Specificity and basic methods of theoretical knowledge: abstraction, idealization, formalization, thought experiment. Special theoretical methods of scientific knowledge abstraction, idealization, formal

20.09.2019

The process of cognition always begins with the consideration of specific, sensually perceived objects and phenomena, their external signs, properties, relationships. Only as a result of studying the sensory-concrete does a person come to some generalized ideas, concepts, to certain theoretical positions, i.e. scientific abstractions. Obtaining these abstractions is connected with the complex abstracting activity of thinking.

In the process of abstraction, there is a departure (ascension) from sensually perceived concrete objects (with all their properties, aspects, etc.) to abstract ideas about them reproduced in thinking.

abstraction, Thus, it consists in a mental abstraction from some - less significant - properties, aspects, features of the object under study with the simultaneous selection, formation of one or more essential aspects, properties, features of this object. The result obtained in the process of abstraction is called abstraction(or use the term abstract- Unlike specific).

In scientific knowledge, abstractions of identification and isolating abstractions are widely used, for example. Identification abstraction is a concept that is obtained as a result of the identification of a certain set of objects (at the same time, they are abstracted from the

logo of a number of individual properties, features of these objects) and combining them into a special group. An example is the grouping of the entire multitude of plants and animals living on our planet into special species, genera, orders, etc. Isolating abstraction is obtained by separating certain properties, relationships, inextricably linked with the objects of the material world, into independent entities (“stability”, “solubility”, “electrical conductivity”, etc.).

The transition from the sensory-concrete to the abstract is always associated with a certain simplification of reality. At the same time, ascending from the sensory-concrete to the abstract, theoretical, the researcher gets the opportunity to better understand the object under study, to reveal its essence.

Of course, in the history of science there have also been false, incorrect abstractions that did not reflect absolutely anything in the objective world (ether, caloric, vital force, electric fluid, etc.). The use of such "dead abstractions" created only the appearance of explaining the observed phenomena. In reality, there was no deepening of knowledge in this case.

The development of natural science entailed the discovery of more and more real aspects, properties, relationships of objects and phenomena of the material world. A necessary condition for the progress of knowledge was the formation of truly scientific, "non-absurd" abstractions that would allow a deeper understanding of the essence of the phenomena being studied. The process of transition from sensory-empirical, visual representations of the phenomena being studied to the formation of certain abstract, theoretical structures that reflect the essence of these phenomena underlies the development of any science.

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

As a result of such changes, for example, some properties, aspects, attributes of objects can be excluded from consideration. So, widespread in the fur-

nike idealization, called a material point, implies a body devoid of any dimensions. Such an abstract object, the dimensions of which are neglected, is convenient in describing motion. Moreover, such an abstraction makes it possible to replace a variety of real objects in the study: from molecules or atoms when solving many problems of statistical mechanics and to the planets of the solar system when studying, for example, their movement around the Sun.

Changes in the object, achieved in the process of idealization, can also be carried out by endowing it with some special properties that are not feasible in reality. An example is the abstraction introduced into physics by idealization, known as absolutely black body. Such a body is endowed with a property that does not exist in nature to absorb absolutely all the radiant energy that falls on it, reflecting nothing and passing nothing through itself. The radiation spectrum of a black body is an ideal case, because it is not affected by the nature of the substance of the emitter or the state of its surface. And if one can theoretically describe the spectral distribution of the radiation energy density for the ideal case, then one can learn something about the radiation process in general. This idealization played an important role in the progress of scientific knowledge in the field of physics, because it helped to reveal the fallacy of some of the ideas that existed in the second half of the 19th century. In addition, working with such an idealized object helped lay the foundations of quantum theory, which marked a radical revolution in science.

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

First, idealization is expedient when the real objects to be studied are sufficiently complex for the available means of theoretical, in particular, mathematical, analysis. And in relation to the idealized case, it is possible, by applying these means, to construct and develop a theory, effective under certain conditions and goals, for describing the properties and behavior of these real objects. (The latter, in essence, certifies the fruitfulness of idealization, distinguishes it from fruitless fantasy).

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

F. Engels drew attention to this epistemological possibility of idealization, who showed it using the example of a study conducted by Sadi Carnot: “He studied the steam engine, analyzed it, found that the main process in it does not appear in its pure form, but is obscured by all kinds of side processes , eliminated these secondary circumstances indifferent to the main process and constructed an ideal steam engine (or gas engine), which, it is true, also cannot be realized, just as it is impossible, for example, to realize a geometric line or a geometric plane, but which, in its own way, has the same services like these mathematical abstractions. It represents the process under consideration in a pure, independent, undistorted form” 4 .

Thirdly, the use of idealization is advisable when the properties, sides, and connections of the object under study that are excluded from consideration do not affect its essence within the framework of this study. It has already been mentioned above, for example, that the abstraction of a material point allows in some cases to represent a wide variety of objects - from molecules or atoms to giant space objects. Wherein right choice the admissibility of such an idealization plays a very important role. If in a number of cases it is possible and expedient to consider atoms in the form of material points, then such idealization becomes inadmissible when studying the structure of the atom. In the same way, our planet can be considered a material point when considering its rotation around the Sun, but by no means when considering its own daily rotation.

Being a kind of abstraction, idealization allows an element of sensory visualization (the usual process of abstraction leads to the formation of mental abstractions that do not have any visualization). This feature of idealization is very important for the implementation of such a specific method of theoretical knowledge as

you are thought experiment (it is also called mental, subjective, imaginary, idealized).

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

At the same time, the thought experiment also plays an independent role in science. At the same time, while maintaining similarity with the real experiment, it at the same time differs significantly from it. These differences are as follows.

A real experiment is a method associated with practical, object-manipulative, "tool" knowledge of the world around. In a mental experiment, the researcher operates not with material objects, but with their idealized images, and the operation itself is carried out in his mind, that is, purely speculative.

The possibility of setting up a real experiment is determined by the availability of appropriate logistical (and sometimes financial) support. A thought experiment does not require such provision.

In a real experiment, one has to take into account the real physical and other limitations of its implementation, with the impossibility in some cases to eliminate external influences interfering with the course of the experiment, with distortion of the results obtained due to the indicated reasons. In this regard, a thought experiment has a clear advantage over a real experiment. In a thought experiment, one can abstract from the action of undesirable factors by conducting it in an idealized, "pure" form.

