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 with different sides.

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 drawback 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.). Typical mathematical model- this 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. Thereby 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 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, absolutely black body, socio-economic formation, state, etc.

Deduction- the method of scientific knowledge, which is the receipt of particular conclusions on the basis of 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 of 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 in a 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 already 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 either receives experimental confirmation or is 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 of individual aspects of the subject in thinking 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 mental-concrete is the process of moving from individual general abstractions to their unity, the concrete-universal; the methods of synthesis and deduction dominate here.

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- carried out in the course of practice active process generalized and mediated reflections of reality, 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 put forward not 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. Theory is strictly scientific sense- this is a system of already confirmed knowledge, comprehensively revealing 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.

There are two levels in the structure of scientific knowledge: empirical and theoretical. These two levels should be distinguished from the two stages of the cognitive process as a whole - sensual and rational. Sensory knowledge is close, but not identical, to empirical, rational differs from theoretical.

Sensual and rational are forms of human knowledge in general, both scientific and everyday; empirical and theoretical knowledge is characteristic of science. Empirical knowledge is not limited to sensory knowledge, it includes moments of reflection, understanding, interpretation of observational data and formation special type knowledge is a scientific fact. The latter is the interaction of sensory and rational knowledge.

Theoretical knowledge is dominated by forms of rational knowledge (concepts, judgments, conclusions), but visual model representations such as an ideal ball, an absolutely rigid body are also used. A theory always contains sensory-visual components. Thus, at both levels of cognition, both feelings and reason function.

The difference between the empirical and theoretical levels of scientific knowledge occurs for the following reasons (Table 2):

The level of reflection of reality,

The nature of the subject of study,

Applied methods of study,

Forms of knowledge,

Language tools.

table 2

The difference between empirical and theoretical levels of knowledge

empirical and theoretical study is aimed at cognition of the same objective reality, but its vision, reflection in knowledge occurs in different ways. Empirical research is fundamentally focused on the study external relations and sides of objects, phenomena and dependencies between them. As a result of this study, empirical dependencies are clarified. They are the result of an inductive generalization of experience and represent probabilistically true knowledge. This is, for example, the Boyle-Mariotte law, which describes the correlation between the pressure and volume of a gas: РV= сonst, where Р is the gas pressure, V is its volume. At first, it was discovered by R. Boyle as an inductive generalization of experimental data, when a relationship was found in the experiment between the volume of gas compressed under pressure and the value of this pressure.

At the theoretical level of cognition, there is a selection of internal, essential connections of the object, which are fixed in the laws. No matter how many experiments we make and generalize their data, a simple inductive generalization does not lead to theoretical knowledge. Theory is not constructed by inductive generalization of facts. Einstein considered this conclusion to be one of the important epistemological lessons of the development of physics in the 20th century. theoretical law It is always reliable knowledge.

Empirical research is based on the direct practical interaction of the researcher with the object under study. And in this interaction, the nature of objects, their properties and features are known. The truth of empirical knowledge is verified by direct appeal to experience, to practice. At the same time, the objects of empirical knowledge should be distinguished from the objects of reality, which have an infinite number signs. Empirical objects are abstractions that have a fixed and limited set of features.

In a theoretical study, there is no direct practical interaction with objects. They are studied only indirectly, in a thought experiment, but not in a real one. Theoretical ideal objects are studied here, which are called idealized objects, abstract objects or constructs. Their examples are a material point, an ideal product, an absolutely rigid body, an ideal gas, etc. For example, a material point is defined as a body devoid of size, but concentrating in itself the entire mass of the body. There are no such bodies in nature, they are constructed by thinking to reveal the essential aspects of the object under study. Verification of theoretical knowledge by referring to experience is impossible, and therefore it is associated with practice through empirical interpretation.

The levels of scientific knowledge also differ in functions: at the empirical level, a description of reality takes place, at the theoretical level, an explanation and prediction.

The empirical and theoretical levels differ in the methods and forms of knowledge used. The study of empirical objects is carried out with the help of observation, comparison, measurement and experiment. means empirical research are devices, installations and other means of real observation and experiment.

At the theoretical level, there are no means of material, practical interaction with the object under study. Special methods are used here: idealization, formalization, thought experiment, axiomatic, ascent from the abstract to the concrete.

The results of empirical research are expressed in natural language with the addition of special concepts in the form of scientific facts. They fix the objective, reliable information about the objects under study.

The results of theoretical research are expressed in the form of law and theory. For this, special language systems are created in which the concepts of science are formalized and mathematized.

The specificity of theoretical knowledge is its reflexivity, focus on itself, the study of the very process of knowledge, its methods, forms, conceptual apparatus. In empirical knowledge, this kind of research, as a rule, is not conducted.

In real cognition of reality, empirical and theoretical knowledge always interact as two opposites. The data of experience, arising independently of theory, are sooner or later covered by theory and become knowledge, conclusions from it.

On the other hand, scientific theories, arising on their own special theoretical basis, are built relatively independently, without a rigid and unambiguous dependence on empirical knowledge, but obey them, representing, in the final analysis, a generalization of experimental data.

Violation of the unity of empirical and theoretical knowledge, absolutization of any of these levels leads to erroneous one-sided conclusions - empiricism or scholastic theorizing. Examples of the latter are the concept of building communism in the USSR in 1980, the theory of developed socialism, Lysenko's antigenetic doctrine. Empiricism absolutizes the role of facts and underestimates the role of thinking, denies its active role and relative independence. The only source of knowledge is experience, sensory knowledge.

