General scientific methods that are applied in human cognition in general, analysis, synthesis, abstraction, comparison, induction, deduction, analogy, etc.

Some general scientific methods are applied only at the empirical level of knowledge (observation, experiment, measurement), others - only at the theoretical level (abstraction, idealization, formalization, induction and deduction), and some (analysis and synthesis, analogy and modeling) - both at the empirical level. as well as at the theoretical level.

abstraction - abstraction from a number of properties and relations of objects. The result of abstraction is the development of abstract concepts that characterize objects from different angles.

In the process of cognition, such a technique is used as analogy - inference about the similarity of objects in a certain respect on the basis of their similarity in a number of other respects.

Associated with this approach simulation method , which has received special distribution in modern conditions. This method is based on the principle of similarity. Its essence lies in the fact that not the object itself is directly investigated, but its analogue, its substitute, its model, and then the results obtained during the study of the model are transferred to the object itself according to special rules. Modeling is used in cases where the object itself is either difficult to access, or its direct study is economically unprofitable, etc. Distinguish the following types models:

1) abstract patterns - ideal constructions built by means of thinking (consciousness). These models are a kind of final product of thinking, ready to be transferred to other subjects. Obviously, abstract models include verbal constructions, symbolic representations, and mathematical descriptions. Verbal models that operate with certain concepts and categories get vague results that are difficult to evaluate. Without detracting from the merits of this research method, it is appropriate to point out the often encountered shortcoming of "verbal" modeling. not using mathematical symbols human logic is often entangled in verbal definitions and therefore draws erroneous conclusions. To reveal this mistake behind the "music" of words is sometimes worth a lot of work and endless, often fruitless, disputes. The mathematical model involves the use mathematical concepts(such as variables, equations, matrices, algorithms, etc.). A typical mathematical model is an equation or a system of equations that describes the relationship between various variables and constants. Models built on the basis of mathematical formalization have maximum accuracy. But in order to reach their use in any area, it is necessary to obtain a sufficient amount of reliable knowledge for this.
2) real models - material constructions obtained with the help of the environment. Real models can be of direct similarity (for example, a model of a city for evaluating the aesthetic perception of newly erected structures) and indirect similarity (for example, the body of experimental animals in medicine as an analogue of the human body).
3) Information (computer) models - These are abstract, as a rule, mathematical models that have real content. Information models represent reality, and at the same time their behavior is quite independent of the functioning of this reality. Thus, information models can be considered as having their own existence, as the simplest virtual reality, the presence of which allows a deeper and more complete knowledge of the systems under study. Examples of information models are models implemented using computer technology.

A special type of modeling is the inclusion in the experiment not of the object itself, but of its model, due to which the latter acquires the character of a model experiment.

Is organically connected with modeling idealization - mental construction of concepts, theories about objects that do not exist and are not feasible in reality, but those for which there is a close prototype or analogue in real world. All sciences operate with this kind of ideal objects - an ideal gas, an absolutely black body, a socio-economic formation, the state, etc.

Deduction- a method of scientific knowledge, which is the receipt of private conclusions based on general knowledge, the conclusion from the general to the particular.

theoretical methods of scientific knowledge

Formalization - displaying meaningful 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.). Formalization, therefore, is a generalization of the forms of processes that differ in content, the abstraction of these forms from their content. It clarifies the content by identifying its form and can be carried out with varying degrees completeness. But, as the Austrian logician and mathematician Godel showed, in a theory there always remains an unrevealed, non-formalizable remainder. The ever deeper formalization of the content of knowledge will never reach absolute completeness. This means that formalization is internally limited in its capabilities. It is proved that there is no general method that allows any reasoning to be replaced by a calculation.

Axiomatic Method - a method of constructing a scientific theory, in which it is based on some initial provisions - axioms (postulates), from which all other statements of this theory are derived from them purely logical way and through proof.

Hypothetical-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 have a probabilistic character. The general structure of the hypothetical-deductive method:

• a) familiarization with factual material that requires a theoretical explanation and an attempt to do so with the help of existing theories and laws. If not, then:
• b) putting forward guesses (hypotheses, assumptions) about the causes and patterns of these phenomena using a variety of logical techniques;
• c) an assessment of the solidity and seriousness of the assumptions and the selection of the most probable from the set of them;
• d) deduction from the hypothesis (usually by deductive means) of consequences with specification of its content;
• e) experimental verification of the consequences derived from the hypothesis. Here the hypothesis or gets experimental confirmation, or refuted. However, the confirmation of individual consequences does not guarantee its truth (or falsity) as a whole. The hypothesis that is best based on the test results goes into theory.

Climbing from the abstract to the concrete - a method of theoretical research and presentation, consisting in the movement of scientific thought from the original abstraction through successive stages of deepening and expanding knowledge to the result - a holistic reproduction of the theory of the subject under study. As its prerequisite, this method includes the ascent from the sensory-concrete to the abstract, to the separation in thinking of individual aspects of the subject and their “fixing” in the corresponding abstract definitions. The movement of cognition from the sensory-concrete to the abstract is precisely the movement from the individual to the general; such logical methods as analysis and induction prevail here. The ascent from the abstract to the mentally concrete is the process of moving from individual general abstractions to their unity, the concrete-universal, here the methods of synthesis and deduction dominate.

A characteristic feature of theoretical knowledge is its focus on itself, intrascientific reflection , i.e. study of the process of cognition , its forms, techniques, methods, conceptual apparatus, etc. On the basis of a theoretical explanation and known laws, a prediction, a scientific prediction of the future, is carried out. At the theoretical stage of science predominant (in comparison with living contemplation) is rational cognition, which is most fully and adequately expressed in thinking. Thinking- an active process of generalized and indirect reflection of reality, carried out in the course of practice, which ensures the disclosure of its regular connections on the basis of sensory data and their expression in a system of abstractions (concepts, categories, etc.). Human thinking is carried out in the closest connection with speech, and its results are fixed in the language as a certain sign system , which can be natural or artificial (the language of mathematics, formal logic, chemical formulas, etc.).

forms of scientific knowledge

The forms of scientific knowledge include problems, scientific facts, hypotheses, theories, ideas, principles, categories and laws.

