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

Empirical level of scientific knowledge characterized by direct exploration of real-life, sensory-perceptible objects. The special role of empirics in science lies in the fact that only at this level of research we deal with the direct interaction of a person with the natural or social objects being studied. Living contemplation (sensory cognition) predominates here; the rational element and its forms (judgments, concepts, etc.) are present here, but have a subordinate significance. Therefore, the object under study is reflected primarily from its external connections and manifestations, accessible to living contemplation and expressing internal relationships. At this level, the process of accumulating information about the objects and phenomena under study is carried out by conducting observations, performing various measurements, and delivering experiments. Here, the primary systematization of the obtained factual data is also carried out in the form of tables, diagrams, graphs, etc. In addition, already at the second level of scientific knowledge - as a consequence of the generalization of scientific facts - it is possible to formulate some empirical patterns.

Theoretical level of scientific knowledge characterized by the predominance of the rational moment - concepts, theories, laws and other forms and “mental operations”. The lack of direct practical interaction with objects determines the peculiarity that an object at a given level of scientific knowledge can only be studied indirectly, in a thought experiment, but not in a real one. However, living contemplation is not eliminated here, but becomes a subordinate (but very important) aspect of the cognitive process.
At this level, the most profound essential aspects, connections, patterns inherent in the objects and phenomena being studied are revealed by processing the data of empirical knowledge. This processing is carried out using systems of “higher order” abstractions - such as concepts, inferences, laws, categories, principles, etc. However, at the theoretical level we will not find a fixation or abbreviated summary of empirical data; theoretical thinking cannot be reduced to the summation of empirically given material. It turns out that theory does not grow out of empirics, but as if next to it, or rather, above it and in connection with it.”
The theoretical level is a higher level in scientific knowledge. “The theoretical level of knowledge is aimed at the formation of theoretical laws that meet the requirements of possibility and necessity, i.e. operate everywhere and always.” The results of theoretical knowledge are hypotheses, theories, laws.
While distinguishing these two different levels in scientific research, one should not, however, separate them from each other and oppose them. After all, the empirical and theoretical levels of knowledge are interconnected. The empirical level acts as the basis, the foundation of the theoretical. Hypotheses and theories are formed in the process of theoretical understanding of scientific facts and statistical data obtained at the empirical level. In addition, theoretical thinking inevitably relies on sensory-visual images (including diagrams, graphs, etc.), with which the empirical level of research deals.
In turn, the empirical level of scientific knowledge cannot exist without achievements at the theoretical level. Empirical research is usually based on a certain theoretical construct, which determines the direction of this research, determines and justifies the methods used.
According to K. Popper, the belief that we can begin scientific research with “pure observations” without having “something resembling a theory” is absurd. Therefore, some conceptual perspective is absolutely necessary. Naive attempts to do without it can, in his opinion, only lead to self-deception and the uncritical use of some unconscious point of view.
The empirical and theoretical levels of knowledge are interconnected, the boundary between them is conditional and fluid. Empirical research, revealing new data through observations and experiments, stimulates theoretical knowledge (which generalizes and explains them), and poses new, more complex tasks. On the other hand, theoretical knowledge, developing and concretizing its own new content on the basis of empirics, opens up new, broader horizons for empirical knowledge, orients and directs it in the search for new facts, contributes to the improvement of its methods and means, etc.
The third group of methods of scientific knowledge includes methods used only within the framework of research of a specific science or a specific phenomenon. Such methods are called private scientific methods. Each special science (biology, chemistry, geology, etc.) has its own specific research methods.
At the same time, private scientific methods, as a rule, contain certain general scientific methods of cognition in various combinations. Particular scientific methods may include observations, measurements, inductive or deductive inferences, etc. The nature of their combination and use depends on the research conditions and the nature of the objects being studied. Thus, specific scientific methods are not divorced from general scientific ones. They are closely related to them and include the specific application of general scientific cognitive techniques for studying a specific area of ​​the objective world. At the same time, particular scientific methods are also connected with the universal, dialectical method, which seems to be refracted through them.