In scientific knowledge, there may be cases when, in the study of certain phenomena, situations, conducting real experiments turns out to be impossible at all.

This gap in knowledge can only be filled by a thought experiment.

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

Real experiments in which it is impossible to eliminate the friction factor seemed to confirm Aristotle's concept, which had prevailed for thousands of years, stating that a moving body stops if the force pushing it ceases to act. Such a statement was based on a simple statement of facts observed in real experiments (a ball or cart that received a force impact and then rolled without it on a horizontal surface inevitably slowed down its movement and eventually stopped). In these experiments, it was impossible to observe a uniform incessant motion by inertia.

Galileo, having done mentally indicated experiments with a phased idealization of rubbing surfaces and bringing friction to a complete exclusion from the interaction, refuted the Aristotelian point of view and made the only correct conclusion. This conclusion could only be obtained with the help of a thought experiment, which made it possible to discover the fundamental law of the mechanics of motion.

The idealization method, which turns out to be very fruitful in many cases, has at the same time certain limitations. The development of scientific knowledge sometimes forces us to abandon previously accepted idealized ideas. This happened, for example, when Einstein created the special theory of relativity, from which the Newtonian idealizations "absolute space" and "absolute time" were excluded. In addition, any idealization is limited to a specific area of phenomena and serves to solve only certain problems. This is clearly seen at least in the example of the above idealization of "absolutely black body».

Idealization itself, although it can be fruitful and even lead to scientific discovery, is still insufficient to make this discovery. Here the decisive role is played by the theoretical principles from which the researcher proceeds. The idealization of the steam engine considered above, successfully carried out by Sadi Carnot, led him to the discovery of the mechanical equivalent of heat, which, however, “... he could not discover and see only because,” notes F. Engels, “that he believed in caloric This is also evidence of the harm of false theories.

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

Formalization. The language of science

Under formalization is understood as a special approach in scientific knowledge, which consists in the use of special symbolism, which allows one to abstract from the study of real objects, from the content of the theoretical provisions that describe them, and instead operate with some set of symbols (signs).

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

To build any formal system, it is necessary:

a) setting the alphabet, i.e. a certain set of characters;

b) setting the rules according to which from the initial signs this
th alphabet can be obtained "words", "formulas";

c) setting the rules by which one can move from one word, formula of a given system to other words and formulas (the so-called inference rules). As a result, a formal sign system in the form of a certain artificial language. An important advantage of this system is the possibility of carrying out within its framework the study of an object in a purely formal way (operating with signs) without directly referring to this object.

Another advantage of formalization is to ensure the brevity and clarity of the recording of scientific information, which opens up great opportunities for operating with it. It would hardly be possible to successfully use, for example, Maxwell's theoretical conclusions if they were not compactly expressed in the form of mathematical equations, but were described using ordinary, natural language. Of course, formalized artificial languages do not have the flexibility and richness of a natural language. But they lack the ambiguity of terms (polysemy), which is characteristic of natural languages. They are characterized by a well-constructed syntax (which establishes the rules for the connection between signs, regardless of their content) and unambiguous semantics (the semantic rules of a formalized language quite unambiguously determine the correlation of a sign system with a specific subject area). Thus, a formalized language has the monosemic property.

The ability to represent certain theoretical positions of science in the form of a formalized sign system is of great importance for cognition. But it should be borne in mind that the formalization of a particular theory is possible only if its content is taken into account. Only in this case can certain formalisms be correctly applied. A bare mathematical equation does not yet represent a physical theory; in order to obtain a physical theory, it is necessary to give concrete empirical content to mathematical symbols.

An instructive example of a formally obtained and at first glance "meaningless" result, which subsequently revealed a very deep physical meaning, are the solutions of the Dirac equation describing the motion of an electron. Among these decisions were

which corresponded to states with negative kinetic energy. Later it was found that these solutions described the behavior of hitherto unknown particles - the positron, which is the antipode of the electron. In this case, a certain set of formal transformations led to a meaningful and interesting result for science.

The growing use of formalization as a method of theoretical knowledge is connected not only with the development of mathematics. In chemistry, for example, the corresponding chemical symbolism, together with the rules for operating it, was one of the variants of a formalized artificial language. The method of formalization occupied an increasingly important place in logic as it developed. The works of Leibniz laid the foundation for the creation of the method of logical calculus. The latter led to the formation in the middle of the XIX century mathematical logic, which in the second half of our century played an important role in the development of cybernetics, in the emergence of electronic computers, in solving problems of industrial automation, etc.

The language of modern science differs significantly from natural human language. It contains many special terms, expressions, formalization tools are widely used in it, among which central location belongs to mathematical formalization. Based on the needs of science, various artificial languages \u200b\u200bare created to solve certain problems. The entire set of created and being created artificial formalized languages is included in the language of science, forming a powerful means of scientific knowledge.

However, it should be borne in mind that the creation of a single formalized language of science is not possible. The point is that even sufficiently rich formalized languages do not satisfy the requirement of completeness, i.e., some set of correctly formulated sentences of such a language (including true ones) cannot be derived in a purely formal way within this language. This position follows from the results obtained in the early 30s of the XX century by the Austrian logician and mathematician Kurt Gödel.

The famous theorem Gödel claims, that every normal system is either inconsistent or contains some unsolvable (though true) formula, i.e. a formula that in a given system can neither be proved nor disproved.

True, what is not derivable in a given formal system is derivable in another, richer system. But nevertheless, an ever more complete formalization of content can never reach absolute completeness, i.e., the possibilities of any formalized language remain fundamentally limited. Thus, Gödel gave a strictly logical justification for the impracticability of R. Carnap's idea of creating a single, universal, formalized "physicalist" language of science.

Formalized languages cannot be the only form of the language of modern science. In scientific knowledge, it is also necessary to use non-formalized systems. But trend to the increasing formalization of the languages of all and especially the natural sciences is objective and progressive.

Induction and deduction

Induction(from Latin inductio - guidance, motivation) is a method of cognition based on a formal logical conclusion, which leads to a general conclusion based on particular premises. In other words, it is the movement of our thinking from the particular, the individual to the general.