-such hypothetical knowledge, the truth or falsity of which has not yet been proven, but which is not put forward arbitrarily, but subject to a number of requirements, which include the following.

• 1. Absence of contradictions. The main provisions of the proposed hypothesis should not contradict known and verified facts. (Note that there are also false facts which need to be verified).
• 2. Correspondence of the new hypothesis with well-established theories. So, after the discovery of the law of conservation and transformation of energy, all new proposals for the creation of a "perpetual motion machine" are no longer considered.
• 3. The availability of the proposed hypothesis for experimental verification, at least in principle (see below - the principle of verifiability).
• 4. Maximum simplicity of the hypothesis.

Categories of Science - these are the most general concepts of the theory, characterizing the essential properties of the object of the theory, objects and phenomena of the objective world. For example, the most important categories are matter, space, time, movement, causality, quality, quantity, causality, etc.

Laws of Science reflect the essential connections of phenomena in the form of theoretical statements. Principles and laws are expressed through the ratio of two or more categories.

scientific principles - the most general and important fundamental provisions of the theory. Scientific principles play the role of initial, primary premises and are laid in the foundation of the theories being created. The content of the principles is revealed in the totality of laws and categories.

Scientific concepts - the most general and important fundamental provisions of the theories.

scientific theory - is a systematized knowledge in their totality. Scientific theories explain a lot of accumulated scientific facts and describe a certain fragment of reality (for example, electrical phenomena, mechanical movement, the transformation of substances, the evolution of species, etc.) through a system of laws. The main difference between a theory and a hypothesis is reliability, proof. the term theory itself has many meanings. A theory in a strictly scientific sense is a system of already confirmed knowledge that comprehensively reveals the structure, functioning and development of the object under study, the relationship of all its elements, aspects and theories.

Scientific picture of the world is a system of scientific theories describing reality.

Theoretical level of knowledge

The purpose of theoretical research is the establishment of laws and principles that allow one to systematize, explain and predict the facts established in the course of empirical research.

At the theoretical level of cognition, an object is studied from the side of its essential connections, often hidden from direct perception. At this level of cognition, laws are formulated that essentially relate not to an empirically given reality, but to reality as it is represented by idealized objects (objects of theoretical cognition).

An idealized object is a mental cognitive construction that is the result of idealization and abstraction. Theoretical objects, unlike empirical objects, are endowed not only with those features that we can find in real objects, but also with features that no real object has. For example, material point- a body devoid of size, but concentrating in itself the entire mass; ideal gas, perfect black body). Theoretical knowledge is knowledge, the content of which does not have a directly sensible carrier (correlative).

Theoretical knowledge can be developed relatively independently of empirical research by thought experiment with idealized objects; by introducing various hypothetical assumptions or theoretical models (especially mathematical ones); through sign-symbolic operations according to the rules of mathematics or logical formalisms.

Mathematics is the best example of this. N. Lobachevsky, the founder of non-Euclidean geometry, who built a system of geometric positions by replacing the Euclidean postulate of parallel lines with a new postulate, did not rely on observational data.

An indisputable fact in modern science the assertion is considered that theoretical discoveries are fundamentally not reducible to those sensory data on which they are based to one degree or another. There is no logical transition in principle from sense data and empirical generalizations to theoretical generalizations, which by their very nature, i.e. as a discovery of the general and universal, they go far beyond the always incomplete, limited, insufficient sphere of sensory data.

Science in its theoretical conclusions constantly goes beyond the boundaries of available sensory data and thus comes into conflict with them. Moreover, it quite often refutes the sensual, visual picture of the world, as has already been discussed in connection with the heliocentric system. The contradiction between scientific theory and direct sensory data is quite natural even if these sensory data were the empirical basis of the theory. Within the boundaries of the sensible reflection of the external world, there is no difference between appearance and essence. This difference can only be established by scientific, mainly theoretical research.

The formation of internally differentiated and at the same time integral theoretical systems marks the transition of science to the theoretical stage, which is characterized by the emergence of special theoretical models of reality (for example, the molecular-kinetic model of a gas is an ideal gas, etc.). Such means of cognition determine the movement of theoretical thought, relatively independent of empirical level research, expand its heuristic possibilities.

Process scientific research even at a theoretical level is not strictly rational. Just before the stage scientific discovery imagination, the creation of images are important, and at the very stage of discovery - intuition. Therefore, the discovery cannot be logically deduced, like a theorem in mathematics. The importance of intuition in science is well evidenced by the words of the outstanding mathematician Gauss: “Here is my result, but I do not yet know how to get it. The result is intuitive, but there is no argument to support it.” Intuition is present in science (the so-called "sense of the object"), but it does not mean anything in the sense of substantiating the results. We also need objective rational methods that would substantiate them; methods adopted by the scientific community.

Methods of knowledge

Theoretical statements, as a rule, directly relate not to real, but to idealized objects, cognitive activity with which allows you to establish significant connections and patterns that are inaccessible in the study of real objects, taken in all the variety of their empirical properties and relationships.

1. Induction- the movement of thought from the individual (experience, facts) to the general (their generalization in the conclusions) and deduction- the ascent of the process of cognition from the general to the individual. These are opposite, mutually complementary trains of thought. Since experience is always infinite and incomplete, inductive conclusions always have a problematic (probabilistic) character. Inductive generalizations are usually considered as empirical truths (empirical laws).

From the types of inductive generalizations, popular, incomplete, complete, scientific and mathematical induction is distinguished. Logic also considers inductive methods for establishing causal relationships - the canons of induction (the rules of inductive research by Bacon-Mill). These include methods: the only similarity, the only difference, similarity and difference, concomitant changes and the method of residuals.