As mentioned above, the theoretical level of science is qualitatively different from the empirical level. First of all, there is no direct interaction of the researcher with objects of the real world. Objects of theoretical knowledge are abstractions. Theoretical cognition explores the symbolic or sign-

whole field of scientific thinking. A significant difference between objects of theoretical knowledge is their idealized character. These are the results ultimate a type of abstraction (distraction) from the properties of real objects. The resulting products may be things that do not exist and, in principle, cannot exist in reality. In nature there are no ideal gases, material points, or absolutely solid bodies. A “material point” is a body that has mass but lacks extension. An “absolutely solid body” never, under any circumstances, changes its shape. Despite the fact that such bodies do not exist, and the corresponding concepts demonstrate more “flight” than “departure” from reality, science successfully operates with them, formulating laws, building high-level theories.

The point is that these idealized objects are not completely subjective fantasy. Under certain circumstances they can be interpreted in terms real objects. One of the reasons for this is the adequate execution of the abstraction procedure. This includes the highly professional use of scientific language, which accurately expresses the relationships between universal, specific and individual terms. An important condition for the functional fruitfulness of idealized objects is their relationships, connections, consistency. In the process of systematization, idealized objects form certain specific logical images, reproducing reality in the main features, the main development trends. At this level of thinking, it can form arbitrarily voluminous systems of knowledge, up to scientific picture of the world.

To the theoretical methods scientific knowledge should be attributed abstraction and its types, idealization, induction, deduction formalization, axiomatic method, hypothetico-deductive method etc.

Abstraction(Latin abstrahere - distract) - highlighting essential features, aspects, properties, connections of an object from unimportant, random ones. In the process of abstraction, a mental image is created in which the totality of essential aspects of a phenomenon or process is reproduced. Abstract the image has ideal content and a certain iconic form. It doesn't match specific phenomena and does not oppose them. Their relationship can be expressed through the categories of abstract and concrete, essence and phenomenon, content and form. With the help of a grid of these categories, it is possible to philosophically determine the differences between a sensory image (image of perception) and a rational (logical image), scientific and artistic

physical, empirical (abstract image, for example, view animals) and theoretical (image concrete universality - theory of relativity or scientific picture of the world). The theoretical concrete is already an image created by reflection on the abstract. It represents the form of our thoughts, in which the essential connections of reality, its laws and development trends are expressed.

The result of abstraction is abstraction. “The methods of forming an abstraction (for example, a general concept) and the methods of abstraction and distraction can be very different. It all depends on what real objects you have to deal with and what specific goal is set before abstraction. If it is necessary to form a general concept about a certain class of objects, then in this case the abstraction of identification is usually used, when one mentally abstracts from the dissimilar, different characteristics of objects of this class, and at the same time selects common characteristics inherent in all objects, and such common characteristics that distinguish this class from all other classes. This method of abstraction is therefore called the abstraction of identification because in the course of abstraction the identity of objects of this class is established by common features. Sometimes this type of abstraction is called a generalizing abstraction.” 47

There are many abstractions, different both in form and content. Abstraction can appear in the form of a sensory image, concept, judgment, category. In modern science, the abstractness of many concepts is deepening. They act as abstractions from higher order abstractions. New concepts and logical models appear: “formal neutron”, “formal nervous network”, “black box” - in cybernetic modeling; “vacuum bag”, “string” model, explaining the impossibility of knocking out a free quark from a hadron. A quark feature was introduced - “color” (hence one of the major physical achievements of the second half of the 20th century - chromodynamics). Thus, the “string model”, which is a pair of quarks (they are called sea quarks), which have a tension that holds them in the “bowels” of hadrons, was created by scientists at Moscow State University and was recently used to describe the properties of such a complex natural phenomenon as widespread air showers in cosmic rays.

Scientific abstractions ultimately reflect reality, and their criterion is practice. Thus, F. Engels wrote: “Marx reduces the general content that lies in things and relationships to his most generalized thought.

line expression. His abstraction, therefore, only reflects in the form of thought the content that is already contained in 9 things.” 48

The most frequently used abstractions (isolating or analytical, abstraction of identification, abstraction of potential feasibility) perform the functions of a method of theoretical knowledge. Isolating abstraction - This is a type of abstraction in which the properties denoted by a certain name (for example, heat capacity, immobility) are abstracted from other objects and properties with which the given name is inextricably linked. As a result of isolating abstraction, abstract general concepts, representing units of scientific language, with the help of which analytical and other thinking operations are carried out.

