing facts and experimental data. With the help of sensations, perceptions and ideas, a concept of phenomena and objects is created, which manifests itself as a form of knowledge about it.

At the stage of abstract thinking, mathematical apparatus and logical conclusions are widely used. This stage allows science to look ahead into the realm of the unknown, make important scientific discoveries, and obtain useful practical results.

Practice and human production activity are the highest function of science, a criterion for the reliability of conclusions obtained at the stage of abstract theoretical thinking, an important stage in the process of cognition. It allows you to establish the scope of application of the results obtained and correct them. Based on it, a more correct idea is created. The considered stages of the process of scientific knowledge characterize the general dialectical principles of the approach to the study of the laws of development of nature and society. In specific cases, this process is carried out using certain methods of scientific research. A research method is a set of techniques or operations that facilitate the study of the surrounding reality or the practical implementation of any phenomenon or process. The method used in scientific research depends on the nature of the object being studied, for example, the spectral analysis method is used to study radiating bodies.

The research method is determined by the research tools available for a given period. Research methods and tools are closely interconnected and stimulate each other’s development.

In every scientific research, two main levels can be distinguished: 1) empirical, at which the process of sensory perception, establishment and accumulation of facts occurs; 2) theoretical, in which a synthesis of knowledge is achieved, most often manifested in the form of the creation of a scientific theory. In this regard, general scientific research methods are divided into three groups:

1) methods of empirical research;

2) methods of theoretical level of research;

3) methods of empirical and theoretical levels of research - universal scientific methods.

The empirical level of research is associated with performing experiments and observations, and therefore the role of sensory forms of reflection of the surrounding world is great here. The main methods of empirical research include observation, measurement and experiment.

Observation is a purposeful and organized perception of the object of study, which allows one to obtain primary material for its study. This method is used both independently and in combination with other methods. During the process of observation, there is no direct influence of the observer on the object of study. During observations, various devices and instruments are widely used.

For an observation to be fruitful, it must satisfy a number of requirements.

1. It must be conducted for a specific, clearly defined task.

2. First of all, the aspects of the phenomenon that interest the researcher should be considered.

3. Observation must be active.

4. We must look for certain features of the phenomenon, the necessary objects.

5. Observation must be carried out according to the developed plan (scheme).

Measurement is a procedure for determining the numerical value of the characteristics of the material objects under study (mass, length, speed, force, etc.). Measurements are carried out using appropriate measuring instruments and are reduced to comparing the measured value with a reference value. Measurements provide fairly accurate quantitative definitions of the description of the properties of objects, significantly expanding knowledge about the surrounding reality.

Measurement using instruments and tools cannot be absolutely accurate. In this regard, during measurements, great importance is given to assessing the measurement error.

An experiment is a system of operations, influences and observations aimed at obtaining information about an object during research tests, which can be carried out in natural and artificial conditions when the nature of the process changes.

The experiment is used at the final stage of the study and is a criterion for the truth of theories and hypotheses. On the other hand, experiment in many cases is a source of new theoretical concepts developed on the basis of experimental data.

Experiments can be full-scale, model or computer-based. A natural experiment studies phenomena and objects in their natural state. Model - simulates these processes, allows you to study a wider range of changes in determining factors.

In mechanical engineering, both full-scale and computer experiments are widely used. A computer experiment is based on the study of mathematical models that describe a real process or object.

At the theoretical level of research, such general scientific methods as idealization, formalization, hypothesis acceptance, and theory creation are used.

Idealization is the mental creation of objects and conditions that do not exist in reality and cannot be created practically. It makes it possible to deprive real objects of some of their inherent properties or mentally endow them with unreal properties, allowing one to obtain a solution to the problem in its final form. For example, in mechanical engineering technology the concept of an absolutely rigid system, an ideal cutting process, etc. is widely used. Naturally, any idealization is legitimate only within certain limits.

Formalization is a method of studying various objects, in which the basic patterns of phenomena and processes are displayed in symbolic form using formulas or special symbols. Formalization ensures a generalized approach to solving various problems, allows you to form iconic models of objects and phenomena, and establish natural connections between the facts being studied. The symbolism of artificial languages ​​gives brevity and clarity to the recording of meanings and does not allow ambiguous interpretations, which is impossible in ordinary language.