A characteristic feature of deduction is that it always leads from true premises to a true, reliable conclusion, and not to a probabilistic (problematic) one. Deductive reasoning makes it possible to obtain new truths from existing knowledge, and, moreover, with the help of pure reasoning, without resorting to experience, intuition, common sense, etc.

2. Analogy(correspondence, similarity) - the establishment of similarities in some aspects, properties and relationships between non-identical objects. On the basis of the revealed similarity, an appropriate conclusion is made - a conclusion by analogy. Its general scheme is: object B has features a, b, c, d; object C has features b, c, d; therefore, the object C probably has the attribute a. Thus, analogy provides not reliable, but probable knowledge. When inferring by analogy, the knowledge obtained from the consideration of an object ("model") is transferred to another, less studied and less accessible object for research.

3. Modeling- a method of studying certain objects by reproducing their characteristics on another object - a model that is an analogue of one or another fragment of reality (real or mental) - the original model. Between the model and the object of interest to the researcher, there must be a known similarity (similarity) - in physical characteristics, structure, functions, etc.

The forms of modeling are very diverse and depend on the models used and the scope of modeling. By the nature of the models, material (objective) and ideal modeling are distinguished, expressed in the corresponding sign form. Material models are natural objects, obeying in their functioning the natural laws of physics, mechanics, etc. In the material (objective) modeling of a specific object, its study is replaced by the study of some model that has the same physical nature, as the original (models of aircraft, ships, spacecraft, etc.).

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

4. Philosophical and general scientific research methodology. Dialectics, systemic approach, synergetics.

Synergetic approach and ideas of global evolutionism. The study of self-developing synergetic systems takes place within the framework of interdisciplinary research in several directions. This is the model proposed by the founder of synergetics Hocken, the model of Prigozhin, Kurdyumov. Start new discipline put Hocken's speech in 1973 at the first conference devoted to the problem of self-organization. However, Prigogine used a different term - non-equilibrium thermodynamics. In the modern post-non-classical picture of the world, orderliness, structure, as well as chaos, stochasticity, are recognized as objective universal characteristics of reality that are present at all structural levels of development. That. the problem of irregular behavior of non-equilibrium systems is the subject of synergetics (Greek - assistance, complicity). The subject of synergetics is to identify the most general patterns spontaneous structure genesis. That is, an indicator of progress, as a state of striving to increase the degree of complexity of the system, is the presence in it of the internal potential of self-organization. Therefore, self-organization is conceived as a global evolutionary process. Synergetics is understood as continuous cooperation, coordinated action. Synergetics is interested in the question of how exactly subsystems or parts produce changes that are entirely due to self-organization processes. It turned out that all systems during the transition from a disordered state to order behave in a similar way. According to Hocken, the principles of self-organization of systems of various nature (from electrons to people) are the same, if so, then, therefore, we should talk about the general determinants of natural and social processes. Synergetics is aimed at finding these processes. It includes new ideas about reality, that is, new map picture of the world, namely, he draws the concept of an unstable, non-equilibrium world, the idea of ​​a multi-alternative effect, the idea of ​​the emergence of order from chaos. The fundamental idea of ​​synergetics is that disequilibrium is thought to be the source of a new organization, that is, order (order out of chaos). The emergence of order is equated to the spontaneous self-organization of matter, while the intensity and degree of their non-equilibrium are important for the behavior of the system. Non-equilibrium systems cause the effect of corporate behavior of elements that, in equilibrium conditions, behaved independently, that is, autonomously. The behavior of nonequilibrium systems in organic and inorganic chemistry is considered. In the social sciences, they try to describe phenomena from the standpoint of synergetics, the work of the brain is regarded as a masterpiece of cell cooperation. In addition, an attempt to comprehend synergetics, the concepts of chaos are based on the classification of chaos itself - simple, complex, deterministic, and others. chaos entered the post-non-classical picture of the world not as a source of destruction (destruction), but as a state derived from the primary instability of material interactions, which can be the cause of spontaneous structure genesis. Therefore, chaos is considered not just as a formless mass, but as a highly complex organized sequence. Some scientists define chaos as an irregular movement along periodically repeating unstable trajectories, where the correlation of temporal and spatial parameters is characterized by a random distribution. The ideas of synergetics are consonant with the ideas of ancient thinkers (Cosmos was opposed to Chaos). At the same time, they thought of Cosmos and Chaos as some kind of universal characteristics of the universe. Chaos was conceived as an all-encompassing principle, in particular, in the ancient worldview, chaos is endowed with a formative power, the primary state of matter. Chaos is a kind of primary potentiality of the world, which, opening up, spews out rows of life-giving entities. Such ideas have found their embodiment in synergetics. In fact, they believe that chaos is the discovery of a new kind of movement, that it is as fundamental as the discovery of elementary particles quarks, gluons. That is, the science of chaos is the science of processes, not of state, the science of becoming, not being. Synergetics is associated with such concepts as bifurcation, fluctuation, chaos, dissipation, uncertainty. At the same time, these concepts acquire an ideological coloring, a categorical status. In conclusion, we note that the ideas of synergetics, one way or another, are consonant with the ideas of dialectics. Therefore, some modern researchers believe that the synergetic approach reveals and clarifies some dialectical ideas.

Systems approach- a set of general scientific methodological principles(requirements), which are based on the consideration of objects as systems. These requirements include: a) identifying the dependence of each element on its place and functions in the system, taking into account the fact that the properties of the whole are not reducible to the sum of the properties of its elements; b) analysis of the extent to which the behavior of the system is determined both by the characteristics of its individual elements and by the properties of its structure; c) study of the mechanism of interaction between the system and the environment; d) study of the nature of the hierarchy inherent in this system; e) providing a comprehensive multi-aspect description of the system; f) consideration of the system as a dynamic, developing integrity.