Methods of scientific knowledge

Consider the essence of general scientific methods of cognition. These methods originate in the bosom of one science, and then are used in a number of others. Such methods include mathematical methods, experiment, modeling. General scientific methods are divided into those applied at the empirical level of knowledge and at the theoretical level. The methods of empirical research include observation, comparison, measurement, experiment.

Observation- systematic purposeful perception of the phenomena of reality, during which we gain knowledge about the external aspects, properties and their relationships. Observation is an active cognitive process, based primarily on the work of the human senses and its objective material activity. This, of course, does not mean that human thinking is excluded from this process. The observer consciously searches for objects, guided by a certain idea, hypothesis or previous experience. Observation results always require a certain interpretation in the light of existing theoretical positions. The interpretation of observational data enables the scientist to separate essential facts from non-essential ones, to notice what a non-specialist can ignore. Therefore, nowadays in science it rarely happens that discoveries are made by non-specialists.

Einstein in a conversation with Heisenberg noted that the possibility of observing a given phenomenon or not depends on the theory. It is the theory that must establish what can be observed and what cannot.

The progress of observation as a method of scientific knowledge is inseparable from the progress of means of observation (for example, a telescope, microscope, spectroscope, radar). Devices not only enhance the power of the senses, but also give us, as it were, additional bodies perception. So, devices allow you to "see" the electric field.

For surveillance to be effective, it must meet the following requirements:

Intention or intentionality

planning,

Activity,

Systematic.

Observation can be direct, when the object affects the senses of the researcher, and indirect, when the subject uses technical means, devices. AT last case scientists make a conclusion about the objects under study through the perception of the results of the interaction of unobserved objects with observed objects. Such a conclusion is based on a certain theory that establishes a certain relationship between observable and unobservable objects.

Description is a necessary aspect of observation. It is a fixation of the results of observation with the help of concepts, signs, diagrams, graphs. The main requirements that apply to a scientific description are aimed at making it as complete, accurate and objective as possible. The description should give a reliable and adequate picture of the object itself, accurately reflect the phenomenon under study. It is important that the terms used for description have a clear and unambiguous meaning. Description is divided into two types: qualitative and quantitative. Qualitative description involves fixing the properties of the object under study, it gives the most general knowledge about it. A quantitative description involves the use of mathematics and a numerical description of the properties, aspects and relationships of the object under study.

In scientific research, observation performs two main functions: providing empirical information about an object and testing hypotheses and theories of science. Often, observation can also play an important heuristic role, contributing to the development of new ideas.

Comparison- this is the establishment of similarities and differences between objects and phenomena of reality. As a result of comparison, something common is established that is inherent in several objects, and this leads to the knowledge of the law. Only those objects between which an objective commonality can exist should be compared. In addition, the comparison should be carried out according to the most important, essential features. Comparison is the basis of inference by analogy, which plays a large role: the properties of phenomena known to us can be extended to unknown phenomena that have something in common with each other.

Comparison is not only an elementary operation applied in a certain field of knowledge. In some sciences, comparison has grown to the level of a basic method. For example comparative anatomy, comparative embryology. This indicates the ever-increasing role of comparison in the process of scientific knowledge.

Measurement historically, as a method, it developed from the comparison operation, but unlike it, it is a more powerful and universal cognitive tool.

Measurement - determination procedure numerical value some value by comparison with the value taken as a unit of measurement. In order to measure, it is necessary to have an object of measurement, a unit of measurement, a measuring instrument, a certain method of measurement, an observer.

Measurements are either direct or indirect. At direct measurement the result comes directly from the process itself. With indirect measurement, the desired value is determined mathematically based on the knowledge of other quantities obtained by direct measurement. For example, the determination of the mass of stars, measurements in the microcosm. Measurement makes it possible to find and formulate empirical laws and, in some cases, serves as a source for the formulation of scientific theories. In particular, the measurement of the atomic weights of elements was one of the prerequisites for the creation of the periodic system by D.I. Mendeleev, which is a theory of the properties of chemical elements. Michelson's famous measurements of the speed of light subsequently led to a radical break in the ideas established in physics.

The most important indicator of the quality of measurement, its scientific value is accuracy. The latter depends on the quality and diligence of the scientist, on the methods used by him, but mainly on the available measuring instruments. Therefore, the main ways to improve the measurement accuracy are:

Quality improvement measuring instruments operating
based on certain established principles,

Creation of devices operating on the basis of new principles.
Measurement is one of the most important prerequisites for the application of mathematical methods in science.

Most often, the measurement is an elementary method that is included as an integral part of the experiment.

Experiment- the most important and complex method empirical knowledge. An experiment is understood as such a method of studying an object, when the researcher actively influences it by creating artificial conditions necessary to identify the relevant properties of this object.

The experiment involves the use of observation, comparison and measurement as more elementary research methods. The main feature of the experiment is the intervention of the experimenter during natural processes, which determines the active nature of this method of cognition.

What advantages follow from the specific features of the experiment in comparison with observation?

During the experiment, it becomes possible to study this
phenomena in pure form”, i.e., various side factors are excluded,
obscuring the essence of the main process.

The experiment allows you to explore the properties of objects of reality in extreme conditions(at extra low or extra high
temperatures, at highest pressure). This can lead to unexpected effects, whereby new properties of objects are discovered. This method was used, for example, to discover the properties of superfluidity and
superconductivity.