Induction is widely used in scientific knowledge. Finding similar features, properties in many objects of a certain class, the researcher concludes that these features, properties are inherent in all objects of this class. For example, in the process of experimental study of electrical phenomena, current conductors made of various metals were used. Based on numerous individual experiments, a general conclusion was formed about the electrical conductivity of all metals. Along with other methods of cognition, the inductive method played an important role in the discovery of some laws of nature (universal gravitation, atmospheric pressure, thermal expansion of bodies, etc.).

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

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

2. Single difference method (if circumstances
the occurrence of a phenomenon or circumstance
which it does not arise, are similar and different in almost everything.
only one factor, present only in
first case, we can conclude that this factor and
there is a reason for this.)

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

4. Accompanying change method (if certain
changes in one phenomenon each time entail not
which are changes in another phenomenon, then it follows from this
there is no conclusion about the causal relationship of these phenomena).

5. Method of residuals (if a complex phenomenon is caused
multifactorial cause, some of which
tori are known to be the cause of some part of a given phenomenon.
nia, then the conclusion follows from this: the cause of the other part of the phenomenon
niya - other factors included in common cause
this phenomenon).

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

In fact, the above methods of scientific induction serve mainly to find empirical relationships between the experimentally observed properties of objects and phenomena. They systematize the simplest formal logical techniques that were spontaneously used by natural scientists in any empirical study. As natural science developed, it became more and more clear that the methods of classical induction do not play the all-encompassing role in scientific knowledge that they

attributed to F. Bacon and his followers until the end of the 19th century.

Such an unjustifiably extended understanding of the role of induction in scientific knowledge has been called all inductivism. Its failure is due to the fact that induction is considered in isolation from other methods of cognition and turns into the only, universal means of the cognitive process. All-inductivism was criticized by F. Engels, who pointed out that induction cannot, in particular, be separated from another method of cognition - deduction.

Deduction(from lat. deductio - derivation) is the receipt of private conclusions based on the knowledge of some general provisions. In other words, it is the movement of our thinking from the general to the particular, the individual. For example, from general position that all metals have electrical conductivity, it is possible to make a deductive conclusion about the electrical conductivity of a particular copper wire (knowing that copper is a metal). If the initial general propositions are an established scientific truth, then the true conclusion will always be obtained by the method of deduction. General principles and laws do not allow scientists to go astray in the process of deductive research: they help to correctly understand the specific phenomena of reality.

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

In the science of modern times, the prominent mathematician and philosopher R. Descartes was the propagandist of the deductive method of cognition. Inspired by his mathematical successes, being convinced of the infallibility of a correctly reasoning mind, Descartes one-sidedly exaggerated the importance of the intellectual side at the expense of the experienced in the process of knowing the truth. Descartes' deductive methodology was in direct opposition to Bacon's empirical inductivism.

But, despite the attempts that have taken place in the history of science and philosophy to separate induction from deduction, the opposite

Law 671 33

compare them in the real process of scientific knowledge, these two methods are not used as isolated, isolated from each other. Each of them is used at a corresponding stage of the cognitive process.

Moreover, in the process of using the inductive method, often “in covert» there is also deduction.

Generalizing the facts in accordance with some ideas, we thereby indirectly derive the generalizations we receive from these ideas, and we are far from always aware of this. It seems that our thought moves directly from facts to generalizations, that is, that there is pure induction here. In fact, in conformity with some ideas, in other words, being implicitly guided by them in the process of generalizing facts, our thought indirectly proceeds from ideas to these generalizations, and, consequently, deduction also takes place here. It can be said that in all cases when we generalize (consistent, for example, with some philosophical provisions), our conclusions are not only induction, but also a hidden deduction.

Emphasizing the necessary connection between induction and deduction, F. Engels urgently advised scientists: from the sight of their connection with each other, their mutual complement to each other” 6 .

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

3.1. Analysis and synthesis

Under analysis understand the division of an object (mentally or actually) into its component parts for the purpose of their separate study. As such parts, there may be some material elements of the object or its properties, features, relationships, etc.

Analysis is a necessary stage in the cognition of an object. Since ancient times, analysis has been used, for example, for

decomposition into constituents of certain substances. In particular, already in ancient Rome, analysis was used to check the quality of gold and silver in the form of so-called cupellation (the analyzed substance was weighed before and after heating). Gradually, analytical chemistry was formed, which can rightly be called the mother of modern chemistry: after all, before using a particular substance for specific purposes, it is necessary to find out its chemical composition.

However, in the science of modern times, the analytical method was absolutized. During this period, scientists, studying nature, “cut it into parts” (in the words of F. Bacon) and, examining the parts, did not notice the significance of the whole. This was the result of the metaphysical method of thought which then dominated the minds of natural scientists.

Undoubtedly, analysis occupies an important place in the study of objects of the material world. But it is only the first stage of the process of cognition. If, say, chemists were limited only to analysis, that is, to the isolation and study of individual chemical elements, then they would not be able to cognize all those complex substances that include these elements. No matter how deeply the properties of carbon and hydrogen, for example, have been studied, according to this information, nothing can be said about the numerous substances consisting of various combinations of these chemical elements.

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

In the process of synthesis, the constituent parts (sides, properties, features, etc.) of the object under study, dissected as a result of the analysis, are joined together. On this basis, further study of the object takes place, but already as a single whole. At the same time, synthesis does not mean a simple mechanical connection of disconnected elements into a single system. It reveals the place and role of each

element in the system of the whole, establishes their relationship and interdependence, i.e., allows you to understand the true dialectical unity of the object under study.

Analysis and synthesis are also successfully used in the sphere of human mental activity, that is, in theoretical knowledge. But here, as well as at the empirical level of knowledge, analysis and synthesis are not two operations separated from each other. In essence, they are, as it were, two sides of a single analytical-synthetic method of cognition. As F. Engels emphasized, “thinking consists as much in the decomposition of objects of consciousness into their elements as in the unification of elements connected with each other into a certain unity. Without analysis, there is no synthesis” 7 .

Analogy and modeling

Under analogy similarity, the similarity of some properties, features or relationships of objects that are generally different is understood. The establishment of similarities (or differences) between objects is carried out as a result of their comparison. Thus, comparison underlies the method of analogy.