A hypothesis is a scientifically based system of inferences, through which, based on a number of factors, a conclusion is made about the existence of an object, connection or cause of a phenomenon. A hypothesis is a form of transition from facts to laws, an interweaving of everything reliable and fundamentally verifiable. Due to its probabilistic nature, a hypothesis requires testing, after which it is modified, rejected, or becomes a scientific theory.

In its development, the hypothesis goes through three main stages. At the stage of empirical knowledge, factual material is accumulated and certain assumptions are made on its basis. Next, based on the assumptions made, a conjectural theory is developed—a hypothesis is formed. At the final stage, the hypothesis is tested and clarified. Thus, the basis for transforming a hypothesis into a scientific theory is practice.

Theory represents the highest form of generalization and systematization of knowledge. It describes, explains and predicts a set of phenomena in a certain area of ​​reality. The creation of theory is based on the results obtained at the empirical level of research. Then these results at the theoretical level of research are ordered and brought into a coherent system, united by a common idea. Subsequently, using these results, a hypothesis is put forward, which, after successful testing by practice, becomes a scientific theory. Thus, unlike a hypothesis, a theory has an objective basis.

New theories have several basic requirements. A scientific theory must be adequate to the object or phenomenon being described, i.e. must reproduce them correctly. The theory must satisfy the requirement of completeness of description of some area of ​​reality. The theory must be consistent with empirical data. Otherwise, it must be improved or rejected.

There can be two independent stages in the development of a theory: evolutionary, when the theory retains its qualitative certainty, and revolutionary, when its basic initial principles, components of the mathematical apparatus and methodology are changed. Essentially, this leap is the creation of a new theory; it occurs when the possibilities of the old theory have been exhausted.

An idea acts as the initial thought that unites the concepts and judgments included in the theory into an integral system. It reflects the fundamental pattern underlying the theory, while other concepts reflect certain essential aspects and aspects of this pattern. Ideas can not only serve as the basis of a theory, but also link a number of theories into a science, a separate field of knowledge.

A law is a theory that is highly reliable and confirmed by numerous experiments. The law expresses general relationships and connections that are characteristic of all phenomena of a given series or class. It exists independently of people's consciousness.

At the theoretical and empirical levels of research, analysis, synthesis, induction, deduction, analogy, modeling and abstraction are used.

Analysis is a method of cognition that consists in the mental division of the subject of research or phenomenon into component, simpler parts and the identification of its individual properties and connections. Analysis is not the final goal of research.

Synthesis is a method of cognition, consisting in the mental connection of connections between individual parts of a complex phenomenon and knowledge of the whole in its unity. Understanding the internal structure of an object is achieved through the synthesis of the phenomenon. Synthesis complements analysis and is in inextricable unity with it. Without studying the parts, it is impossible to know the whole; without studying the whole through synthesis, it is impossible to fully understand the functions of the parts in the composition of the whole.

In the natural sciences, analysis and synthesis can be carried out not only theoretically, but also practically: the objects under study are actually dissected and combined, their composition, connections, etc. are established.

The transition from analysis of facts to theoretical synthesis is carried out using special methods, among which induction and deduction are the most important.

Induction is a method of transition from knowledge of individual facts to general knowledge, empirical generalization and the establishment of a general position reflecting a law or other essential connection.

The inductive method is widely used in deriving theoretical and empirical formulas in the theory of metalworking.

The inductive method of moving from the particular to the general can be successfully used only if it is possible to verify the results obtained or conduct a special control experiment.

Deduction is a method of moving from general provisions to particular ones, obtaining new truths from known truths using the laws and rules of logic. An important rule of deduction is the following: “If statement A implies statement B, and statement A is true, then statement B is also true.”

Inductive methods are important in sciences where experiment, its generalization, and the development of hypotheses predominate. Deductive methods are primarily used in theoretical sciences. But scientific evidence can only be obtained if there is a close connection between induction and deduction. F. Engels, in this regard, pointed out: “Induction and deduction are related to each other in the same necessary way as synthesis and analysis... We must try to apply each in its place, not lose sight of their connection with each other, their mutual complementarity.” friend."