The most important advantage of the experiment is its repeatability, and its conditions can be systematically changed.

Classification of experiments is carried out on various grounds.

Depending on the goals, several types of experiment can be distinguished:

- research– carried out in order to detect the object has no
previously known properties ( classic example- Rutherford's experiments on

scattering of a-particles, as a result of which the planetary
atom structure);

- verification- is carried out to test certain statements of science (an example of a testing experiment is testing the hypothesis of the existence of the planet Neptune);

- measuring- is carried out to obtain accurate values ​​of certain properties of objects (for example, experimental melting of metals, alloys; experiments to study the strength of structures).

Physical, chemical, biological, psychological, social experiments are distinguished by the nature of the object under study.

According to the method and results of the study, experiments can be divided into qualitative and quantitative. The first of them are rather exploratory, exploratory in nature, the second provide an accurate measurement of all significant factors influencing the course of the process under study.

An experiment of any kind can be carried out both directly with the object of interest, and with its substitute - the model. Accordingly, experiments are natural and model. Models are used in cases where the experiment is impossible or impractical.

The experiment has received the greatest application in natural science. modern science began with the experiments of G. Galileo. However, at present all more development he gets in the study of social processes. Such a spread of the experiment in an increasing number of branches of scientific knowledge speaks of the growing importance of this research method. With its help, problems are solved to obtain the values ​​of the properties of certain objects, experimental testing of hypotheses and theories is carried out, and the heuristic value of the experiment in finding new aspects of the studied phenomena is also great. The effectiveness of the experiment also increases in connection with the progress of experimental technology. There is also such a feature: the more experiment is used in science, the faster it develops. It is no coincidence that textbooks in experimental sciences age much faster than those in descriptive sciences.

Science is not limited to the empirical level of research, it goes further, revealing the essential connections and relationships in the object under study, which, taking shape in a law known by man, acquire a certain theoretical form.

At the theoretical level of cognition, other means and methods of cognition are used. The methods of theoretical research include: idealization, formalization, the method of ascent from the abstract to the concrete, axiomatic, thought experiment.

Method of ascent from the abstract to the concrete. The concept of "abstract" is used mainly to characterize human knowledge. Abstract is understood as one-sided, incomplete knowledge, when only those properties that are of interest to the researcher are highlighted.

The concept of "concrete" in philosophy can be used in two senses: a) "concrete" - reality itself, taken in all its variety of properties, connections and relationships; b) "concrete" - the designation of multifaceted, comprehensive knowledge about the object. The concrete in this sense acts as the opposite of abstract knowledge, i.e. knowledge, poor in content, one-sided.

What is the essence of the method of ascent from the abstract to the concrete? The ascent from the abstract to the concrete is the general form of the movement of knowledge. According to this method, the process of cognition is divided into two relatively independent stages. At the first stage, the transition from the sensory-concrete to its abstract definitions is carried out. The object itself in the process of this operation, as it were, “evaporates”, turning into a set of abstractions fixed by thinking, one-sided definitions.

The second stage of the process of cognition is actually the ascent from the abstract to the concrete. Its essence lies in the fact that thought moves from abstract definitions of an object to a comprehensive, multifaceted knowledge about an object, to concrete knowledge. It should be noted that these are two sides of the same process, which have only relative independence.

Idealization- the mental construction of objects that do not exist in reality. Such ideal objects include, for example, an absolutely black body, a material point, a point electric charge. The process of constructing an ideal object necessarily implies an abstracting activity of consciousness. So, speaking of a completely black body, we abstract from the fact that all real bodies have the ability to reflect the light falling on them. Other mental operations are also of great importance for the formation of ideal objects. This is due to the fact that when creating ideal objects, we must achieve the following goals:

Deprive real objects of some of their inherent properties;
- mentally endow these objects with certain unrealistic properties. This requires a mental transition to the limiting case in the development of some property and the rejection of some real properties of objects.

Ideal objects play an important role in science; they make it possible to significantly simplify complex systems, which makes it possible to apply mathematical methods of investigation to them. Moreover, science knows many examples when the study of ideal objects led to outstanding discoveries (Galileo's discovery of the principle of inertia). Any idealization is justified only within certain limits, it serves to scientific solution only certain problems. Otherwise, the use of idealization can lead to some misconceptions. Only with this in mind can one correctly assess the role of idealization in cognition.

Formalization- a method of studying a wide variety of objects by displaying their content and structure in a sign form and studying the logical structure of the theory. The advantage of formalization is the following:

Ensuring the completeness of the review of a certain area of ​​​​problems, the generalization of the approach to solving them. A general algorithm for solving problems is being created, for example, calculating the areas of various figures using integral calculus;

The use of special symbols, the introduction of which ensures the brevity and clarity of fixing knowledge;

Attribution to individual symbols or their systems certain values, which avoids the ambiguity of terms, which is characteristic natural languages. Therefore, when operating with formalized systems, reasoning is distinguished by clarity and rigor, and conclusions by evidence;

The ability to form iconic models of objects and replace the study of real things and processes with the study of these models. This simplifies cognitive tasks. Artificial languages ​​have a relatively large independence, independence of the sign form in relation to the content, therefore, in the process of formalization, it is possible to temporarily digress from the content of the model and explore only the formal side. Such a distraction from the content can lead to paradoxical, but truly ingenious discoveries. For example, with the help of formalization, the existence of the positron was predicted by P. Dirac.