If a logical conclusion is made about the presence of any property, attribute, relationship of the object under study on the basis of establishing its similarity with other objects, then this conclusion is called inference by analogy. The course of such a conclusion can be represented as follows. Let there be, for example, two objects A and B. It is known that the object A has properties P 1 P 2 ,..., P n , P n +1 . The study of object B showed that it has properties Р 1 Р 2 ,..., Р n , coinciding, respectively, with the properties of object A. Based on the similarity of a number of properties (Р 1 Р 2 ,..., Р n), both objects can be made an assumption about the presence of property P n +1 in object B.

The degree of probability of obtaining a correct conclusion by analogy will be the higher: 1) the more common properties of the compared objects are known; 2) the more essential the common properties found in them; and 3) the deeper the mutual regular connection of these similar properties is known. At the same time, it must be borne in mind that if the object, in relation to which the conclusion is made by analogy with another object, has some property that is incompatible with that property, the existence

which the conclusion is to be drawn, then the general similarity of these objects loses all significance.

These considerations about the inference by analogy can also be supplemented with the following rules:

1) common properties must be any properties of the compared objects, i.e., they must be selected “without prejudice” against properties of any type; 2) the property P n +1 must be of the same type as the general properties P 1 P 2 ,..., P n ; 3) general properties Р 1 Р 2 , ..., Р n should be as specific as possible for the compared objects, i.e. belong to the smallest possible circle of objects; 4) property P n +1, on the contrary, should be the least specific, i.e., belong to the largest possible circle of objects.

Exist Various types conclusions by analogy. But what they have in common is that in all cases one object is directly investigated, and a conclusion is made about another object. Therefore, the conclusion by analogy in the very general sense can be defined as the transfer of information from one object to another. In this case, the first object, which is actually subjected to research, is called model, and another object, to which the information obtained as a result of the study of the first object (model) is transferred, is called original(sometimes - a prototype, sample, etc.). Thus, the model always acts as an analogy, i.e., the model and the object (original) displayed with its help are in a certain similarity (similarity).

"Under modeling is understood as the study of a simulated object (original), based on the one-to-one correspondence of a certain part of the properties of the original and the object (model) that replaces it in the study, and includes the construction of a model, studying it and transferring the information obtained to the simulated object - the original "8.

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

1. Mental (ideal) modeling. This type of modeling includes a variety of mental representations in the form of certain imaginary models. For example, in the ideal model of the electromagnetic field created by J. Maxwell, the lines of force are represented

They were in the form of tubes of various sections, through which an imaginary liquid flows, which does not have inertia and compressibility. The model of the atom proposed by E. Rutherford resembled the solar system: electrons (“planets”) revolved around the nucleus (“Sun”). It should be noted that mental (ideal) models can often be realized materially in the form of sensually perceived physical models.

2. Physical modeling. It is characterized
physical similarity between the model and the original and
aims to reproduce in the process model, its
related to the original. According to the results of a study of
or other physical properties of the model judge the phenomena
occurring (or likely to occur) in the so-called
my "natural conditions". Neglect of the result
MI of such model studies can have severe
effects. An instructive example of this is
the sinking of an English armored ship that went down in history
the nose "Captain", built in 1870. Research
famous shipbuilder W. Reed, carried out
on the ship model, revealed serious defects in its con
structures. But the statement of the scientist, substantiated by experience with
"toy model" was not taken into account
Lean Admiralty. As a result, when exiting
the sea "Captain" turned over, which led to the death
over 500 sailors.

At present, physical modeling is widely used for the development and experimental study of various structures (dams of power plants, irrigation systems, etc.), machines (the aerodynamic qualities of aircraft, for example, are studied on their models blown by an air flow in a wind tunnel), for a better understanding of some natural phenomena, to study effective and safe ways reference mining etc.

3. Symbolic (sign) modeling. It is sacred
but with conditional-sign representation of some properties,
relations of the original object. To the symbolic (sign
vym) models about

The discovery of stable connections and dependencies is only the first stage in the process of scientific knowledge of the phenomena of reality. It is necessary to explain their grounds and causes, to reveal the essence of phenomena and processes. And this is possible only at the theoretical level of scientific knowledge. The theoretical level includes all those forms of cognition in which laws and other universal and necessary connections of the objective world are formulated in a logical form, as well as conclusions obtained using logical means, and consequences arising from theoretical premises. The theoretical level represents various forms, techniques and stages of mediated cognition of reality.

Methods and forms of knowledge of the theoretical level, depending on the functions they perform, can be divided into two groups. The first group - methods and forms of cognition, with the help of which an idealized object is created and studied, representing the basic, defining relationships and properties, as it were, in a "pure" form. The second group - methods for constructing and justifying theoretical knowledge, which is given in the form of a hypothesis, which as a result acquires the status of a theory.

The methods of constructing and studying an idealized object include: abstraction, idealization, formalization, thought experiment, mathematical modeling.

A) Abstraction and idealization. The concept of an idealized object

It is known that 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 abstract from certain differences in the subjects it studies in certain respects. From the point of view of psychology, the process of mental abstraction from certain aspects, properties of the objects being studied, from certain relations between them is called abstraction. Mentally selected properties and relationships are in the foreground, appear as necessary for solving problems, act as a subject of study.

The process of abstraction in scientific knowledge is not arbitrary. He obeys certain rules. One of these rules is abstraction interval. The interval of abstractions is the limits of the rational validity of this or that abstraction, the conditions for its "objective truth" and the limits of applicability, established on the basis of information obtained by empirical or logical means. The interval of abstraction depends, firstly, on the assigned cognitive task; secondly, what is distracted from in the process of comprehending an object must be outsiders(according to a clearly defined criterion) for a specific object that is subject to abstraction; thirdly, the researcher must know to what extent a given distraction is valid.

The abstraction method involves, when studying complex objects, to produce a conceptual unfolding and conceptual assembly of objects. Conceptual development means displaying the same original object of study in different mental planes (projections) and, accordingly, finding a set of abstraction intervals for it. So, for example, in quantum mechanics, the same object (elementary particle) can be alternately represented within the framework of two projections: as a corpuscle (under certain experimental conditions), then as a wave (under other conditions). These projections are logically incompatible with each other, but only taken together they exhaust all the necessary information about the behavior of particles.