Abstraction of identification - this kind of it, where there is a distraction from differences in objects and their properties and focuses on similarity. As a result, it becomes possible to present a whole series of objects as one and the same object. This type of abstraction produces general concepts that serve as the basis generalizations objects and their properties.

Abstractions often used in logic and mathematics are of interest - abstraction of actual infinity And abstraction of potential infinity. The first is a distraction from the incompleteness of processes the formation of any constructive set. It is believed that the object completed, since it exists and all the basic parameters are given to it. For example, this object is the set of real numbers contained between 0 and 1. This set is actually infinite, despite the fact that it has a “beginning” and an “end”. The meaning of infinity here is that there is no end to the recalculation, and the relevance is expressed in the fact that all numbers are given at the same time. Abstraction of potential infinity is a logical-mathematical method that is based on the assumption of the potential feasibility of constructive processes. Examples of its application are the assumptions that one can be added to any natural number, that no matter how large these numbers are, they can be added. The need to use this method is realized in computational mathematics, computer science, and cybernetics.

Idealization has already been discussed above in connection with the characteristics of the object of theoretical knowledge. This is the ultimate type of abstraction, distraction, as a result of which concepts are formed, the content of which does not include the essential features of the displayed objects. Analogues of these concepts in the real world

there may not be one at all. However, such concepts play a large methodological and prognostic role in science. They are widely used in methods formalization. Formalization is the process of constructing abstract mathematical models that reveal the essence of the phenomena of reality. It involves the use of special symbols. Instead of a real object - symbols, signs. Knowledge of the alphabet, rules for obtaining formulas, and rules of “inference” are required. From the middle of the 19th century, mathematical logic began to be used here.

Axiomatic method is the construction of theories based on axioms. An axiom, as we know, is a self-evident truth that does not require proof. Its functional significance in scientific knowledge is expressed in the fact that it acts as a starting point, the initial position underlying the proof of other provisions (theorems) of a scientific theory, within which it is accepted without proof. The beginning of the axiomatic method is associated with Euclid. Based on the axiom, a logical conclusion is drawn, the truth is transferred from the axiom to the consequences. Euclid’s “Principles” represent meaningful axiomatics. Here the “rules” have not yet been fixed, since they are also obvious. Next, there was a transition to formal axiomatics, and then to formalized mathematics. Axioms are considered as primary concepts. And the means is mathematical logic. The axiomatic system is constructed as a special formalized language, calculus. Great successes have given rise to the idea of development scientific knowledge using purely formal means. However, in the 30s of the XX century. K. Gödel proved the limitations of developed formal systems. There are limits to the applicability of the axiomatic method.

Hypothetico-deductive method used in creating a system of deductively interconnected hypotheses from which statements about empirical facts are derived. “Hypothesis, translated from Greek - basis, assumption - 1) a justified (incomplete) assumption about the causes of a phenomenon, about unobservable connections between phenomena, etc., 2) a process of cognition, which consists in putting forward an assumption, its justification (incomplete ) and proof or refutation.” 49 The assumption can be made on the basis analogy or incomplete induction. However, in this way, as a rule, it is difficult to make any justification, so such an assumption cannot yet be called a scientific hypothesis. In order for an assumption to be considered a hypothesis, it is necessary, based on this idea, explain existing facts, make a forecast, explain new facts.

A hypothesis as a tool of scientific knowledge must satisfy a number of regulatory requirements. The proposed idea should not contradict the fundamental principles of science. Nevertheless, in a certain sense, such contradictions (if they are resolved) can give rise not just to a new theory, but also to an entire scientific direction. For example, the idea of ​​intuitionistic mathematics, which is based on the concept of potential infinity, was and is in conflict with the axiomatic method that mathematics has traditionally used. But this applies more to fundamental ideas, the proof of which is extremely difficult. And both the formation of a hypothesis and its testing sometimes take a long historical time. Such ideas that require a qualitative restructuring of any major theory or physical (cosmic) picture of the world include the “idea of ​​relativity” (wandering in the minds of scientists for three hundred years: G. Galileo, E. Mach, A. Poincaré, A. Einstein ), “wave theory of light” (H. Huygens, Louis de Broglie), “idea of ​​gene divisibility” (N.P. Dubinin), etc.