Analogy is a method of scientific research when knowledge about unknown objects and phenomena is achieved on the basis of comparison with the general characteristics of objects and phenomena that are known to the researcher.

The essence of the conclusion by analogy is as follows: let phenomenon A have signs X1, X2, X3, ..., Xn, Xn+1, and phenomenon B have signs X1, X2, X3, ..., Xn. Therefore, we can assume that phenomenon B also has the characteristic Xn+1. This conclusion introduces a probabilistic character. The probability of obtaining a true conclusion can be increased if there are a large number of similar features in the objects being compared and if there is a deep relationship between these features.

Modeling is a method of scientific knowledge, which consists in replacing the object or phenomenon being studied with a special model that reproduces the main features of the original, and its subsequent study. Thus, when modeling, an experiment is carried out on a model, and the research results are extended to the original using special methods.

Models can be physical or mathematical. In this regard, a distinction is made between physical and mathematical modeling.

In physical modeling, the model and the original have the same physical nature. Any experimental setup is a physical model of a process. The creation of experimental installations and generalization of the results of physical experiments are carried out on the basis of the theory of similarity.

In mathematical modeling, the model and the original can have the same or different physical nature. In the first case, a phenomenon or process is studied on the basis of its mathematical model, which is a system of equations with the corresponding conditions of unambiguity; in the second, the fact that the mathematical description of phenomena of different physical natures is identical in external form is used.

Abstraction is a method of scientific cognition, which consists in mental abstraction from a number of properties, connections, relationships of objects and the selection of several properties or characteristics of interest to the researcher.

Abstraction allows us to replace in the human mind a complex process that nevertheless characterizes the most essential features of an object or phenomenon, which is especially important for the formation of many concepts. Chapter 4. Main stages of implementation and forecasting of scientific research

Considering scientific research work, we can distinguish fundamental and applied research, as well as experimental design developments.

The first stage of scientific research is a detailed analysis of the current state of the problem under consideration. It is performed on the basis of information search with the widespread use of computers. Based on the results of the analysis, reviews and abstracts are compiled, a classification of the main directions is made, and specific research objectives are set.

The second stage of scientific research comes down to solving the problems posed at the first stage using mathematical or physical modeling, as well as a combination of these methods.

The third stage of scientific research is the analysis of the results obtained and their presentation. A comparison of theory and experiment is made, an analysis of the effectiveness of the study, and the possibility of discrepancies is given.

At the present stage of development of science, forecasting scientific discoveries and technical solutions is of particular importance.

In scientific and technical forecasting, three intervals are distinguished: forecasts of the first, second and third echelons. First-tier forecasts are designed for 15-20 years and are compiled on the basis of established trends in the development of science and technology. During this period, there is a sharp increase in the number of scientists and the volume of scientific and technical information, the science-production cycle is completed, and a new generation of scientists will reach the forefront. Second-tier forecasts cover a period of 40-50 years based on qualitative assessments, since over these years the volume of concepts, theories and methods accepted in modern science will practically double. The purpose of this forecast, based on a broad system of scientific ideas, is not economic opportunities, but the fundamental laws and principles of natural science. For third-tier forecasts that are hypothetical in nature, periods of 100 years or more are determined. During such a period, a radical transformation of science may occur, and scientific ideas will appear, many aspects of which are not yet known. These forecasts are based on the creative imagination of prominent scientists, taking into account the most general laws of natural science. History has brought us enough examples when people could foresee the occurrence of important events.

Foresights M.V. Lomonosova, D.I. Mendeleev, K.E. Tsiolkovsky and other major scientists were based on deep scientific analysis.

There are three parts to the forecast: dissemination of already introduced innovations; implementation of achievements that have gone beyond the walls of laboratories; direction of fundamental research. The forecast of science and technology is complemented by an assessment of the social and economic consequences of their development. When forecasting, statistical and heuristic methods of forecasting expert assessments are used. Statistical methods involve constructing a forecast model based on available material, which allows one to extrapolate trends observed in the past into the future. The resulting time series are used in practice due to their simplicity and sufficient reliability of forecasts for short periods of time. That is, statistical methods that make it possible to determine average values ​​characterizing the entire set of subjects being studied. "Using a statistical method, we cannot predict the behavior of a single individual in a population. We can only predict the probability that he will behave in some particular way. Statistical laws can only be applied to large populations, but not to the individual individuals who form these populations" ( A. Einstein, L. Infeld).