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

In knowledge, two levels are distinguished: empirical and theoretical.

Empirical (from gretriria - experience) level of knowledge - this is knowledge obtained directly from experience with some rational processing of the properties and relations of the object is known. It is always the basis, the basis for the theoretical level of knowledge.

The theoretical level is knowledge gained through abstract thinking

A person begins the process of cognition of an object from its external description, fixes its individual properties, sides. Then it delves into the content of the object, reveals the laws to which it is subject, proceeds to an explanation of the properties of the object, combines knowledge about the individual aspects of the subject into a single, integral system, and the resulting deep versatile specific knowledge about the subject is a theory that has a certain internal logical structure.

It is necessary to distinguish the concepts of "sensual" and "rational" from the concepts of "empirical" and "theoretical" "Sensual" and "rational" characterize the dialectics of the process of reflection in general, and "empirical" and "theoretical" do not refer to the sphere of only scientific knowledge empirically "i" theoretically" lie down to the sphere of less than scientific knowledge.

Empirical knowledge is formed in the process of interaction with the object of study, when we directly influence it, interact with it, process the results and draw a conclusion. But getting separate. The EMF of empirical facts and laws does not yet allow us to build a system of laws. In order to know the essence, it is necessary to go to the theoretical level of scientific knowledge.

Empirical and theoretical levels of knowledge are always inextricably linked and mutually condition each other. Thus, empirical research, revealing new facts, new observational and experimental data, stimulates the development of the theoretical level, poses new problems and tasks for it. In turn, theoretical research, considering and concretizing the theoretical content of science, opens up new perspectives. IVI explanations and predictions of facts and thereby orients and directs empirical knowledge. Empirical knowledge is mediated by theoretical knowledge - theoretical knowledge indicates exactly which phenomena and events should be the object of empirical research and under what conditions the experiment should be carried out. At the theoretical level, the boundaries are also identified and indicated, in which the results at the empirical level are true, in which empirical knowledge can be used in practice. This is precisely the heuristic function of the theoretical level of scientific knowledge.

The boundary between the empirical and theoretical levels is very arbitrary, their independence relative to each other is relative. The empirical turns into the theoretical, and what was once theoretical, on another, more high stage development becomes empirically available. In any sphere of scientific knowledge, at all levels, there is a dialectical unity of the theoretical and empirical. The leading role in this unity of dependence on the subject, conditions, and already existing, obtained scientific results belongs either to the empirical or to the theoretical. The basis of the unity of the empirical and theoretical levels of scientific knowledge is the unity of scientific theory and research practice.

50 Basic methods of scientific knowledge

Each level of scientific knowledge uses its own methods. So, at the empirical level, such basic methods as observation, experiment, description, measurement, modeling are used. At the theoretical level - analysis, synthesis, abstraction, generalization, induction, deduction, idealization, historical and logical methods, etc.

Observation is systematic and purposeful perception objects and phenomena, their properties and relationships in natural conditions or in experimental conditions with the aim of understanding the object under study

The main monitoring functions are:

Fixation and registration of facts;

Preliminary classification of facts already recorded on the basis of certain principles formulated on the basis of existing theories;

Comparison of recorded facts

With the complication of scientific knowledge, the goal, plan, theoretical guidelines, and comprehension of the results are gaining more and more weight. As a result, the role of theoretical thinking in the observation

It is especially difficult to observe social sciences, where its results largely depend on the worldview and methodological attitudes of the observer, his attitude to the object

The observation method is a limited method, since it can only fix certain properties and relationships of an object, but it is impossible to reveal their essence, nature, development trends. Comprehensive with the observation of the object is the basis for the experiment.

An experiment is a study of any phenomena by actively influencing them by creating new conditions that correspond to the goals of the study, or by changing the course of the process in a certain direction.

Unlike simple observation, which does not involve active influence on the object, an experiment is an active intervention of the researcher into natural phenomena, in the course of the studied. An experiment is a type of practice in which practical action goes well with theoretical work thoughts.

The significance of the experiment lies not only in the fact that with its help science explains the phenomena material world, but also in the fact that science, relying on experiment, directly masters one or another dos of the studied phenomena. Therefore, the experiment serves as one of the main means of communication between science and production. After all, it makes it possible to verify the correctness of scientific conclusions and discoveries, new laws and data. The experiment serves as a means of research and invention of new devices, machines, materials and processes in industrial production, a necessary stage in the practical testing of new scientific and technical discoveries.

The experiment is widely used not only in the natural sciences, but also in social practice, where it plays an important role in the knowledge and management of social processes.

The experiment has its specific features compared to other methods:

The experiment allows you to explore objects in the so-called pure form;

The experiment allows you to explore the properties of objects in extreme conditions, which contributes to a deeper penetration into their essence;

An important advantage of the experiment is its repeatability, due to which this method acquires special significance and value in scientific knowledge.

A description is an indication of the features of an object or phenomenon, both essential and non-essential. Description, as a rule, is applied to single, individual objects for a more complete acquaintance with them. His method is to give the most complete information about the object.

Measurement is a specific system for fixing and recording the quantitative characteristics of the object under study using various measuring instruments and devices with the help of measurement, the ratio of one quantitative characteristic of an object to another, homogeneous with it, taken as a unit of measurement, is determined. The main functions of the measurement method are, firstly, fixing quantitative characteristics to the object, secondly, the classification and comparison of measurement results.

Modeling is the study of an object (original) by creating and studying its copy (model), which, by its properties to a certain extent, reproduces the properties of the object under study.

Modeling is used when the direct study of objects for some reason is impossible, difficult or impractical. There are two main types of modeling: physical and mathematical. At the present stage of development of scientific knowledge, especially big role assigned computer simulation. A computer, which operates according to a special program, is able to simulate the most real processes: fluctuations in market prices, orbits of spaceships, demographic processes, other quantitative parameters of the development of nature, society, an individual human being.