When we are talking about the development of science in an evolutionary mode, the requirement consistency hypothesis is the norm.

An important requirement for the proposed assumption, which can subsequently be considered as a scientific hypothesis, is its verifiability. Distinguish practical verifiability and principled. In the first case, it is possible to practically test the assumption and recognize it as a hypothesis. For example, the idea of ​​“gene divisibility” was unrecognized for ten years. But it turned out to be completely testable during the scientist’s life. In the second case, the possibility of verification exists in principle. This could happen at any time, perhaps in the distant future. As mentioned above, guesses that are of fundamental importance sometimes cannot be verified for centuries and even millennia. For example, the idea of ​​heliocentrism was expressed by the famous ancient astronomer Eratosthenes (2nd century BC). After 18 centuries, this idea acquired the status of a hypothesis among N. Copernicus. And then in the “celestial laws” of I. Kepler and with the help of telescopes of G. Galileo and I. Newton, it became a scientific fact. If an idea cannot in principle be proven or disproved, it cannot be interpreted as a scientific hypothesis.

The new idea put forward should cover as many facts as possible. Otherwise there is no point in it. The wider the application area, the greater the possible significance of the proposed idea. This regulatory requirement is called the principle of simplicity. It consists in the absence of facts (in the field of application

ideas) that she could not explain. Based on this principle, it is possible to compare hypothetical ideas and select the simplest one.

Satisfaction of the listed regulatory requirements corresponds to the recognition of a new idea as a scientific hypothesis. Recognized hypothetical ideas vary in nature. They, like all scientific knowledge, can be represented by goals and levels. Eat factual hypotheses, the purpose of which is, on the basis of an accepted assumption, to anticipate and discover any new objects, phenomena, processes. A classic example is often cited here with the discovery of the planet Neptune based on the assumption of the cause of a gravitational disturbance that changes the trajectory of the planet Uranus. The hypothesis thus becomes proven.

Another type of hypothesis differs in purpose build a theory presupposing certain patterns. Such a hypothesis is called theoretical. Constructed deductively, a hypothetical theory can be considered proven if it can be used to explain many heterogeneous facts, including the prediction and discovery of new facts and phenomena. This makes the hypothesis stable and reliable. It can function proven (not completely) for quite a long time until a new, more effective theoretical system appears.

A theory constructed using the hypothetico-deductive method may not be tested for some time. But there are situations when the core of the design must be revised. As a rule, several competing theories arise, with different bases and research patterns. The winner is the one that describes the most facts and demonstrates forecasting capabilities.

Thus, we have analyzed general scientific and “level” methods of cognition, which allow modern science to develop very intensively. The evolution of science has its own logic. The nature of the development of scientific knowledge at different levels has its own characteristics.

Empirical knowledge is characterized by a cumulative nature. A negative result is included in the general information collection and contributes to the development of science. The theoretical level has a spasmodic character, and each new theory represents a qualitative transformation of the knowledge system. The most widespread now is the so-called paradigmatic concept of scientific knowledge, put forward and developed by T. Kuhn. It has already been discussed above. Paradigm - the main research

body installation based on a number of principles and component sample research, including methods, technology, instrumental and material support, is a structural unit of scientific knowledge. This unit is of a higher level of generalization than a separate theory. An even higher structural formation is the scientific picture of the world, which unites the most significant scientific ideas of the era. It includes as a basis a number of fundamental principles (basic provisions) expressing the unity of a diverse world.

It makes sense to talk about three historically special pictures of the world: essential pre-scientific, mechanistic and evolutionary, in which science is viewed as a complex, open system.