Concept assembly- representation of an object in a multidimensional cognitive space by establishing logical connections and transitions between different intervals that form a single semantic configuration. So, in classical mechanics, the same physical event can be displayed by an observer in different systems in the form of a corresponding set of experimental truths. These different projections, however, can form a conceptual whole thanks to the "Galilean transformation rules" that govern how one moves from one group of statements to another.

Abstraction as the most important technique cognitive activity of a person is widely used at all stages of scientific and cognitive activity, including at the level of empirical knowledge. Empirical objects are created on its basis. As V.S. Stepin noted, empirical objects are abstractions that fix the signs of real objects of experience. They are certain schematizations of fragments real world. Any sign, the "carrier" of which is an empirical object, can be found in the corresponding real objects (but not vice versa, since the empirical object does not represent all, but only some of the signs of real objects, abstracted from reality in accordance with the tasks of cognition and practice) . Empirical objects make up the meaning of such terms of the empirical language as "Earth", "wire with current", "distance between the Earth and the Moon", etc.

Theoretical objects, unlike empirical ones, are not just abstractions, but idealizations, "logical reconstructions of reality." They can be endowed not only with attributes that correspond to the properties and relationships of real objects, but also with attributes that none of such an object possesses. Theoretical objects form the meaning of such terms as "point", "ideal gas", "black body", etc.

In logical and methodological studies, theoretical objects are sometimes called theoretical constructs, as well as abstract objects. Objects of this kind serve as the most important means of knowing real objects and the relationships between them. They are called idealized objects, and the process of creating them is called idealization. Thus, idealization is the process of creating mental objects, conditions, situations 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 actually possess or cannot possess, with the purpose of a deeper and more accurate knowledge of reality.

The creation of an idealized object necessarily includes abstraction - a distraction from a number of aspects and properties of the specific objects being studied. But if we confine ourselves to this, then we will not get any integral object, 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. And this is achieved by using idealization method.

Idealization helps the researcher to single out in a pure form the aspects of reality that interest him. As a result of idealization, the object acquires properties that are not in demand in empirical experience. In contrast to conventional abstraction, idealization focuses not on the operations of abstraction, but on the mechanism replenishment. Idealization gives an absolutely exact construct, mental construct, in which this or that property, state is represented in marginal, most expressed. Creative constructs, abstract objects act as ideal model.

Why is it necessary to use abstract objects (theoretical constructs) in cognition? The fact is that a real object is always complex, significant for a given researcher and secondary properties are intertwined in it, the necessary regular relations are obscured by random ones. Constructs, ideal models are objects endowed with a small number of specific and essential properties that have a relatively simple structure.

The researcher, relying on a relatively simple idealized object, to give a deeper and more complete description of these aspects. Cognition moves from concrete objects to their abstract, ideal models, which, becoming more and more precise, perfect and numerous, gradually give us a more and more adequate image of concrete objects. This ubiquitous use of idealized objects is one of the most characteristic features human knowledge.

It should be noted that idealization is used both at the empirical and theoretical levels. The objects to which scientific propositions refer are always idealized objects. Even in those cases when we use empirical methods of cognition - observation, measurement, experiment, the results of these procedures are directly related to idealized objects, and only due to the fact that idealized objects at this level are abstract models of real things, the data of empirical procedures can be attributed to actual items.

However, the role of idealization sharply increases in the transition from the empirical to the theoretical level of scientific knowledge. The modern hypothetical-deductive theory is based on some empirical basis - a set of facts that need explanation and make it necessary to create a theory. But theory is not a simple generalization of facts and cannot be deduced from them in a logical way. In order to make it possible to create a special system of concepts and statements called a theory, an idealized object is first introduced, which is an abstract model of reality, endowed with a small number of properties and having a relatively simple structure. This idealized object expresses the specificity and essential features of the field of phenomena under study. It is the idealized object that makes it possible to create a theory. Scientific theories, first of all, are distinguished by the idealized objects underlying them. In the special theory of relativity, an idealized object is an abstract pseudo-Euclidean four-dimensional set of coordinates and instants of time, provided that there is no gravitational field. Quantum mechanics is characterized by an idealized object, represented in the case of a collection of n particles by a wave in an n-dimensional configuration space, the properties of which are related to the quantum of action.

The concepts and statements of a theory are introduced and formulated precisely as characteristics of its idealized object. The main properties of an idealized object are described by a system of fundamental equations of the theory. The difference between the idealized objects of theories leads to the fact that each hypothetical-deductive theory has its own specific system of fundamental equations. In classical mechanics we deal with Newton's equations, in electrodynamics - with Maxwell's equations, in the theory of relativity - with Einstein's equations, etc. The idealized object gives an interpretation of the concepts and equations of the theory. Refinement of the equations of the theory, their experimental confirmation and correction lead to a refinement of the idealized object or even to its change. Replacing the idealized object of the theory means reinterpreting the basic equations of the theory. No scientific theory can be guaranteed that its equations will not be reinterpreted sooner or later. In some cases, this happens relatively quickly, in others - after a long time. So, for example, in the doctrine of heat, the original idealized object - caloric - was replaced by another - a set of randomly moving material points. Sometimes a modification or replacement of an idealized object of a theory does not significantly change the form of its fundamental equations. In this case, it is often said that the theory is preserved, but its interpretation changes. It is clear that one can say this only with a formalistic understanding of scientific theory. If by theory we understand not only certain mathematical formulas, but also a certain interpretation of these formulas, then the change of the idealized object should be considered as a transition to a new theory.

Theoretical methods-operations have a wide field of application, both in scientific research and in practice.

Theoretical methods - operations are determined (considered) according to the main mental operations, which are: analysis and synthesis, comparison, abstraction and concretization, generalization, formalization, induction and deduction, idealization, analogy, modeling, thought experiment.

Analysis- this is the decomposition of the whole under study into parts, the allocation of individual features and qualities of a phenomenon, process or relations of phenomena, processes. Analysis procedures are an integral part of any scientific research and usually form its first phase, when the researcher moves from an undivided description of the object under study to the identification of its structure, composition, properties and features.

One and the same phenomenon, process can be analyzed in many aspects. A comprehensive analysis of the phenomenon allows you to consider it deeper.