Methods of the theoretical level of knowledge

Analysis is the division of an object into its components (sides, features, properties, relationships) with the aim of their comprehensive study.

Synthesis is the union of previously identified parts (sides, features, properties, relationships) of an object into a single whole.

Analysis and synthesis are dialectically contradictory and interdependent methods of cognition. Cognition of an object in its concrete integrity presupposes a preliminary division of it into components and consideration of each of them. This is the task of the analysis. It makes it possible to single out the essential, that which forms the basis of the connection of all aspects of the object under study, is, dialectical analysis is a means of penetrating the essence of things. But playing an important role in cognition, analysis does not provide knowledge of the concrete, knowledge of the object as a unity of the manifold, the unity of various definitions. This task is performed by synthesis. Consequently, analysis and synthesis are organically interacting with emopoyazani and mutually condition each other at each stage of the process of theoretical knowledge and knowledge.

Abstraction is a method of abstracting from certain properties and relations of an object and, at the same time, focusing on those that are the direct subject of scientific research. Abstraction with contributes to the penetration of knowledge into the essence of phenomena, the movement of knowledge from the phenomenon to the essence. It is clear that abstraction dismembers, coarsens, schematizes an integral mobile reality. However, this is precisely what makes it possible to more deeply study the individual aspects of the subject "in its pure form" and, therefore, to penetrate into their essence of their essence.

Generalization is a method of scientific knowledge that fixes common features and the properties of a certain group of objects, carries out the transition from the singular to the special and general, from the less general to the more common.

In the process of cognition, it is often necessary, relying on already existing knowledge, draw conclusions that are new knowledge about the unknown. This is done using methods such as induction and deduction.

Induction is such a method of scientific knowledge, when, on the basis of knowledge about the individual, a conclusion is made about the general. This is a method of reasoning by which the validity of the put forward assumption or hypothesis is established. AT real knowledge induction always acts in unity with deduction, is organically connected with it.

Deduction is a method of cognition when, on the basis of general principle in a logical way, from certain propositions as true, new true knowledge about the individual is necessarily derived. With the help of this method, the individual is known on the basis of knowledge of general laws.

Idealization is a method of logical modeling through which idealized objects are created. Idealization is aimed at the processes of conceivable construction possible objects. The results of idealization are not arbitrary. In the limiting case, they correspond to individual real properties of objects or allow their interpretation based on the data of the empirical level of scientific knowledge. Idealization is associated with a "thought experiment", as a result of which, from a hypothetical minimum of some signs of the behavior of objects, the laws of their functioning are discovered or generalized. The boundaries of the effectiveness of idealization are determined by practice.

Historical and logical methods are organically combined. historical method involves consideration of the objective process of development of the object, its real history with all its twists and turns, features. This is a certain way in reproducing in thinking the historical process in its chronological sequence and concreteness.

The logical method is the way in which thinking reproduces the real historical process in its theoretical form, in the system of concepts

task historical research is the disclosure of specific conditions for the development of certain phenomena. The task of logical research is to reveal the role that individual elements of the system play in the development of the whole.

1.2 Methods of theoretical research

Idealization. Idealization is the process of creating mental objects that do not exist in reality, by means of a mental abstraction from some properties of real objects and relations between them, or by endowing objects and situations with those properties that they do not possess in order to deeper and more accurate knowledge of reality. Objects of this kind serve the most important means knowledge of real objects and relationships between them. They're called idealized objects. These include such objects as, for example, a material point, an ideal gas, an absolutely black body, objects of geometry, etc.

Idealization is sometimes confused with abstraction, but this is wrong, because although idealization essentially relies on the process of abstraction, it is not reduced to it. In logic, abstract objects, unlike concrete ones, include only such objects that do not interact in space and time. Ideal objects cannot be considered as really existing, they are quasi-objects. Any scientific theory studies either a certain fragment of reality, a certain subject area, or a certain side, one of the aspects of real things and processes. At the same time, the theory is forced to digress from those aspects of the subjects it studies that do not interest it. In addition, the theory is often forced to digress from certain differences in the subjects it studies in certain respects. This process of mental abstraction from certain aspects, properties of the objects being studied, from certain relations between them is called abstraction.

Abstraction. Creation idealized object necessarily includes abstraction - a distraction from a number of aspects and properties of the studied specific subjects. But if we limit ourselves to this, then we will not get any integral object yet, but simply destroy the real object or situation. After abstraction, we still need to highlight the properties of interest to us, strengthen or weaken them, combine and present them as properties of some independent object that exists, functions and develops according to its own laws. All this, of course, is a much more difficult and creative task than simple abstraction. Idealization and abstraction are ways of forming a theoretical object. It can be any real object that is conceived in non-existent, ideal conditions. Thus, for example, the concepts of "inertia", "material point", "absolutely black body", "ideal gas" arise.

Formalization(from lat. forma view, image). Formalization refers to the display of objects of a certain subject area using the symbols of a certain language. When formalizing the objects under study, their properties and relations are put in correspondence with some stable, well-observable and identifiable material constructions, which make it possible to identify and fix the essential aspects of objects. Formalization clarifies the content by revealing its form and can be carried out with varying degrees of completeness. Expression of thought in natural language can be considered as the first step of formalization. Its further deepening is achieved by the introduction of various kinds of special signs into ordinary language and the creation of partially artificial and artificial languages. Logical formalization is aimed at identifying and fixing the logical form of conclusions and evidence. A complete formalization of a theory takes place when one completely abstracts from the meaningful meaning of its original concepts and provisions and enumerates all the rules of logical inference used in the proofs. Such formalization includes three points: 1) the designation of all original, undefined terms; 2) enumeration of formulas (axioms) accepted without proof; 3) introduction of rules for transforming these formulas to obtain new formulas (theorems) from them. A striking example of formalization is the mathematical descriptions of various objects and phenomena widely used in science based on the relevant theories. Despite the widespread use of formalization in science, there are limits to formalization. In 1930, Kurt Godel formulated a theorem called the incompleteness theorem: it is impossible to create such a formal system of logically valid formal proof rules that would be sufficient to prove all true theorems of elementary arithmetic.