End of work -

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Actually theoretical methods of scientific knowledge

General logical methods

"Scientific hypothesis

always works out

beyond the facts

which served as the basis

to build it"

V.I.Vernadsky

The actual theoretical methods of scientific knowledge include axiomatic, hypothetical and formalization. There are also methods that are used both at the empirical and theoretical levels of scientific knowledge: general logical methods (analysis, synthesis, induction, deduction, analogy), modeling, classification, abstraction, generalization, historical method.

1. The actual theoretical methods of scientific knowledge

Axiomatic method – a method of research, which consists in the fact that some statements (axioms, postulates) are accepted without proof and then, according to certain logical rules, the rest of the knowledge is derived from them.

Hypothetical method – a method of research using a scientific hypothesis, i.e. assumptions about the cause that causes a given effect, or about the existence of some phenomenon or object.

A variation of this method is hypothetico-deductive a method of research, the essence of which is to create a system of deductively interconnected hypotheses from which statements about empirical facts are derived.

The structure of the hypothetico-deductive method includes:

1) making conjectures (assumptions) about the causes and patterns of the phenomena and objects being studied;

2) selection from a set of guesses the most probable, plausible;

3) deducing a consequence (conclusion) from a selected assumption (premise) using deduction;

4) experimental verification of the consequences derived from the hypothesis.

Formalization – display of a phenomenon or object in the symbolic form of any artificial language (logic, mathematics, chemistry) and the study of this phenomenon or object through operations with the corresponding signs. The use of artificial formalized language in scientific research allows us to eliminate such shortcomings of natural language as ambiguity, inaccuracy, and uncertainty. When formalizing, instead of reasoning about the objects of research, they operate with signs (formulas). By operating with formulas in artificial languages, one can obtain new formulas and prove the truth of any proposition. Formalization is the basis for algorithmization and programming, without which computerization of knowledge and the research process cannot do.

General logical methods

General logical methods are analysis, synthesis, induction, deduction and analogy.

Analysis – this is the dismemberment, decomposition of the object of study into its component parts. Types of analysis are classification and periodization. The analysis method is used in both real and mental activities.

Synthesis – this is the connection of individual sides, parts of the object of study into a single whole. The result of the synthesis is a completely new formation, the properties of which are the result of their internal interconnection and interdependence.

Induction – the process of deriving a general position from observing a number of particular facts, i.e. knowledge from the particular to the general. In practice, incomplete induction is most often used, which involves making a conclusion about all objects of a set based on knowledge of only part of the object. Incomplete induction, based on experimental studies and including theoretical justification, is called scientific induction. The conclusions of such induction are often probabilistic in nature. With a strict setup of the experiment, logical consistency and rigor of conclusions, it is able to give a reliable conclusion.

Deduction – the process of analytical reasoning from the general to the particular or less general (cognition from the general to the particular). It is closely related to generalization. If the initial general provisions are an established scientific truth, then the method of deduction will always produce a true conclusion. The deductive method is especially important in mathematical analysis. Mathematicians operate with mathematical abstractions and base their reasoning on general principles. These general provisions apply to solving private, specific problems.

In the history of science, there have been attempts to absolutize the meaning in science of the inductive method (F. Bacon) or the deductive method (R. Descartes), to give them universal meaning. But these methods cannot be used as separate, isolated from each other; each of them is used at a certain stage of the cognition process.

Analogy - a probable, plausible conclusion about the similarity of two objects or phenomena in some characteristic, based on their established similarity in other characteristics. An analogy with a simple phenomenon allows us to understand a more complex one. Analogy forms the basis of modeling.

Methods of theoretical and empirical levels of scientific knowledge

In addition to general logical methods, modeling, classification, abstraction, generalization, and the historical method are also used at the theoretical and empirical levels of scientific knowledge.

Modeling at the theoretical level of scientific knowledge it is divided into: heuristic and symbolic. Mathematical modeling is the most important type of symbolic modeling.