Heuristic methods are based on a forecast by interviewing highly qualified specialists (experts) in a narrow field of science, technology, and production.

A characteristic feature of modern natural science is also that research methods increasingly influence its results.

Chapter 5. Application of mathematical research methods

in natural science

Mathematics is a science located, as it were, on the borders of natural science. As a result, it is sometimes considered within the framework of the concepts of modern natural science, but most authors take it beyond this framework. Mathematics should be considered together with other natural science concepts, since it has played a unifying role for individual sciences for many centuries. In this role, mathematics contributes to the formation of stable connections between natural science and philosophy.

History of mathematics

Over the millennia of its existence, mathematics has come a long and complex path, during which its nature, content and style of presentation have repeatedly changed. From the primitive art of calculation, mathematics has evolved into a broad scientific discipline with its own subject of study and specific method of research. She developed her own language, very economical and precise, which turned out to be extremely effective not only within mathematics, but also in numerous areas of its applications.

The primitive mathematical apparatus of those distant times turned out to be insufficient when astronomy began to develop and long-distance travel required methods of orientation in space. Life practice, including the practice of developing natural sciences, stimulated the further development of mathematics.

In Ancient Greece, there were schools in which mathematics was studied as a logically developed science. It, as Plato wrote in his works, should be aimed at knowing not “everything,” but “existence.” Humanity has realized the importance of mathematical knowledge as such, regardless of the tasks of specific practice.

The prerequisites for a new rapid surge and the subsequent ever-increasing progress of mathematical knowledge were created by the era of sea voyages and the development of manufacturing production. The Renaissance, which gave the world an amazing flowering of art, also caused the development of exact sciences, including mathematics, and the teaching of Copernicus appeared. The Church fiercely fought the progress of natural science.

The last three centuries have brought many ideas and results to mathematics, as well as the opportunity for a more complete and in-depth study of natural phenomena. The content of mathematics is constantly changing. This is a natural process, since as we study nature, develop technology, economics and other fields of knowledge, new problems arise, for the solution of which previous mathematical concepts and research methods are not sufficient. There is a need for further improvement of mathematical science, expanding the arsenal of its research tools.

Applied Mathematics

Astronomers and physicists understood earlier than others that mathematical methods for them are not only methods of calculation, but also one of the main ways to penetrate into the essence of the laws they study. In our time, many sciences and areas of natural science, which until recently were far from the use of mathematical means, are now intensively

They will rush to catch up. The reason for such attention to mathematics is that a qualitative study of natural phenomena, technology, and economics is often insufficient. How can you create an automatically operating machine if there are only general ideas about the duration of the aftereffect of transmitted impulses on the elements? How can one automate the process of steel smelting or oil cracking without knowing the exact quantitative laws of these processes? That is why automation causes further development of mathematics, honing its methods to solve a huge number of new and difficult problems.

The role of mathematics in the development of other sciences and in practical areas of human activity cannot be established for all times. Not only those issues that require prompt resolution are changing, but also the nature of the problems being solved. By creating a mathematical model of a real process, we inevitably simplify it and study only its approximate scheme. As our knowledge is refined and the role of previously unspecified factors is clarified, the mathematical description of the process can be made more complete. The clarification procedure cannot be limited, just as the development of knowledge itself cannot be limited. Mathematization of science does not consist in excluding observation and experiment from the process of knowledge. They are indispensable components of a full-fledged study of the phenomena of the world around us. The meaning of mathematization of knowledge is to derive consequences that are inaccessible to direct observation from precisely formulated initial premises; using the mathematical apparatus, not only describe established facts, but also predict new patterns, forecast the course of phenomena, and thereby gain the ability to control them.