Axiomatization found wide application in mathematics and mathematic sciences.

The axiomatic method of constructing theories is understood as such an organization when a number of statements are introduced without proof, and all the rest are deduced from them according to certain logical rules. Propositions accepted without proof are called axioms or postulates. This method was first used to construct elementary geometry by Euclid, then it was used in various sciences.

A number of requirements are imposed on an axiomatically constructed system of knowledge. According to the requirement of consistency in the system of axioms, a proposition and its negation must not be deduced simultaneously. According to the requirement of completeness, any sentence that can be formulated in a given system of axioms can be proved or refuted in it. According to the requirement of independence of axioms, any of them must not be deducible from other axioms.

What are the advantages of the axiomatic method? First of all, the axiomatization of science requires exact definition concepts used and adherence to the rigor of the conclusions. In empirical knowledge, both have not been achieved, which is why the application of the axiomatic method requires the progress of this field of knowledge in this respect. In addition, axiomatization streamlines knowledge, excludes unnecessary elements from it, eliminates ambiguities and contradictions. In other words, axiomatization rationalizes the organization of scientific knowledge.

At present, attempts are being made to apply this method in non-mathematized sciences: biology, linguistics, geology.

thought experiment is carried out not with material objects, but with ideal copies. The thought experiment is like perfect shape real experiment and can lead to important discoveries. It was a thought experiment that allowed Galileo to discover the physical principle of inertia, which formed the basis of all classical mechanics. This principle could not be discovered in any experiment with real objects, in real environments.

The methods used both at the empirical and theoretical levels of research include generalization, abstraction, analogy, analysis and synthesis, induction and deduction, modeling, historical and logical methods, and mathematical methods.

abstraction has the most universal character in mental activity. The essence of this method is the mental abstraction from non-essential properties, connections and the simultaneous selection of one or more aspects of the subject being studied that are of interest to the researcher. The process of abstraction has a two-stage character: the separation of the essential, the identification of the most important; the realization of the possibility of abstraction, i.e., the actual act of abstraction or abstraction.

The result of abstraction is the formation of various kinds of abstractions - both individual concepts and their systems. It should be noted that this method is integral part to all other methods that are more complex in structure.

When we abstract some property or relations of a number of objects, we thereby create the basis for their unification into a single class. In relation to the individual features of each of the objects included in this class, the feature that unites them acts as a common feature.

Generalization- a method, a method of cognition, as a result of which general properties and signs of objects. The generalization operation is carried out as a transition from a particular or less general concept and judgment to a more general concept or judgment. For example, concepts such as "pine", "larch", "spruce" are primary generalizations from which one can move on to the more general concept of "coniferous tree". Then you can move on to such concepts as "tree", "plant", "living organism".

Analysis- a method of cognition, the content of which is a set of methods for dividing an object into its constituent parts for the purpose of their comprehensive study.

Synthesis- a method of cognition, the content of which is a set of methods for connecting individual parts of an object into a single whole.

These methods complement, condition and accompany each other. To make it possible to analyze a thing, it must be fixed as a whole, for which its synthetic perception is necessary. Conversely, the latter presupposes its subsequent dismemberment.

Analysis and synthesis are the most elementary methods knowledge that lies at the very foundation human thinking. At the same time, they are also the most universal techniques, characteristic of all its levels and forms.

The possibility of analyzing an object is, in principle, unlimited, which logically follows from the proposition of the inexhaustibility of matter. However, the choice of elementary components of the object is always carried out, determined by the purpose of the study.

Analysis and synthesis are closely interconnected with other methods of cognition: experiment, modeling, induction, deduction.

Induction and deduction. The division of these methods is based on the allocation of two types of reasoning: deductive and inductive. In deductive reasoning, a conclusion is made about a certain element of a set based on knowledge of the general properties of the entire set.

All fish breathe with gills.

perch - fish

__________________________

Therefore, the perch breathes with gills.

One of the premises of deduction is necessarily a general judgment. Here there is a movement of thought from the general to the particular. This movement of thought is very often used in scientific research. Thus, Maxwell, from several equations expressing the most general laws of electrodynamics, successively developed the complete theory of the electromagnetic field.

Especially great cognitive significance of deduction is manifested in the case when a new scientific hypothesis acts as a general premise. In this case, deduction is the starting point for the birth of a new theoretical system. The knowledge created in this way determines the further course of empirical research and directs the construction of new inductive generalizations.

Consequently, the content of deduction as a method of cognition is the use of general scientific statements in the study of specific phenomena.

Induction is a conclusion from the particular to the general, when, on the basis of knowledge about a part of the objects of a class, a conclusion is made about the class as a whole. Induction as a method of cognition is a set of cognitive operations, as a result of which the movement of thought from less general provisions to more general ones is carried out. Thus, induction and deduction are directly opposite directions of the train of thought. The immediate basis of inductive reasoning is the repetition of the phenomena of reality. discovering similarities many objects of a certain class, we conclude that these features are inherent in all objects of this class.