Heuristic modeling is based on general ideas and considerations about real phenomena without the use of strictly fixed mathematical or other sign systems. Such analysis is inherent in any research at its initial stage. Heuristic models are used in the study of complex systems for which it is difficult to construct a mathematical model. In these cases, the researcher comes to the aid of intuition, accumulated experience, and the ability to formulate certain stages of the problem-solving algorithm. In computational terms, complex algorithms are replaced by simplified ones without any evidence, based on subconscious decisions. Heuristic models are often called scenarios of a phenomenon. They require a multi-stage approach: collecting missing information and repeatedly adjusting the results.

At the core iconic modeling is the study of phenomena using symbolic formations of various natures: diagrams, graphs, drawings, formulas, graphs, mathematical equations, logical relationships written in symbols of natural or artificial languages. The most important form of sign modeling is mathematical, which is usually understood as a system of equations that describe the course of the process being studied.

Mathematical model is a mathematical abstraction that characterizes a biological, physical, chemical or some other process. Mathematical models with different physical natures are based on the identity of the mathematical description of the processes occurring in them and in the original.

Mathematical modeling– a method for studying complex processes based on a broad physical analogy, when the model and its original are described by identical equations. A characteristic feature and advantage of this method is the ability to apply it to individual sections of a complex system, as well as to quantitatively study phenomena that are difficult to study using physical models.

Mathematical modeling presupposes the presence of a complete picture of knowledge about the physical nature of the phenomenon being studied. This picture is refined on the basis of specially designed experiments to a degree that allows us to capture the most important characteristic properties of the phenomena. Mathematical modeling is inextricably linked with the use of a special mathematical apparatus to solve problems. There are analytical solution methods for obtaining the studied patterns in explicit form, numerical– to obtain quantitative results when specifying specific values ​​of the initial data, quality– to find individual properties of the solution. Mathematical modeling can be divided into three stages:

1. algorithm

   program.

Classification – distribution of certain objects into classes (departments, categories) depending on their general characteristics, fixing natural connections between classes of objects in a unified system of a specific branch of knowledge. The formation of each science is associated with the creation of classifications of the objects and phenomena being studied.

Classification is the process of organizing information. In the process of studying new objects, a conclusion is made in relation to each such object: whether it belongs to already established classification groups. In some cases, this reveals the need to rebuild the classification system. There is a special theory of classification - taxonomy. It examines the principles of classification and systematization of complexly organized areas of reality, which usually have a hierarchical structure. One of the first classifications in biology was the classification of flora and fauna.

Abstraction – mental abstraction from some properties and relationships of the subject being studied and highlighting the properties and relationships that interest the researcher. Usually, when abstracting, the secondary properties and connections of the object under study are separated from the essential properties and connections. There are two types of abstraction:

abstraction of identification– the result of identifying the common properties and relationships of the objects being studied, establishing what is identical in them, abstracting from the differences between them, combining objects into a special class;

isolating abstraction– the result of identifying certain properties and relationships that are considered as independent subjects of research.

The theory distinguishes two more types of abstraction: potential feasibility and actual infinity.

Generalization – establishment of general properties and relationships of objects and phenomena, definition of a general concept that reflects the essential, basic characteristics of objects or phenomena of a given class. At the same time, generalization can be expressed in highlighting non-essential, but any signs of an object or phenomenon. This method of scientific research is based on philosophical categories general, special and individual.

Historical method consists in identifying historical facts and, on this basis, in such a mental reconstruction of the historical process in which the logic of its movement is revealed. The logical method is, in essence, a logical reproduction of the history of the object being studied. At the same time history is freed from everything accidental, unimportant, i.e. it is the same historical method, but freed from its historical form.

The theoretical level of scientific knowledge is characterized by the predominance of the rational moment - concepts, theories, laws and other forms and “mental operations”. The lack of direct practical interaction with objects determines the peculiarity that an object can only be studied indirectly, in a thought experiment, but not in a real one.

At this level, the most profound essential aspects, connections, patterns inherent in the objects and phenomena being studied are revealed by processing the data of empirical knowledge. This processing is carried out using systems of “higher order” abstractions - such as concepts, inferences, laws, categories, principles, etc.

Theoretical thinking cannot be reduced to the summation of empirically given material. It turns out that theory does not grow out of empirics, but as if next to it, or rather, above it and in connection with it.