Mathematization of our knowledge consists not only in using ready-made mathematical methods and results, but in starting the search for that specific mathematical apparatus that would allow us to most fully describe the range of phenomena that interest us, and to derive new consequences from this description in order to confidently use the features of these phenomena in practice. This happened at a time when the study of motion became an urgent necessity, and Newton and Leibniz completed the creation of the principles of mathematical analysis. This mathematical apparatus is still one of the main tools of applied mathematics. Nowadays, the development of control theory has led to a number of outstanding mathematical studies, which lay the foundations for optimal control of deterministic and random processes.

The twentieth century dramatically changed ideas about applied mathematics. If earlier the arsenal of applied mathematics included arithmetic and elements of geometry, then the eighteenth and nineteenth centuries added powerful methods of mathematical analysis to them. In our time, it is difficult to name at least one significant branch of modern mathematics that, to one degree or another, would not find applications in the great ocean of applied problems. Mathematics is a tool for understanding nature and its laws.

When solving practical problems, general techniques are developed that make it possible to cover a wide range of different issues. This approach is especially important for the progress of science. This benefits not only this area of ​​applications, but also all others, and first of all theoretical mathematics itself. It is this approach to mathematics that makes one look for new methods, new concepts that can cover a new range of problems; it expands the field of mathematical research. The last decades have given us many examples of this kind. To be convinced of this, it is enough to recall the appearance in mathematics of such now central branches as the theory of random processes, information theory, the theory of optimal process control, the theory of queuing, and a number of areas related to electronic computers.

Mathematics is the language of science

For the first time, the great Galileo Galilei said clearly and clearly about mathematics, as the language of science, four hundred years ago: “Philosophy is written in a grandiose book, which is always open to everyone - I’m talking about nature. But only those who have learned to understand it can understand it.” the language and signs with which it is written. It is written in a mathematical language, and the signs are its mathematical formulas." There is no doubt that since then science has made enormous progress and mathematics has been its faithful assistant. Without mathematics, many advances in science and technology would simply be impossible. It is not for nothing that one of the leading physicists, W. Heisenberg, described the place of mathematics in theoretical physics as follows: “The primary language that is developed in the process of scientific assimilation of facts is usually the language of mathematics in theoretical physics, namely a mathematical scheme that allows physicists to predict the results of future experiments."

To communicate and express their thoughts, people have created the greatest spoken means - a living spoken language and its written recording. Language does not remain unchanged, it adapts to living conditions, enriches itself with vocabulary, and develops new means for expressing the subtlest shades of thought.

In science, clarity and precision in the expression of thoughts is especially important. The scientific presentation should be brief, but quite definite. That is why science is obliged to develop its own language, capable of conveying its peculiarities as accurately as possible. The famous French physicist Louis de Broglie said beautifully: “... where a mathematical approach can be applied to problems, science is forced to use a special language, a symbolic language, a kind of shorthand for abstract thought, the formulas of which, when correctly written, apparently do not leave There is no room for any uncertainty or any imprecise interpretation." But we must add to this that mathematical symbolism not only leaves no room for inaccuracy of expression and vague interpretation, mathematical symbolism also makes it possible to automate the implementation of those actions that are necessary to obtain conclusions.

Mathematical symbolism allows you to reduce the recording of information, making it visible and convenient for subsequent processing.

In recent years, a new line in the development of formalized languages ​​has emerged, associated with computer technology and the use of electronic computers to control production processes. It is necessary to communicate with the machine; it is necessary to present it with the opportunity at each moment to independently choose the correct action under the given conditions. But the machine does not understand ordinary human speech; you need to “talk” to it in a language that it understands. This language should not allow for different interpretations, uncertainty, insufficiency or excessive redundancy of the information provided. Currently, several language systems have been developed with the help of which the machine unambiguously perceives the information communicated to it and acts taking into account the current situation. This is what makes electronic computers so flexible when performing complex computational and logical operations.

Use of mathematical method and mathematical result

There are no natural phenomena, technical or social processes that would be the subject of the study of mathematics, but would not be related to physical, biological, chemical, engineering or social phenomena. Each natural scientific discipline: biology and physics, chemistry and psychology - is determined by the material features of its subject, the specific features of the area of ​​​​the real world that it studies. The object or phenomenon itself can be studied by different methods, including mathematical ones, but by changing the methods, we still remain within the boundaries of this discipline, since the content of this science is the real object, and not the research method. For mathematics, the material subject of research is not of decisive importance; the method used is important. For example, trigonometric functions can be used both to study oscillatory motion and to determine the height of an inaccessible object. What real world phenomena can be studied using the mathematical method? These phenomena are determined not by their material nature, but exclusively by their formal structural properties and, above all, by the quantitative relationships and spatial forms in which they exist.