Synthesis - the connection of various elements, sides of the subject into a single whole (system). Synthesis is not a simple summation, but a semantic connection. If we simply connect phenomena, no system of connections will arise between them, only a chaotic accumulation of individual facts is formed. Synthesis is opposed to analysis, with which it is inextricably linked. Synthesis as a cognitive operation appears in various functions of theoretical research. Any process of formation of concepts is based on the unity of the processes of analysis and synthesis. Empirical data obtained in a particular study are synthesized during their theoretical generalization. In theoretical scientific knowledge, synthesis acts as a function of the relationship of theories related to the same subject area, as well as a function of combining competing theories (for example, the synthesis of corpuscular and wave representations in physics).

Synthesis also plays an important role in empirical research.

Analysis and synthesis are closely related. If the researcher has a more developed ability to analyze, there may be a danger that he will not be able to find a place for details in the phenomenon as a whole. The relative predominance of synthesis leads to superficiality, to the fact that details essential for the study, which can be of great importance for understanding the phenomenon as a whole, will not be noticed.

Comparison is a cognitive operation that underlies judgments about the similarity or difference of objects. With the help of comparison, quantitative and qualitative characteristics of objects are revealed, their classification, ordering and evaluation are carried out. Comparison is comparing one thing with another. In this case, an important role is played by the bases, or signs of comparison, which determine the possible relationships between objects.

Comparison makes sense only in a set of homogeneous objects that form a class. Comparison of objects in a particular class is carried out according to the principles essential for this consideration. At the same time, objects that are comparable in one feature may not be comparable in other features. The more accurately the signs are estimated, the more thoroughly the comparison of phenomena is possible. Integral part comparison is always analysis, since for any comparison in phenomena it is necessary to isolate the corresponding signs of comparison. Since comparison is the establishment of certain relationships between phenomena, then, naturally, synthesis is also used in the course of comparison.

abstraction- one of the main mental operations that allows you to mentally isolate and turn into an independent object of consideration certain aspects, properties or states of the object in its pure form. Abstraction underlies the processes of generalization and concept formation.

Abstraction consists in isolating such properties of an object that do not exist by themselves and independently of it. Such isolation is possible only in the mental plane - in abstraction. Thus, the geometric figure of the body does not really exist by itself and cannot be separated from the body. But thanks to abstraction, it is mentally singled out, fixed, for example, with the help of a drawing, and independently considered in its special properties.

One of the main functions of abstraction is to highlight the common properties of a certain set of objects and fix these properties, for example, through concepts.

Specification- a process opposite to abstraction, that is, finding a holistic, interconnected, multilateral and complex. The researcher initially forms various abstractions, and then, on their basis, through concretization, reproduces this integrity (mental concrete), but at a qualitatively different level of cognition of the concrete. Therefore, dialectics distinguishes in the process of cognition in the coordinates "abstraction - concretization" two processes of ascent: the ascent from the concrete to the abstract and then the process of ascent from the abstract to the new concrete (G. Hegel). The dialectic of theoretical thinking consists in the unity of abstraction, the creation of various abstractions and concretization, the movement towards the concrete and its reproduction.

Generalization- one of the main cognitive mental operations, consisting in the selection and fixation of relatively stable, invariant properties of objects and their relationships. Generalization allows you to display the properties and relationships of objects, regardless of the particular and random conditions of their observation. Comparing objects of a certain group from a certain point of view, a person finds, singles out and designates with a word their identical, common properties, which can become the content of the concept of this group, class of objects. Separating general properties from private ones and designating them with a word makes it possible to cover the entire variety of objects in an abbreviated, concise form, reduce them to certain classes, and then, through abstractions, operate with concepts without directly referring to individual objects. One and the same real object can be included in both narrow and wide classes, for which the scales of common features are built according to the principle of genus-species relations. The function of generalization consists in ordering the variety of objects, their classification.

Formalization- displaying the results of thinking in precise terms or statements. It is, as it were, a mental operation of the “second order”. Formalization is opposed to intuitive thinking. In mathematics and formal logic, formalization is understood as the display of meaningful knowledge in a sign form or in a formalized language. Formalization, that is, the abstraction of concepts from their content, ensures the systematization of knowledge, in which its individual elements coordinate with each other. Formalization plays an essential role in the development of scientific knowledge, since intuitive concepts, although they seem clearer from the point of view of everyday consciousness, are of little use for science: in scientific knowledge it is often impossible not only to solve, but even to formulate and pose problems until the structure of the concepts related to them will be clarified. True science is possible only on the basis of abstract thinking, consistent reasoning of the researcher, flowing in a logical language form through concepts, judgments and conclusions.

In scientific judgments, links are established between objects, phenomena or between their specific features. In scientific conclusions, one judgment proceeds from another; on the basis of already existing conclusions, a new one is made. There are two main types of inference: inductive (induction) and deductive (deduction).

Induction- this is a conclusion from particular objects, phenomena to a general conclusion, from individual facts to generalizations.

Deduction- this is a conclusion from the general to the particular, from general judgments to particular conclusions.

Idealization- mental construction of ideas about objects that do not exist or are not feasible in reality, but those for which there are prototypes in the real world. The process of idealization is characterized by abstraction from the properties and relations inherent in the objects of reality and the introduction into the content of the formed concepts of such features that, in principle, cannot belong to their real prototypes. Examples of concepts that are the result of idealization can be the mathematical concepts of "point", "line"; in physics - "material point", "absolutely black body", "ideal gas", etc.

It is said about the concepts that are the result of idealization that idealized (or ideal) objects are conceived in them. Having formed concepts of this kind about objects with the help of idealization, one can subsequently operate with them in reasoning as with really existing objects and build abstract schemes of real processes that serve for a deeper understanding of them. In this sense, idealization is closely related to modeling.

Analogy, modeling. Analogy- a mental operation, when the knowledge obtained from the consideration of any one object (model) is transferred to another, less studied or less accessible for study, less visual object, called the prototype, the original. It opens up the possibility of transferring information by analogy from model to prototype. This is the essence of one of the special methods of the theoretical level - modeling (building and researching models). The difference between analogy and modeling lies in the fact that if analogy is one of the mental operations, then modeling can be considered in different cases both as a mental operation and as an independent method - a method-action.

A model is an auxiliary object, chosen or transformed for cognitive purposes, which provides new information about the main object. Modeling forms are diverse and depend on the models used and their scope. By the nature of the models, subject and sign (information) modeling are distinguished.