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

While distinguishing these two different levels in scientific research, one should not, however, separate them from each other and oppose them. After all, the empirical and theoretical levels of knowledge are interconnected. The empirical level acts as a basis, a theoretical foundation. Hypotheses and theories are formed in the process of theoretical understanding of scientific facts and statistical data obtained at the empirical level.

In turn, the empirical level of scientific knowledge cannot exist without achievements at the theoretical level. Empirical research is usually based on a certain theoretical construct, which determines the direction of this research, determines and justifies the methods used.

22. Scientific problem and problematic situation

K. Popper believed that science begins not with a fact, but with a problem situation.

Problem - from Greek - an obstacle, difficulty, task in the methodology of science - a question or a set of questions that arise in the course of cognition. A problem is a question for which there is no answer in the accumulated knowledge.

Problems arise in 3 situations:

- a consequence of a contradiction in one theory;

— clash of two theories;

— the clash of theory and observations.

Ancient philosophers gave a definition: a problem is a question that creates an open alternative (2 opposites) from a dispute, a search for truth.

A problem situation is any situation (theoretical or practical) in which there is no solution appropriate to the circumstances, which makes you stop and think. This is an objective state of inconsistency of scientific knowledge as a result of incompleteness and limitation.

Types of problem situations:

— discrepancy between theory and experimental data;

— confrontation of theories in one subject area;

―problem situations that arise when paradigms collide (styles of scientific research, research programs).

The way the problem is stated is influenced by:

- the nature of thinking of the era;

- level of knowledge about those areas that relate to the problem at hand.

The problem statement assumes:

― separation of the unknown from the already known, separation of facts explained by science from facts that require explanation,

- formulation of a question expressing the main meaning of the problem,

— preliminary determination of possible ways to resolve the issue.

The problem can be defined as “knowing about our ignorance.” Most often, solving a scientific problem begins with putting forward hypotheses.

The theoretical level of scientific knowledge is characterized by the predominance of the rational element - concepts, theories, laws and other forms of thinking. Thinking is an active process of generalized and indirect reflection of reality that occurs during practice. Human thinking is carried out in close connection with speech, and its results are recorded in language as a certain sign system.

Theoretical knowledge reflects phenomena and processes from their universal internal connections and patterns, comprehended through rational processing of empirical knowledge data. This processing is carried out using inference, laws, categories, principles, etc.

The theory is constructed in such a way that it describes not the surrounding reality, but idealized objects. Idealization is the main logical operation of theoretical thinking. Its goal and result is the creation, construction of a special type of objects - idealized objects, work with which is an essential characteristic of theoretical knowledge.

A characteristic feature of theoretical cognition is the study of the process of cognition itself, its forms, techniques, methods, conceptual apparatus, etc. On the basis of theoretical explanation and known laws, prediction and foresight of the future is carried out.

Methods of theoretical knowledge.

1. Formalization - display of content knowledge in a sign-symbolic form. When formalizing, reasoning about objects is transferred to the plane of operating with signs (formulas), which is associated with the construction of artificial languages ​​(the language of mathematics, logic, chemistry, etc.).

It is the use of special symbols that makes it possible to eliminate the ambiguity of words in ordinary, natural language. In formalized reasoning, each symbol is strictly unambiguous.

Formalization clarifies the content by identifying its form and can be carried out with varying degrees of completeness. The ever-deepening formalization of the content of knowledge never reaches absolute completeness, because the development (change) of the subject of knowledge and knowledge about it never stops.

2. Axiomatic method - a method of constructing a scientific theory in which it is based on certain initial provisions - axioms (postulates), from which all other statements of this theory are deduced from them in a purely logical way, through proof. To derive theorems from axioms (and in general some formulas from others), special rules of inference are formulated. Consequently, a proof in the axiomatic method is a certain sequence of formulas, each of which is either an axiom or is obtained from previous formulas according to some rule of inference.

The axiomatic method is only one of the methods for constructing already acquired scientific knowledge. The famous French physicist Louis de Broglie drew attention to the fact that “the axiomatic method may be a good method of classification or teaching, but it is not a method of discovery.”