A mathematical result has the property that it can not only be used in the study of one particular phenomenon or process, but also used to study other phenomena, the physical nature of which is fundamentally different from those previously considered. Thus, the rules of arithmetic are applicable in economic problems, in technological processes, in solving agricultural problems, and in scientific research.

Mathematics as a creative force has as its goal the development of general rules that should be used in numerous special cases. The one who creates these rules creates something new, creates. Anyone who applies ready-made rules in mathematics itself no longer creates, but creates new values ​​in other areas of knowledge with the help of mathematical rules. Nowadays, interpretation data from space images, as well as information about the composition and age of rocks, geochemical, geographical and geophysical anomalies are processed using a computer. There is no doubt that the use of computers in geological research leaves these studies geological. The principles of computer operation and their software were developed without taking into account the possibility of their use in the interests of geological science. This possibility itself is determined by the fact that the structural properties of geological data are in accordance with the logic of certain computer programs.

Mathematical concepts are taken from and related to the real world. In essence, this explains the amazing applicability of the results of mathematics to the phenomena of the world around us.

Mathematics, before studying any phenomenon using its own methods, creates its mathematical model, i.e. lists all the features of the phenomenon that will be taken into account. The model forces the researcher to choose those mathematical tools that will allow him to adequately convey the features of the phenomenon being studied and its evolution.

Let's take a model of a planetary system as an example. The sun and planets are considered as material points with corresponding masses. The interaction of every two points is determined by the force of attraction between them. The model is simple, but for more than three hundred years it has been conveying with great accuracy the features of the movement of the planets of the Solar system.

Mathematical models are used in the study of biological and physical natural phenomena.

Mathematics and Environment

Everywhere we are surrounded by movement, variables and their relationships. Various types of movement and their patterns constitute the main object of study of specific sciences: physics, geology, biology, sociology and others. Therefore, precise language and corresponding methods for describing and studying variable quantities turned out to be necessary in all areas of knowledge to approximately the same extent as numbers and arithmetic are necessary in the description of quantitative relationships. Mathematical analysis forms the basis of the language and mathematical methods for describing variables and their relationships. Nowadays, without mathematical analysis it is impossible not only to calculate space trajectories, the operation of nuclear reactors, the movement of ocean waves and patterns of cyclone development, but also to economically manage production, resource distribution, organization of technological processes, predict the course of chemical reactions or changes in the number of various species of animals and plants interconnected in nature, because all of these are dynamic processes.

One of the most interesting applications of modern mathematics is called catastrophe theory. Its creator is one of the world's outstanding mathematicians, Rene Tom. Thom's theory is essentially a mathematical theory of processes with "jumps". It shows that the occurrence of “jumps” in continuous systems can be described mathematically and changes in type can be predicted qualitatively. Models built on the basis of catastrophe theory have already led to useful insights into many real-life cases: in physics (an example is the breaking of waves on water), physiology (the action of heart contractions or nerve impulses) and social sciences. The prospects for the application of this theory, most likely in biology, are enormous.

Mathematics made it possible to deal with other practical issues that required not only the use of existing mathematical tools, but also the development of mathematical science itself.

Similar documents

Empirical, theoretical and production-technical forms of scientific knowledge. The use of special methods (observation, measurement, comparison, experiment, analysis, synthesis, induction, deduction, hypothesis) and private scientific methods in natural science.

abstract, added 03/13/2011


The essence of the principle of systematicity in natural science. Description of the ecosystem of a fresh water body, deciduous forest and its mammals, tundra, ocean, desert, steppe, gully lands. Scientific revolutions in natural science. General methods of scientific knowledge.

test, added 10/20/2009


Study of the concept of scientific revolution, global change in the process and content of the system of scientific knowledge. Aristotle's geocentric system of the world. Studies of Nicolaus Copernicus. Johannes Kepler's laws of planetary motion. The main achievements of I. Newton.