Models and Simulation in scientific research . A model is such a material or mentally represented object that, in the process of studying, replaces the original object, retaining some of its typical features that are important for this study. The model allows you to learn how to control an object by testing various options control on the model of this object. Experimenting with a real object for this purpose is at best inconvenient, and often simply harmful or even impossible due to a number of reasons (long duration of the experiment in time, risk of bringing the object into an undesirable and irreversible state, etc.). The process of building a model is called modeling. So, modeling is the process of studying the structure and properties of the original with the help of a model.

Distinguish between material and ideal modeling. material modeling, in turn, is divided into physical and analog modeling. It is customary to call physical modeling, in which a real object is opposed to its enlarged or reduced copy, which allows research (as a rule, in laboratory conditions) with the help of the subsequent transfer of the properties of the studied processes and phenomena from model to object based on the theory of similarity. Examples: planetarium in astronomy, models of buildings in architecture, models of aircraft in aircraft construction, environmental modeling - modeling of processes in the biosphere, etc. Analog or mathematical modeling is based on the analogy of processes and phenomena that have a different physical nature, but are described formally in the same way (by the same mathematical equations). Symbolic language mathematics allows you to express the properties, sides, relationships of objects and phenomena of a very different nature. Relationships between various quantities that describe the functioning of such an object can be represented by the corresponding equations and their systems.

Induction(from Latin induction - guidance, motivation), there is a conclusion that leads to obtaining general conclusion based on private premises, this is the movement of thinking from the particular to the general. The most important, and sometimes the only method of scientific knowledge for a long time considered inductive method. According to the inductivist methodology, dating back to F. Bacon, scientific knowledge begins with observation and statement of facts. After the facts are established, we proceed to generalize them and build a theory. The theory is seen as a generalization of facts and therefore is considered reliable. However, even D. Hume noted that a general statement cannot be deduced from the facts, and therefore any inductive generalization is unreliable. This is how the problem of justifying inductive inference arose: what allows us to move from facts to general statements? Huge contribution D. Mil contributed to the development and justification of the inductive method.

Awareness of the unsolvability of the problem of justifying induction and the interpretation of inductive inference as claiming the reliability of its conclusions led Popper to reject the inductive method of cognition in general. Popper spent a lot of effort trying to show that the procedure that he describes inductive method, is not and cannot be used in science. The fallacy of inductivism, according to Popper, lies mainly in the fact that inductivism tries to substantiate theories through observation and experiment. But, as postpositivism has shown, there is no direct path from experience to theory, such a justification is impossible. Theories always remain just unfounded risky assumptions. Facts and observations are used in science not for substantiation, not as a basis for induction, but only for testing and refuting theories - as a basis for falsification. This removes the old philosophical problem of justifying induction. Facts and observations give rise to a hypothesis, which is not at all their generalization. Then, with the help of facts, they try to falsify the hypothesis. The falsifying conclusion is deductive. Induction is not used in this case, therefore, there is no need to worry about its justification.

According to K. Popper, not the inductive method, but the trial and error method is the main one in science. The cognizing subject confronts the world not as tabula rasa, on which nature draws its portrait, a person always relies on certain theoretical principles in the cognition of reality. The process of cognition does not begin with observations, but with the advancement of conjectures, assumptions that explain the world. We correlate our guesses with the results of observations and discard them after falsification, replacing them with new guesses. Trial and error is what makes up the method of science. For knowledge of the world, Popper argues, there is no more rational procedure than the method of trial and error - assumptions and rebuttals: the bold advancement of a theory; attempts the best way to show the fallacy of these theories and their temporary acceptance if criticism fails.

Deduction(from lat. deduction - derivation) is the receipt of private conclusions based on the knowledge of some general provisions is the movement of thought from the general to the particular. Hypothetical-deductive method. It is based on the derivation (deduction) of conclusions from hypotheses and other premises, the truth value of which is unknown. In scientific knowledge, the hypothetical-deductive method became widespread and developed in the 17th-18th centuries, when significant progress was made in the study of the mechanical movement of the earth and celestial bodies. The first attempts to apply the hypothetical-deductive method were made in mechanics, in particular, in the studies of Galileo. The theory of mechanics set forth in Newton's "Mathematical Principles of Natural Philosophy" is a hypothetical-deductive system, the premises of which are the basic laws of motion. The success of the hypothetical-deductive method in the field of mechanics and the influence of Newton's ideas led to the widespread use of this method in the field of exact natural science.

2.2. Forms of theoretical knowledge. Problem. Hypothesis. Law. Theory.

The main form of organization of knowledge at the theoretical level is theory. Preliminarily, the following definition of theory can be given: theory is knowledge about the subject area, which covers the subject in general and in particular and is a system of ideas, concepts, definitions, hypotheses, laws, axioms, theorems, etc., connected in a strictly logical way. What is the structure of the theory, how it is formed - the main problem of the methodology of science.

Problem. Cognition does not begin with observations and facts, it begins with problems, with the tension between knowledge and ignorance, notes L.A. Mikeshin. A problem is a question to which the theory as a whole is the answer. As K. Popper emphasizes, science does not begin with observations, but with problems, and its development proceeds from one problem to another - deeper ones. A scientific problem is expressed in the presence of a contradictory situation. Even Plato noticed that the question is more difficult than the answer. The decisive influence on the formulation of the problem and the method of solution has the nature of the thinking of the era, the level of knowledge about those objects that the problem concerns: “in the matter of choosing a problem, tradition, the course of historical development play essential role» . Scientific problems should be distinguished from non-scientific (pseudo-problems), an example of which is the problem perpetual motion machine. A. Einstein noted the importance of the procedure for posing a problem in scientific research: “The formulation of a problem is often more significant than its solution, which can only be a matter of mathematical or experimental art. The posing of new questions, the development of new possibilities, the consideration of old problems from a new angle require creative imagination and reflect real success in science. In order to solve the problems of science, hypotheses are put forward.