There are the following types of induction:

-full induction, in which a general conclusion about a class of objects is made on the basis of the study of all objects of the class. Complete induction gives
reliable conclusions and can be used as evidence;

-incomplete induction, in which the general conclusion is obtained from the premises,
not covering all items of the class. There are three types of incomplete
induction:

Induction by simple enumeration or popular induction, in which a general conclusion about a class of objects is made on the basis that among the observed facts there was not one that contradicted the generalization;

Induction through the selection of facts is carried out by selecting them from the general mass according to a certain principle that reduces the likelihood random coincidences;

Scientific induction, in which the general conclusion about all items in the class
is done on the basis of knowledge of the necessary signs or causal
connections of a part of class objects. Scientific induction can give not only
probable, but also reliable conclusions.

Causal relationships can be established by methods of scientific induction. The following canons of induction are distinguished (Bacon-Mill rules of inductive research):

Single similarity method: if two or more cases of the phenomenon under study have only one circumstance in common, and all the others
circumstances are different, then this is the only similar circumstance and
there is a reason this phenomenon;

Single difference method: if the cases in which the phenomenon
occurs or does not occur, differ only in one previous circumstance, and all other circumstances are identical, then this circumstance is the cause of this phenomenon;

The combined method of similarity and difference, which is
a combination of the first two methods;

Concomitant change method: if a change in one circumstance always causes a change in another, then the first circumstance
there is a reason for the second;

Residual method: if it is known that the cause of the phenomenon under study
the circumstances necessary for it do not serve, except for one, then this one circumstance is the cause of this phenomenon.

The attractiveness of induction lies in its close connection with facts, with practice. It plays an important role in scientific research - in putting forward hypotheses, in discovering empirical laws, in the process of introducing new concepts into science. Noting the role of induction in science, Louis de Broglie wrote: “Induction, insofar as it seeks to avoid paths already beaten, inasmuch as it inevitably tries to push apart already existing borders thought, is the true source of truly scientific progress” 1 .

But induction cannot lead to universal judgments in which regularities are expressed. Inductive generalizations cannot make the transition from empiricism to theory. Therefore, it would be wrong to absolutize the role of induction, as Bacon did, to the detriment of deduction. F. Engels wrote that deduction and induction are interconnected in the same necessary way as analysis and synthesis. Only in mutual connection can each of them fully show their merits. Deduction is the main method in mathematics, in the theoretically developed sciences, in the empirical sciences, inductive conclusions predominate.

Historical and logical methods are closely interconnected. They are used in the study of complex developing objects. The essence of the historical method is that the history of the development of the object under study is reproduced in all its versatility, taking into account all laws and chances. It is primarily used for research human history, but plays an important role in the knowledge of the development of inanimate and living nature.

The history of the object is reconstructed in a logical way based on the study of certain traces of the past, the remnants of past eras, captured in material formations(natural or man-made). For historical research characteristic chronological after

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1 Broglie L. On the paths of science. M., S. 178.

consistency of consideration of the material, analysis of the stages of development of the objects of study. With the help of the historical method, the entire evolution of an object from its inception to its current state is traced, the genetic relationships of the developing object are studied, the driving forces and conditions for the development of the object are clarified.

The content of the historical method is revealed by the structure of the study: 1) the study of "traces of the past" as the results of historical processes; 2) comparing them with the results of modern processes; 3) reconstruction of past events in their spatio-temporal relations based on the interpretation of "traces of the past" with the help of knowledge about modern processes; 4) identification of the main stages of development and the reasons for the transition from one stage of development to another.

The logical method of research is the reproduction in thinking of a developing object in the form of a historical theory. In logical research, one abstracts from all historical accidents, reproducing history in general view, liberated from all non-essential. The principle of the unity of the historical and the logical requires that the logic of thought should follow the historical process. This does not mean that thought is passive; on the contrary, its activity consists in isolating from history the essential, the very essence of the historical process. We can say that the historical and logical methods of cognition are not only different, but also largely coincide. It is no coincidence that F. Engels noted that the logical method is, in essence, the same historical method, but freed from the historical form. They complement each other.

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 goes deep 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". 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 what 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 passes into the theoretical, and what was once theoretical, at another, higher stage of development, becomes empirically accessible. 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 a systematic and purposeful perception of 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

Especially difficult is observation in the social sciences, where its results largely depend on the worldview and methodological attitudes of the observer, his attitude to the object

The method of observation is a limited method, since it can only fix certain properties and connections 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 of the 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. It makes it possible to check the correctness scientific findings and discoveries, new laws and rnosti. 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 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 own 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 an object under study using various measuring instruments and apparatus. Measurement is used to determine the ratio of one quantitative characteristic of an object to another, homogeneous with it, taken as a unit of measurement. 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 that operates special program, is able to simulate the most real processes: fluctuations in market prices, orbits spaceships, demographic processes, other quantitative parameters of the development of nature, society, an individual person.

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 into 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 captures common features and properties certain group objects, carries out the transition from the singular to the special and general, from the less general to the more zagal.

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. In real cognition, induction always acts in unity with deduction, is organically connected with it.

Deduction is a method of cognition, when, on the basis of a general principle, a new true knowledge about a separate one is necessarily derived from some provisions as true ones. 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. it certain way in the reproduction in thinking of 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 a system of concepts.

The task of historical research is to reveal the 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.

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The specificity of the theoretical level of cognition is characterized by the predominance of the rational side of the cognitive process: concepts, judgments, conclusions, principles, laws. Theoretical knowledge is abstract, mediated knowledge.

Theoretical knowledge reflects objects, phenomena, objects and processes in terms of their universal internal connections, patterns. They are comprehended with the help of rational data processing of empirical knowledge.