presentation, added 03/26/2015


Basic methods of isolating and studying an empirical object. Observation of empirical scientific knowledge. Techniques for obtaining quantitative information. Methods that involve working with the information received. Scientific facts of empirical research.

abstract, added 03/12/2011


Methodology of natural science as a system of human cognitive activity. Basic methods of scientific study. General scientific approaches as methodological principles of cognition of integral objects. Modern trends in the development of natural science studies.

abstract, added 06/05/2008


Synergetics as a theory of self-organizing systems in the modern scientific world. History and logic of the emergence of a synergetic approach in natural science. The influence of this approach on the development of science. Methodological significance of synergetics in modern science.

abstract, added 12/27/2016


Comparison, analysis and synthesis. Main achievements of scientific and technological revolution. Vernadsky's concept of the noosphere. The origin of life on earth, basic principles. Environmental problems of the Kurgan region. The importance of natural science for the socio-economic development of society.

test, added 11/26/2009


The essence of the process of natural science knowledge. Special forms (sides) of scientific knowledge: empirical, theoretical and production and technical. The role of scientific experiment and mathematical research apparatus in the system of modern natural science.

report, added 02/11/2011


Application of mathematical methods in natural science. Periodic law D.I. Mendeleev, his modern formulation. Periodic properties of chemical elements. Theory of atomic structure. Main types of ecosystems according to their origin and energy source.

abstract, added 03/11/2016


Development of science in the twentieth century. under the influence of the revolution in natural science at the turn of the 19th–20th centuries: discoveries, their practical application - telephone, radio, cinema, changes in physics, chemistry, development of interdisciplinary sciences; Psyche, intelligence in philosophical theories.

Methods of science are a set of techniques and operations for practical and theoretical knowledge of reality.

Research methods optimize human activities and equip them with the most rational ways of organizing activities. A.P. Sadokhin, in addition to highlighting the levels of knowledge when classifying scientific methods, takes into account the criterion of applicability of the method and identifies general, special and particular methods of scientific knowledge. The selected methods are often combined and combined during the research process.

General methods of cognition relate to any discipline and make it possible to connect all stages of the cognition process. These methods are used in any field of research and make it possible to identify connections and characteristics of the objects under study. In the history of science, researchers include metaphysical and dialectical methods among such methods. Private methods of scientific knowledge are methods used only in a particular branch of science. Various methods of natural science (physics, chemistry, biology, ecology, etc.) are particular in relation to the general dialectical method of cognition. Sometimes private methods can be used outside the branches of natural science in which they originated.

For example, physical and chemical methods are used in astronomy, biology, and ecology. Often researchers apply a complex of interrelated private methods to the study of one subject. For example, ecology simultaneously uses the methods of physics, mathematics, chemistry, and biology. Particular methods of cognition are associated with special methods. Special methods examine certain characteristics of the object being studied. They can manifest themselves at the empirical and theoretical levels of knowledge and be universal.

Among the special empirical methods of cognition are observation, measurement and experiment.

Observation is a purposeful process of perceiving objects of reality, a sensory reflection of objects and phenomena, during which a person receives primary information about the world around him. Therefore, research most often begins with observation, and only then do researchers move on to other methods. Observations are not associated with any theory, but the purpose of observation is always related to some problem situation.

Observation presupposes the existence of a specific research plan, an assumption that is subject to analysis and verification. Observations are used where direct experiments cannot be performed (in volcanology, cosmology). The results of the observation are recorded in a description, noting those signs and properties of the object being studied that are the subject of study. The description must be as complete, accurate and objective as possible. It is the descriptions of observation results that constitute the empirical basis of science; on their basis, empirical generalizations, systematization and classification are created.

Measurement is the determination of quantitative values ​​(characteristics) of the studied aspects or properties of an object using special technical devices. The units of measurement with which the data obtained are compared play an important role in the study.

An experiment is a method of cognition by which phenomena of reality are studied under controlled and controlled conditions. It differs from observation by intervention in the object under study, that is, activity in relation to it. When conducting an experiment, the researcher is not limited to passive observation of phenomena, but consciously intervenes in the natural course of their occurrence by directly influencing the process under study or changing the conditions in which this process takes place.