Object modeling is carried out on a model that reproduces certain geometric, physical, dynamic, or functional characteristics of the modeling object - the original; in a special case - analog modeling, when the behavior of the original and the model is described by common mathematical relationships, for example, by common differential equations. In sign modeling, diagrams, drawings, formulas, etc. serve as models. The most important type of such modeling is mathematical modeling.

Simulation is always used together with other research methods, it is especially closely related to the experiment. The study of any phenomenon on its model is a special kind of experiment - a model experiment, which differs from an ordinary experiment in that in the process of cognition an "intermediate link" is included - a model that is both a means and an object of experimental research that replaces the original.

A special kind of modeling is a thought experiment. In such an experiment, the researcher mentally creates ideal objects, correlates them with each other within the framework of a certain dynamic model, mentally imitating the movement and those situations that could take place in a real experiment. At the same time, ideal models and objects help to identify “in pure form” the most important, significant connections and relationships, to mentally play out possible situations, to weed out unnecessary options.

Modeling also serves as a way of constructing a new one that did not exist earlier in practice. The researcher, having studied the characteristic features of real processes and their tendencies, looks for new combinations of them on the basis of the leading idea, makes their mental redesign, that is, models the required state of the system under study (just like any person and even an animal, he builds his activity, activity on the basis of initially formed "model of the necessary future" - according to N.A. Bernshtein). At the same time, models-hypotheses are created that reveal the mechanisms of communication between the components of the studied, which are then tested in practice. In this sense, modeling recent times widely spread in the social and human sciences - in economics, pedagogy, etc., when different authors offer different models of firms, industries, educational systems, etc.

Along with the operations of logical thinking, theoretical methods-operations can also include (possibly conditionally) imagination as a thought process for creating new ideas and images with its specific forms of fantasy (creation of implausible, paradoxical images and concepts) and dreams (as the creation of images of the desired).

Theoretical methods (methods - cognitive actions). The general philosophical, general scientific method of cognition is dialectics - the real logic of meaningful creative thinking, reflecting the objective dialectics of reality itself. The basis of dialectics as a method of scientific knowledge is the ascent from the abstract to the concrete (G. Hegel) - from general and content-poor forms to dissected and richer content, to a system of concepts that allow one to comprehend an object in its essential characteristics. In dialectics, all problems acquire a historical character, the study of the development of an object is a strategic platform for cognition. Finally, dialectics is oriented in cognition to the disclosure and methods of resolving contradictions.

The laws of dialectics: the transition of quantitative changes into qualitative ones, the unity and struggle of opposites, etc.; analysis of paired dialectical categories: historical and logical, phenomenon and essence, general (universal) and singular, etc. are integral components of any well-structured scientific research.

Scientific theories verified by practice: any such theory, in essence, acts as a method in the construction of new theories in this or even other areas of scientific knowledge, as well as in the function of a method that determines the content and sequence of the researcher's experimental activity. Therefore, the difference between scientific theory as a form of scientific knowledge and as a method of cognition in this case is functional: being formed as a theoretical result of past research, the method acts as a starting point and condition for subsequent research.

Proof - method - a theoretical (logical) action, in the process of which the truth of a thought is substantiated with the help of other thoughts. Any proof consists of three parts: the thesis, arguments (arguments) and demonstration. According to the method of conducting evidence, there are direct and indirect, according to the form of inference - inductive and deductive. Evidence Rules:

1. The thesis and arguments must be clear and precise.

2. The thesis must remain identical throughout the proof.

3. The thesis should not contain a logical contradiction.

4. The arguments given in support of the thesis must themselves be true, not subject to doubt, must not contradict each other and be a sufficient basis for this thesis.

5. The proof must be complete.

In the totality of methods of scientific knowledge, an important place belongs to the method of analyzing knowledge systems. Any scientific knowledge system has a certain independence in relation to the reflected subject area. In addition, knowledge in such systems is expressed using a language whose properties affect the relationship of knowledge systems to the objects being studied - for example, if any sufficiently developed psychological, sociological, pedagogical concept is translated into, say, English, German, French - Will it be unequivocally perceived and understood in England, Germany and France? Further, the use of language as a carrier of concepts in such systems presupposes one or another logical systematization and logically organized use of linguistic units to express knowledge. And, finally, no system of knowledge exhausts the entire content of the object under study. In it, only a certain, historically concrete part of such content always receives a description and explanation.

The method of analysis of scientific knowledge systems plays an important role in empirical and theoretical research tasks: when choosing an initial theory, a hypothesis for solving a chosen problem; when distinguishing between empirical and theoretical knowledge, semi-empirical and theoretical solutions to a scientific problem; when substantiating the equivalence or priority of the use of certain mathematical tools in various theories related to the same subject area; when studying the possibilities of disseminating previously formulated theories, concepts, principles, etc. to new subject areas; substantiation of new possibilities for the practical application of knowledge systems; when simplifying and clarifying knowledge systems for training, popularization; to harmonize with other knowledge systems, etc.

- deductive method (synonym - axiomatic method) - a method of constructing scientific theory, in which it is based on some initial provisions of the axiom (synonymous with postulates), from which all other provisions of this theory (theorem) are derived in a purely logical way through proof. The construction of a theory based on the axiomatic method is usually called deductive. All concepts of the deductive theory, except for a fixed number of initial ones (such initial concepts in geometry, for example, are: point, line, plane) are introduced by means of definitions expressing them through previously introduced or derived concepts. The classic example of a deductive theory is the geometry of Euclid. Theories are built by the deductive method in mathematics, mathematical logic, theoretical physics;

- the second method has not received a name in the literature, but it certainly exists, since in all other sciences, except for the above, theories are built according to the method, which we will call inductive-deductive: first, an empirical basis is accumulated, on the basis of which theoretical generalizations (induction) are built, which can be built into several levels - for example, empirical laws and theoretical laws - and then these obtained generalizations can be extended to all objects and phenomena covered by this theory (deduction). The inductive-deductive method is used to construct most of the theories in the sciences of nature, society and man: physics, chemistry, biology, geology, geography, psychology, pedagogy, etc.

Other theoretical research methods (in the sense of methods - cognitive actions): identifying and resolving contradictions, posing a problem, building hypotheses, etc. up to the planning of scientific research, we will consider below in the specifics of the time structure of research activity - the construction of phases, stages and stages of scientific research.