An integral feature, the most characteristic feature of theoretical knowledge is the use of such methods, techniques as abstraction - abstraction from the non-essential features of the object of study, idealization - the creation is often simple mental objects, analysis - the mental division of the object under study into elements, synthesis - the combination of the elements obtained as a result of analysis into a system, induction - the movement of knowledge from the particular to the general, deduction - the movement of thought from the general to the particular, etc.

What are structural components theoretical knowledge? These include: the problem, or rather the formulation of the problem. The problem literally means "obstacle, difficulty", is defined as a situation characterized by the insufficiency of ways, means to achieve a certain goal, ignorance of the ways to achieve it. The problem characterizes not even an obstacle in itself, but the attitude of a scientist to an obstacle.

If we talk about solving the problem, then there is a range of differences. Problem solving can be palliative or radical, temporary or permanent.

A hypothesis as a form of theoretical knowledge contains an assumption formulated on the basis of a number of facts, the true meaning of which is uncertain and needs to be proven. A hypothesis is a probabilistic thing. As a scientific assumption, it differs from arbitrary conjecture in that it relies on facts.

The nature of hypotheses is largely determined by the object in relation to which it is put forward. So, general, particular and working hypotheses are distinguished. General hypotheses this is a substantiation of the assumption about regularities of various kinds. Such hypotheses serve as the foundation for building the foundations of scientific knowledge. Particular hypotheses are reasonable assumptions about the origin and properties of single phenomena, individual events. Working hypotheses are assumptions that are put forward, as a rule, at the first stages of the study and serve as its guiding landmark.

The selection of reliable hypotheses occurs through evidence as a form of knowledge. The most common are inductive and deductive methods proof of. inductive method represents a chain of inferences, the premises of which cover particular judgments and are arguments substantiating the thesis, that is, a general judgment is derived from particular judgments, the transition from the particular to the general in thinking. That's it greater value acquire deductive reasoning.

Theory as a form of cognition and knowledge, and the most complex and developed, gives a holistic reflection of the patterns of a certain area of ​​reality. By its structure scientific theory is a system of initial, initial concepts and fundamental laws, from which, with the help of a definition, all its other concepts can be formed, and the rest of the laws are logically derived from the basic laws. From a methodological point of view, an important role in the formation of the theory is played by the abstract, idealized object(as a reflection of the real object under study). This is a special abstraction that contains meaning theoretical terms(perfect item).

Theory generation is the ultimate goal of the study. The quintessence of the theory - law. It expresses the essential, deep connections of the object. The formulation of laws is one of the main tasks of science. Theoretical knowledge is most adequately reflected in thinking(an active process of generalized and indirect reflection of reality), and here goes the way from thinking within the established framework, according to the model, to an ever greater isolation, creative understanding of the phenomenon under study.

The main ways of reflecting the surrounding reality in thinking are the concept (reflects the general, essential aspects of the object), judgment (reflects the individual characteristics of the object); conclusion (a logical chain that gives birth to new knowledge). With all the differences e. etc. levels of scientific knowledge connected. E. research revealing new data through experiments and observations, stimulates T. cognition(which generalizes and explains them, sets new, more complex tasks for them). On the other hand, t. knowledge, developing and concretizing on the basis of empiricism a new content of its own, opens up new wider horizons for e. knowledge, orients and directs him in search of new facts, contributes to the improvement of his methods and means.

28. Empirical and theoretical level of scientific knowledge. Their main forms and methods

Scientific knowledge has two levels: empirical and theoretical.

- it is direct sensory exploration real and experiential objects.

At the empirical level, the following research processes:

1. Formation of the empirical base of the study:

Accumulation of information about the studied objects and phenomena;

Determining the scope of scientific facts as part of the accumulated information;

Introduction of physical quantities, their measurement and systematization of scientific facts in the form of tables, diagrams, graphs, etc.;

2. Classification and theoretical generalization information about the received scientific facts:

Introduction of concepts and designations;

Identification of patterns in the connections and relationships of objects of knowledge;

Identification of common features in objects of knowledge and their reduction into general classes according to these features;

Primary formulation of initial theoretical positions.

In this way, empirical level scientific knowledge contains two components:

1. Sensory experience.

2. Primary theoretical understanding sensory experience.

The basis of the content of empirical scientific knowledge received in sensory experience, are scientific facts. If any fact, as such, is a reliable, single, independent event or phenomenon, then a scientific fact is a fact that is firmly established, reliably confirmed and correctly described in the ways accepted in science.

Revealed and fixed by the methods accepted in science, a scientific fact has a coercive power for the system of scientific knowledge, that is, it subordinates the logic of the reliability of the study.

Thus, at the empirical level of scientific knowledge, an empirical research base is formed, whose reliability is formed by the coercive force of scientific facts.

Empirical level scientific knowledge uses the following methods:

1. observation. Scientific observation is a system of measures for the sensory collection of information about the properties of the studied object of knowledge. The main methodological condition for correct scientific observation is the independence of the results of observation from the conditions and process of observation. The fulfillment of this condition ensures both the objectivity of observation and the implementation of its main function - the collection of empirical data in their natural, natural state.

Observations according to the method of conducting are divided into:

- immediate(information is obtained directly by the senses);

- indirect(human senses are replaced by technical means).