The development of natural science raises the problem of the rigor of observation and experiment. The fact is that they need special tools and devices, which have recently become so complex that they themselves begin to influence the object of observation and experiment, which, according to the conditions, should not be the case. This primarily applies to research in the field of microworld physics (quantum mechanics, quantum electrodynamics, etc.).

Analogy is a method of cognition in which the transfer of knowledge obtained during the consideration of any one object occurs to another, less studied and currently being studied. The analogy method is based on the similarity of objects according to a number of characteristics, which allows one to obtain completely reliable knowledge about the subject being studied.

The use of the analogy method in scientific knowledge requires some caution. Here it is extremely important to clearly identify the conditions under which it works most effectively. However, in cases where it is possible to develop a system of clearly formulated rules for transferring knowledge from a model to a prototype, the results and conclusions using the analogy method acquire evidentiary force.

Analysis is a method of scientific knowledge, which is based on the procedure of mental or real division of an object into its constituent parts. Dismemberment aims to move from the study of the whole to the study of its parts and is carried out by abstracting from the connection of the parts with each other.

Synthesis is a method of scientific knowledge, which is based on the procedure of combining various elements of a subject into a single whole, a system, without which truly scientific knowledge of this subject is impossible. Synthesis acts not as a method of constructing the whole, but as a method of representing the whole in the form of a unity of knowledge obtained through analysis. In synthesis, there is not just a unification, but a generalization of the analytically identified and studied features of the object. The provisions obtained as a result of synthesis are included in the theory of the object, which, enriched and refined, determines the path of new scientific research.

Induction is a method of scientific knowledge, which is the formulation of a logical conclusion by summarizing observational and experimental data.
Deduction is a method of scientific knowledge, which consists in the transition from certain general premises to particular results and consequences.
The solution to any scientific problem involves putting forward various guesses, assumptions, and most often more or less substantiated hypotheses, with the help of which the researcher tries to explain facts that do not fit into old theories. Hypotheses arise in uncertain situations, the explanation of which becomes relevant for science. In addition, at the level of empirical knowledge (as well as at the level of its explanation), there are often contradictory judgments. To resolve these problems, hypotheses are required.

A hypothesis is any assumption, guess or prediction put forward to eliminate a situation of uncertainty in scientific research. Therefore, a hypothesis is not reliable knowledge, but probable knowledge, the truth or falsity of which has not yet been established.
Any hypothesis must be justified either by the achieved knowledge of a given science or by new facts (uncertain knowledge is not used to substantiate the hypothesis). It must have the property of explaining all facts that relate to a given field of knowledge, systematizing them, as well as facts outside this field, predicting the emergence of new facts (for example, the quantum hypothesis of M. Planck, put forward at the beginning of the 20th century, led to the creation of a quantum mechanics, quantum electrodynamics and other theories). Moreover, the hypothesis should not contradict existing facts. A hypothesis must either be confirmed or refuted.

c) private methods are methods that operate either only within a particular branch of natural science, or outside the branch of natural science where they arose. This is the method of bird ringing used in zoology. And the methods of physics used in other branches of natural science led to the creation of astrophysics, geophysics, crystal physics, etc. A complex of interrelated private methods is often used to study one subject. For example, molecular biology simultaneously uses the methods of physics, mathematics, chemistry, and cybernetics.

Modeling is a method of scientific knowledge based on the study of real objects through the study of models of these objects, i.e. by studying substitute objects of natural or artificial origin that are more accessible to research and (or) intervention and have the properties of real objects.

The properties of any model should not, and cannot, accurately and completely correspond to absolutely all the properties of the corresponding real object in all situations. In mathematical models, any additional parameter can lead to a significant complication of solving the corresponding system of equations, to the need to apply additional assumptions, discard small terms, etc., with numerical modeling, the processing time of the problem by a computer disproportionately increases, and the calculation error increases.

The variety of methods of scientific knowledge creates difficulties in their application and understanding of their role. These problems are solved by a special field of knowledge - methodology. The main objective of the methodology is to study the origin, essence, effectiveness, and development of methods of cognition.