Hypothesis. A hypothesis is an assumption about the properties, causes, structure, relationships of the objects under study. The main feature of a hypothesis lies in its conjectural nature: we do not know whether it will turn out to be true or false. In the process of subsequent verification, the hypothesis may be confirmed and acquire the status of true knowledge, but it is possible that the verification will convince us of the falsity of our assumption and we will have to abandon it. A scientific hypothesis usually differs from a simple assumption in a certain degree of validity. The set of requirements for a scientific hypothesis can be summarized as follows: 1. The hypothesis must explain the known facts; 2. The hypothesis must not have contradictions that are prohibited by formal logic. But contradictions, which are a reflection of objective opposites, are quite admissible; 3. The hypothesis must be simple ("Occam's razor"); 4. A scientific hypothesis must be capable of being verified; 5. The hypothesis must be heuristic (“crazy enough” N. Bohr).

From a logical point of view, a hypothetico-deductive system is a hierarchy of hypotheses, the degree of abstractness and generality of which increases with distance from the empirical basis. At the top are the hypotheses that have the most general character and therefore possessing the greatest logical force. From them, as from premises, hypotheses of a lower level are deduced. Actually lowest level systems are hypotheses that can be compared with empirical data. In modern science, many theories are built in the form of a hypothetical-deductive system. There is another variety of hypotheses that attracts much attention of philosophers and scientists. These are the so-called ad hoc hypotheses(for this case). Hypotheses of this type are distinguished by the fact that their explanatory power is limited to only a small circle. known facts. They don't say anything about new, yet unknown facts and phenomena.

A good hypothesis should not only provide an explanation for the known data, but also direct research towards the search for and discovery of new phenomena, new facts. Hypotheses ad hoc only explain, but do not predict anything new. Therefore, scientists try not to use such hypotheses, although it is often quite difficult to decide whether we are dealing with a fruitful, heuristically strong hypothesis or a hypothesis ad hoc. The hypothetical nature of scientific knowledge was emphasized by K. Popper, W. Quine and others. K Popper characterizes scientific knowledge as hypothetical, he introduces the term probabilism(from lat. probable - probable), noting that scientific thinking is characterized by a probabilistic style. C. Pierce introduced the term “fallibilism” to characterize scientific knowledge (from lat. fallibilis- fallible, fallible), arguing that at any given moment in time our knowledge of reality is partial and conjectural, this knowledge is not absolute, but is a point on a continuum of uncertainty and uncertainty.

Laws are the most important component of the system of theoretical knowledge. A peculiar cell of the organization of theoretical knowledge at each of its sublevels is, notes V.S. Stepin, two-layer construction - a theoretical model and a theoretical law formulated in relation to it.

Law. The concept of "law" is one of the main ones in the system of the scientific worldview and reflects the genesis of science in the context of culture. The belief in the existence of fundamental laws of nature was based on the belief in divine laws, so characteristic of the Judeo-Christian tradition: "God governs all things through the ruthless law of fate, which he established and to which he himself obeys." A. Whitehead, setting the task of understanding how the idea of ​​the law of science arose, showed that faith in the possibility scientific laws was a derivative of medieval theology. In the system of the world, designated as the Universe, and understood as a hierarchized integrity, the existent is characterized through the principle of universalism. In the context of Stoicism, abstract principles of law were established that embodied the tradition of imperial law and were then translated from Roman law into a scientific worldview. Law (from the Greek "nomos" - law, order) opposes fusis, as the human opposes the natural. natural order, as the Greeks believed, is primordial, this is the Cosmos. Among the Latins, the concept of "law" originally arose to designate and regulate social relations. Whitehead draws attention to the decisive role of the cultural-historical context, which was the environment in which the fundamental ideas of the future scientific worldview were born. “The Middle Ages formed one long training session for the Western European intellect, accustoming it to order ... The habit of a certain exact thinking was instilled in the European mind as a result of the dominance of scholastic logic and scholastic theology.” The previously formed idea of ​​fate, demonstrating the ruthless course of things, turned out to be useful not only for illustrating human life, but also influenced the emerging scientific thinking. As Whitehead remarked, “the laws of physics are the dictates of fate.”

The idea of ​​law is a key one in understanding the world and we find confirmation of this in the statements of prominent figures medieval culture, for example, F. Aquinas, who argued that there is an eternal law, namely the mind that exists inside the consciousness of God and controls the entire Universe, and thinkers of the New Age. In particular, R. Descartes wrote about the laws that God put into nature. I. Newton considered it his goal to collect evidence for the existence of laws prescribed by God to nature.

If we compare this style of Western thinking with the thinking tradition of other civilizations, we will see that their cultural identity sets different standards of explanation. For example, in Chinese, as Needham noted, there is no word corresponding to the Western "law of nature." The closest word is "Lee", which Needham translates as the principle of organization. But in Western culture, the core of which is science, the idea of ​​the law corresponded to the main goal setting of the scientific worldview to an objective explanation of reality through the comprehension of the natural laws of nature.

Describing the dynamics of science in Western culture, today it is customary to distinguish three main types of scientific rationality: classical, non-classical and post-non-classical paradigms of scientific rationality (V.S. Stepin). The question posed at the beginning involves an analysis of the transformation of the concept of "law" in these paradigms, as well as in different standards of scientificity, since today the physical model of scientificity is no longer the only one. The experience of biology in the study of evolution, in the search for the laws of evolution, is more significant and therefore relevant for modern physics, into which the "arrow of time" (I. Prigogine) penetrates. Traditions humanities are also important in terms of analyzing the question: is a certain law of evolution possible?