2. Measurement. Scientific observation is always accompanied by measurement. A measurement is a comparison of some physical quantity object of knowledge with the reference unit of this quantity. Measurement is a sign of scientific activity, since any research becomes scientific only when measurements are made in it.

Depending on the nature of the behavior of certain properties of an object in time, measurements are divided into:

- static, in which time-constant values ​​are determined (external dimensions of bodies, weight, hardness, constant pressure, specific heat capacity, density, etc.);

- dynamic, in which time-varying quantities are found (oscillation amplitudes, pressure drops, temperature changes, changes in quantity, saturation, speed, growth rates, etc.).

According to the method of obtaining the measurement results, they are divided into:

- straight(direct measurement of a quantity with a measuring device);

- indirect(by mathematical calculation of a quantity from its known ratios with any quantity obtained by direct measurements).

The purpose of measurement is to express the properties of an object in quantitative characteristics, translate them into a language form and make the basis of a mathematical, graphical or logical description.

3. Description. The measurement results are used for the scientific description of the object of knowledge. Scientific Description is a reliable and accurate picture of the object of knowledge, displayed by means of natural or artificial language.

The purpose of the description is to translate sensory information into a form convenient for rational processing: into concepts, into signs, into diagrams, into drawings, into graphs, into numbers, etc.

4. Experiment. An experiment is a research impact on an object of knowledge to identify new parameters of its known properties or to identify its new, previously unknown properties. An experiment differs from an observation in that the experimenter, unlike the observer, intervenes in the natural state of the object of cognition, actively influences both himself and the processes in which this object participates.

According to the nature of the goals set, the experiments are divided into:

- research, which are aimed at discovering new, unknown properties in an object;

- verification, which serve to test or confirm certain theoretical constructions.

According to the methods of conducting and tasks for obtaining the result, the experiments are divided into:

- quality, which are of an exploratory nature, set the task of revealing the very presence or absence of certain theoretically assumed phenomena, and are not aimed at obtaining quantitative data;

- quantitative, which are aimed at obtaining accurate quantitative data about the object of knowledge or about the processes in which it participates.

After the completion of empirical knowledge, the theoretical level of scientific knowledge begins.

THEORETICAL LEVEL OF SCIENTIFIC KNOWLEDGE is the processing of empirical data by thinking with the help of abstract work thoughts.

Thus, the theoretical level of scientific knowledge is characterized by the predominance of rational moment- concepts, conclusions, ideas, theories, laws, categories, principles, premises, conclusions, conclusions, etc.

The predominance of the rational moment in theoretical knowledge is achieved by abstracting- distraction of consciousness from sensually perceived concrete objects and transition to abstract representations.

Abstract representations are subdivided into:

1. Identification abstractions- grouping a set of objects of knowledge into separate species, genera, classes, orders, etc., according to the principle of identity of any of the most significant features (minerals, mammals, composites, chordates, oxides, protein, explosive, liquids, amorphous, subatomic etc.).

Identification abstractions make it possible to discover the most general and essential forms of interactions and connections between objects of knowledge, and then move from them to particular manifestations, modifications and options, revealing the fullness of the processes occurring between objects of the material world.

Distracting from the non-essential properties of objects, the abstraction of identification allows us to translate specific empirical data into an idealized and simplified system of abstract objects for the purposes of cognition, capable of participating in complex operations of thinking.

2. Isolating abstractions. Unlike abstractions of identification, these abstractions separate into separate groups not objects of knowledge, but their general properties or features (hardness, electrical conductivity, solubility, impact strength, melting point, boiling point, freezing point, hygroscopicity, etc.).

Isolating abstractions also make it possible to idealize empirical experience for the purpose of cognition and express it in terms capable of participating in complex operations of thinking.

Thus, the transition to abstractions allows theoretical knowledge to provide thinking with a generalized abstract material for obtaining scientific knowledge about all the diversity real processes and objects of the material world, which could not be done, limited only by empirical knowledge, without abstraction from each of these innumerable objects or processes.

As a result of abstraction, the following METHODS OF THEORETICAL KNOWLEDGE:

1. Idealization. Idealization is mental creation of objects and phenomena that are not feasible in reality to simplify the process of research and construction of scientific theories.

For example: the concepts of a point or a material point, which are used to designate objects that do not have dimensions; introduction of various conditional concepts, such as: ideal Smooth surface, ideal gas, absolutely black body, absolutely rigid body, absolute density, inertial system reference, etc., for illustration scientific ideas; the orbit of an electron in an atom, the pure formula of a chemical substance without impurities, and other concepts that are impossible in reality, created to explain or formulate scientific theories.

Idealizations are appropriate:

When it is necessary to simplify the object or phenomenon under study in order to build a theory;

When it is necessary to exclude from consideration those properties and connections of the object that do not affect the essence of the planned research results;

When the real complexity of the object of study exceeds the existing scientific possibilities of its analysis;

When the real complexity of the objects of study makes it impossible or makes it difficult to describe them scientifically;

Thus, in theoretical knowledge there is always a replacement real phenomenon or an object of reality by its simplified model.

That is, the idealization method in scientific knowledge is inextricably linked with the modeling method.

2. Modeling. Theoretical modeling is replacement of a real object by its analogue performed by means of language or mentally.