3. Hypothetico-deductive method - a method of scientific knowledge, the essence of which is to create a system of deductively interconnected hypotheses, from which statements about empirical facts are ultimately derived. The conclusion obtained on the basis of this method will inevitably be probabilistic in nature.

General structure of the hypothetico-deductive method:

a) familiarization with factual material that requires a theoretical explanation and an attempt to do so with the help of already existing theories and laws. If not, then:

b) putting forward conjectures (hypotheses, assumptions) about the causes and patterns of these phenomena using a variety of logical techniques;

c) assessing the validity and seriousness of assumptions and selecting the most probable from among many of them;

d) deriving consequences from the hypothesis;

e) experimental verification of the consequences derived from the hypothesis.

The hypothetico-deductive method is not so much a method of discovery as a way of constructing and justifying scientific knowledge, since it shows exactly how one can arrive at a new hypothesis.

4. Ascent from abstract to concrete - a method of theoretical research and presentation, consisting in the movement of scientific thought from the initial abstraction through successive stages of deepening and expanding knowledge to the result - a holistic reproduction in theory of the subject under study. As its premise, this method includes an ascent from the sensory-concrete to the abstract, to the isolation in thinking of individual aspects of an object and their “fixation” in the corresponding abstract definitions. The movement of knowledge from the sensory-concrete to the abstract is the movement from the individual to the general; logical techniques such as analysis and induction predominate here.

General scientific methods and techniques of research.

1. Analysis - real or mental division of an object into its component parts and synthesis - their unification into a single organic whole, and not into a mechanical unit.

2. Abstraction - the process of mental abstraction from a number of properties and relationships of the phenomenon being studied while simultaneously highlighting the properties of interest to the researcher.

3. Generalization - the process of establishing the general properties and characteristics of an object, is closely related to abstraction.

4. Idealization - a mental procedure associated with the formation of abstract (idealized) objects that are fundamentally impossible to implement in reality.

The idealized object ultimately acts as a reflection of real objects and processes.

5. Induction - the movement of thought from the individual to the general and deduction - the ascent of the process of cognition from the general to the individual. Inductive generalizations are usually regarded as empirical truths and are probabilistic in nature.

A characteristic feature of deduction is that from true premises it always leads to a true, reliable conclusion.

6. Analogy - establishing similarities in certain aspects, properties and relationships between non-identical objects. Based on the identified similarities, an appropriate conclusion is drawn. Analogy does not provide reliable, but probable knowledge.

7. Modeling - a method of studying certain objects by reproducing their characteristics on another object - a model, which is an analogue of one or another fragment of reality - the original model. There must be a certain similarity (similarity) between the model and the object of interest to the researcher - in physical characteristics, structure, functions, etc.

According to the nature of the models, material (subject) and ideal modeling are distinguished. Material models are natural objects that obey in their functioning the natural laws of physics, mechanics, etc.

With ideal (sign) modeling, models appear in the form of graphs, drawings, formulas, systems of equations, sentences of natural and artificial (symbols) language, etc. Currently, mathematical (computer) modeling has become widespread.

8. Systematic approach - a set of general scientific methodological principles based on the consideration of objects as systems.

The specificity of the systems approach is determined by the fact that it focuses the research on revealing the integrity of the developing object and the mechanisms that provide it, identifying the diverse types of connections of a complex object and bringing them together into a single theoretical picture.

9. Structural-functional (structural) method is based on the identification of their structure in integral systems - a set of stable relationships and interconnections between its elements and their roles (functions) relative to each other.

Structure is understood as something invariant (unchangeable) under certain transformations, and function as the “purpose” of each of the elements of a given system.

10. Probabilistic-statistical methods are based on taking into account the action of many random factors that are characterized by a stable frequency. This makes it possible to reveal necessity (law), which “breaks through” through the combined action of many accidents.

Probability is a quantitative measure (degree) of the possibility of the occurrence of a certain phenomenon or event under certain conditions. The probability range is from zero (impossibility) to one (reality).

In statistical laws, predictions are not reliable, but only probabilistic in nature, which is determined by the action of many random factors, through the complex interweaving of which necessity is expressed.