Another context in which to analyze the transformation of the concept of “law” in scientific cognition is indicated when we identify various cognitive practices or epistemological schemes that represent models of scientific cognition. For example, in constructivist models of cognition, whether it be radical constructivism or social constructivism, does the concept of the “law” of science retain meaning? It is no coincidence that the trend of relativization and subjectivization of scientific knowledge, noted in the modern philosophy of science, leads to the need to discuss the problem of the relationship between law and interpretation.

Today, the concept of law is given four main meanings. Firstly, law as a necessary connection between events, as "calm in the phenomenon." Here the law is identified with objective laws that exist independently of our knowledge of them (objective laws). Secondly, law as a statement claiming to reflect the internal state of objects that are part of theories(laws of science). Thirdly, laws are understood as axioms and theorems of theories, the subject of which are objects, the meaning of which is given by these theories(logical and mathematical theories). Fourth, law as regulations developed by the community, which must be carried out by the subjects of morality and law (moral laws, criminal laws, state laws).

In terms of the problems of philosophical epistemology, the question of the relationship between objective laws and the laws of science is important. The very formulation of such a question implies an ideological position about the existence of objective laws. D. Hume, I. Kant, E. Mach doubted this. Hume's skepticism is connected with the denial of Hume's law of causality, which states: one cannot extrapolate with certainty past experience for the future. The fact that an event occurred n times does not allow us to say that this event will occur n + 1 times. “Any degree of repetition of our perceptions cannot serve as a basis for us to conclude about more the repetition of some objects that we do not perceive. Supporters of the objective existence of regularities accept Hume's point of view, understanding the laws of science as hypotheses. So, A. Poincaré argued that the laws of science, as the best expression of the inner harmony of the world, are the basic principles, prescriptions that reflect the relationship between things. “However, are these prescriptions arbitrary? No, otherwise they would be fruitless. Experience presents us with free choice, but at the same time it guides us.

According to I. Kant, laws are not extracted by reason from nature, but are prescribed to it. Based on this point of view, the laws of science can be understood as a cognitive order that is instilled in our minds in the course of adaptive evolution. This position is close to the evolutionary epistemology of K. Popper. E. Mach believed that laws are subjective and are generated by our psychological need do not get lost among the phenomena of nature. In modern cognitive science, laws are allowed to be compared with subjective habits, which in turn are explained as a consequence of objective evolution.

So, in epistemology, the concept of the law of science reflects the acceptance of objectively existing interactions in nature. The laws of science are conceptual reconstructions of patterns associated with the adoption of a certain conceptual apparatus and various abstractions. The laws of science are formulated using the artificial languages ​​of their discipline. Allocate "statistical", based on probabilistic hypotheses, and "dynamic" laws, expressed in the form of universal conditions. The study of the laws of reality finds expression in the creation of theories that reflect the subject area. Law - key element theories.

Theory. Theory in Greek means "contemplation" of what really is. scientific knowledge the era of Antiquity was theoretical, but the meaning of this term was completely different, the theories of the ancient Greeks are speculative and, in principle, are not focused on experiment. AT classical science In modern times, theory begins to be understood as a conceptual symbolic system built on the basis of experience. In the structure of theoretical knowledge, fundamental theories and particular ones are distinguished.

According to V.S. Stepin, in the structure of the theory, as its basis, there is a fundamental theoretical scheme associated with the corresponding mathematical formalism. If empirical objects can be compared with real objects, then theoretical objects are idealizations, they are called constructs, they are logical reconstructions of reality. “At the basis of an established theory, one can always find a mutually consistent network of abstract objects that determines the specifics of this theory. This network of objects is called the fundamental theoretical scheme.

Corresponding to the two distinguished sublevels of theoretical knowledge, one can speak of theoretical schemes as part of fundamental theory and as part of particular theories. At the base developed theory one can single out a fundamental theoretical scheme, which is built from a small set of basic abstract objects, constructively independent of each other, and in relation to which fundamental theoretical laws are formulated. The structure of the theory was considered by analogy with the structure of a formalized mathematical theory and was depicted as a hierarchical system of propositions, where from the basic statements of the upper tiers the propositions of the lower tiers are strictly logically derived up to the propositions that are directly comparable with experimental facts. The hierarchy of interconnected abstract objects corresponds to the hierarchical structure of statements. The connections of these objects form theoretical schemes of various levels. And then the deployment of the theory appears not only as an operation with statements, but also as thought experiments with abstract objects of theoretical schemes.

Theoretical schemes play an important role in the development of a theory. The conclusion from the fundamental equations of the theory of their consequences (particular theoretical laws) is carried out not only through formal mathematical and logical operations on statements, but also through meaningful techniques - thought experiments with abstract objects of theoretical schemes that make it possible to reduce the fundamental theoretical scheme to private ones. Their elements of theoretical schemes are abstract objects (theoretical constructs) that are in strictly defined connections and relationships with each other. Theoretical laws are directly formulated in relation to the abstract objects of the theoretical model. They can be applied to describe real situations of experience only if the model is justified as an expression of the essential connections of reality that appear in such situations.

Theoretical knowledge are created to explain and predict the phenomena and processes of objective and subjective reality. Depending on the level of penetration into the essence of the object under study, scientific theories are divided into descriptive-phenomenological (empirical) and deductive (mathematized, axiomatic).

So, theory is an abstract-generalized, constructively constructed, integral and logically unfolding conceptual model of the object of study, which is a logically abbreviated knowledge with explanatory and heuristic abilities.

On the whole, the empirical and theoretical levels of scientific research discussed above are conditional stages of a holistic scientific process. The edifice of science thus characterized rests on a foundation, designated as the foundations of science.