The main condition for modeling is that the created model of the object of knowledge due to high degree its correspondence to reality, allowed:

Conduct research of the object that is not feasible in real conditions;

Conduct research on objects that are in principle inaccessible in real experience;

Conduct research on an object that is directly inaccessible at the moment;

Reduce the cost of research, reduce its time, simplify its technology, etc.;

Optimize the process of building a real object by running the process of building a prototype model.

Thus, theoretical modeling performs two functions in theoretical knowledge: it investigates the object being modeled and develops a program of action for its material embodiment (construction).

3. thought experiment. The thought experiment is mental holding over the object of cognition unrealizable in reality research procedures.

It is used as a theoretical testing ground for planned real research activities, or for the study of phenomena or situations in which a real experiment is generally impossible (for example, quantum physics, the theory of relativity, social, military or economic models of development, etc.).

4. Formalization. Formalization is logical organization of content scientific knowledge means artificial language special symbols (signs, formulas).

Formalization allows:

Bring the theoretical content of the study to the level of general scientific symbols (signs, formulas);

Transfer the theoretical reasoning of the study to the plane of operating with symbols (signs, formulas);

Create a generalized sign-symbolic model of the logical structure of the phenomena and processes under study;

To carry out a formal study of the object of knowledge, that is, to carry out research by operating with signs (formulas) without directly referring to the object of knowledge.

5. Analysis and synthesis. Analysis is a mental decomposition of the whole into its constituent parts, pursuing the following goals:

Study of the structure of the object of knowledge;

The division of a complex whole into simple parts;

Separation of the essential from the non-essential in the composition of the whole;

Classification of objects, processes or phenomena;

Highlighting the stages of a process, etc.

The main purpose of analysis is the study of parts as elements of the whole.

The parts, known and comprehended in a new way, are formed into a whole with the help of synthesis - a method of reasoning that constructs new knowledge about the whole from the union of its parts.

Thus, analysis and synthesis are inseparably linked mental operations as part of the process of cognition.

6. Induction and deduction.

Induction is a process of cognition in which knowledge of individual facts in the aggregate leads to knowledge of the general.

Deduction is a process of cognition in which each subsequent statement logically follows from the previous one.

The above methods of scientific knowledge allow us to reveal the deepest and most significant connections, patterns and characteristics of objects of knowledge, on the basis of which there are FORMS OF SCIENTIFIC KNOWLEDGE - ways of cumulative presentation of research results.

The main forms of scientific knowledge are:

1. Problem - a theoretical or practical scientific question that needs to be solved. A correctly formulated problem partially contains a solution, since it is formulated on the basis of the actual possibility of its solution.

2. Hypothesis - supposed way possible solution Problems. A hypothesis can act not only in the form of assumptions of a scientific nature, but also in the form of a detailed concept or theory.

3. Theory is an integral system of concepts that describes and explains any area of ​​reality.

Scientific theory is the highest form of scientific knowledge, passing in its formation the stage of posing a problem and putting forward a hypothesis, which is refuted or confirmed by the use of methods of scientific knowledge.

Basic terms

ABSTRAGING- distraction of consciousness from sensually perceived concrete objects and the transition to abstract ideas.

ANALYSIS(general concept) - the mental decomposition of the whole into its component parts.

HYPOTHESIS- the proposed way of a possible solution to a scientific problem.

DEDUCTION- the process of cognition, in which each subsequent statement logically follows from the previous one.

SIGN- a symbol that serves to record quantities, concepts, relationships, etc. of reality.

IDEALIZATION- mental creation of objects and phenomena that are impossible in reality to simplify the process of their study and the construction of scientific theories.

MEASUREMENT- comparison of any physical quantity of the object of knowledge with the reference unit of this quantity.

INDUCTION- the process of cognition, in which knowledge of individual facts in the aggregate leads to knowledge of the general.

THOUGHT EXPERIMENT- mental carrying out on the object of cognition of research procedures that are not feasible in reality.

OBSERVATION- a system of measures for the sensory collection of information about the properties of the object or phenomenon under study.

SCIENTIFIC DESCRIPTION- a reliable and accurate picture of the object of knowledge, displayed by means of a natural or artificial language.

SCIENTIFIC FACT- a fact firmly established, reliably confirmed and correctly described in the ways accepted in science.

PARAMETER- a value that characterizes any property of an object.

PROBLEM- a theoretical or practical scientific issue that needs to be addressed.

PROPERTY- an external manifestation of one or another quality of an object, distinguishing it from other objects, or, conversely, related to them.

SYMBOL- the same as the sign.

SYNTHESIS(process of thinking) - a method of reasoning that constructs new knowledge about the whole from the combination of its parts.

THEORETICAL LEVEL OF SCIENTIFIC KNOWLEDGE- processing of empirical data by thinking with the help of abstract work of thought.

THEORETICAL SIMULATION- replacement of a real object with its analogue, made by means of the language or mentally.

THEORY- an integral system of concepts that describes and explains any area of ​​reality.

FACT- reliable, single, independent event or phenomenon.

FORM OF SCIENTIFIC KNOWLEDGE- a way of cumulative presentation of the results of scientific research.

FORMALIZATION- logical organization of scientific knowledge by means of an artificial language or special symbols (signs, formulas).

EXPERIMENT- research impact on the object of knowledge to study previously known or to identify new, previously unknown properties.

EMPIRICAL LEVEL OF SCIENTIFIC KNOWLEDGE- direct sensory study of objects that really exist and are accessible to experience.

EMPIRY- the area of ​​human relations with reality, determined by sensory experience.