Logic and philosophy

The second group is methods for constructing and justifying theoretical knowledge, which is given in the form of a hypothesis, which, as a result, acquires the status of a theory. The modern hypothetical-deductive theory is based on some empirical basis - a set of facts that need to be explained and make it necessary to create a theory. It is the idealized object that makes it possible to create a theory. Scientific theories are primarily distinguished by the idealized objects underlying them.

QUESTION #25

Formalization, idealization and the role of modeling

According to Radugin (p. 123)

Methods for constructing and studying an idealized object

Methods and forms of knowledge of the theoretical level, depending on the functions they perform, can be divided into two groups. The first group is the methods and forms of cognition, with the help of which an idealized object is created and studied, representing the basic, defining relations and properties, as it were, in a “pure” form. The second group is methods for constructing and justifying theoretical knowledge, which is given in the form of a hypothesis, which as a result acquires the status of a theory.

The methods of constructing and studying an idealized object include: abstraction, idealization, formalization, thought experiment, mathematical modeling.

a) Abstraction and idealization. The concept of an idealized object

It is known that 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 abstract from certain differences in the subjects it studies in certain respects. From the point of view of psychologythe process of mental abstraction from certain aspects, properties of the objects being studied, from certain relations between them is called abstraction.Mentally selected properties and relationships are in the foreground, appear as necessary for solving problems, act as a subject of study.

The process of abstraction in scientific knowledge is not arbitrary. He obeys certain rules. One of these rules isabstraction interval.The interval of abstractions is the limits of the rational validity of this or that abstraction, the conditions for its "objective truth" and the limits of applicability, established on the basis of information obtained by empirical or logical means. The interval of abstraction depends, firstly, onthe assigned cognitive task;secondly, what is distracted from in the process of comprehending an object must be outsiders (according to a clearly defined criterion) for a specific object that is subject to abstraction; thirdly, the researcher must know to what extent a given distraction is valid.

The abstraction method involves, when studying complex objects, to produce a conceptual unfolding and conceptual assembly of objects.Conceptual developmentmeans displaying the same original object of study in different mental planes (projections) and, accordingly, finding a set of abstraction intervals for it. So, for example, in quantum mechanics, the same object (elementary particle) can be alternately represented within the framework of two projections: as a corpuscle (under certain experimental conditions), then as a wave (under other conditions). These projections are logically incompatible with each other, but only taken together they exhaust all the necessary information about the behavior of particles.

Concept assembly- representation of an object in a multidimensional cognitive space by establishing logical connections and transitions between different intervals that form a single semantic configuration. So, in classical mechanics, the same physical event can be displayed by an observer in different systems in the form of a corresponding set of experimental truths. These different projections, however, can form a conceptual whole thanks to the "Galilean transformation rules" that govern how one moves from one group of statements to another.

Abstraction as the most important method of human cognitive activity is widely used at all stages of scientific and cognitive activity, including at the level of empirical knowledge. Empirical objects are created on its basis. As V.S. Stepin noted, empirical objects are abstractions that fix the signs of real objects of experience. They are certain schematizations of fragments of the real world. Any sign, the "carrier" of which is an empirical object, can be found in the corresponding real objects (but not vice versa, since the empirical object does not represent all, but only some of the signs of real objects, abstracted from reality in accordance with the tasks of cognition and practice) . Empirical objects make up the meaning of such terms of the empirical language as "Earth", "wire with current", "distance between the Earth and the Moon", etc.

In logical and methodological studies, theoretical objects are sometimes called theoretical constructs, as well as abstract objects. Objects of this kind serve as the most important means of knowing real objects and the relationships between them.They are called idealized objects, and the process of creating them is called idealization. Thus, idealization is the process of creating mental objects, conditions, situations 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 actually possess or cannot possess, with the purpose of a deeper and more accurate knowledge of reality.

The creation of an idealized object necessarily includes abstraction - abstraction from a number of aspects and properties of the specific objects being studied. But if we confine ourselves to this, then we will not get any integral object, 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. And this is achieved by usingidealization method.

Idealization helps the researcher to single out in a pure form the aspects of reality that interest him. As a result of idealization, the object acquires properties that are not in demand in empirical experience. In contrast to conventional abstraction, idealization focuses not on the operations of abstraction, but on the mechanism replenishment . Idealization gives an absolutely exact construct,mental construct, in which this or that property, state is represented in ultimate, most pronounced form . Creative constructs, abstract objects act asideal model.

Researcher , relying on a relatively simple idealized object, to give a deeper and more complete description of these aspects. Cognition moves from concrete objects to theirabstract, ideal models, which, becoming more and more precise, perfect and numerous, gradually give us a more and more adequate image of concrete objects. This widespread use of idealized objects is one of the most characteristic features of human knowledge.

However, the role of idealization sharply increases in the transition from the empirical to the theoretical level of scientific knowledge. The modern hypothetical-deductive theory is based on some empirical basis - a set of facts that need explanation and make it necessary to create a theory. But theory is not a simple generalization of facts and cannot be deduced from them in a logical way. In order to make it possible to create a special system of concepts and statements called a theory, we first introduceidealized object, which is an abstract model of reality, endowed with a small amount ofproperties and having a relatively simple structure. This idealized object expresses the specificity and essential features of the field of phenomena under study. It is the idealized object that makes it possible to create a theory. Scientific theories, first of all, are distinguished by the idealized objects underlying them. In the special theory of relativity, an idealized object is an abstract pseudo-Euclidean four-dimensional set of coordinates and instants of time, provided that there is no gravitational field. Quantum mechanics is characterized by an idealized object, represented in the case of a collection of n particles by a wave in an n-dimensional configuration space, the properties of which are related to the quantum of action.

The concepts and statements of a theory are introduced and formulated precisely as characteristics of its idealized object. The main properties of an idealized object are described by a system of fundamental equations of the theory. The difference between the idealized objects of theories leads to the fact that each hypothetical-deductive theory has its own specific system of fundamental equations. In classical mechanics, we deal with Newton's equations, in electrodynamics, with Maxwell's equations, in relativity theory, with Einstein's equations, and so on. The idealized object gives an interpretation of the concepts and equations of the theory. Refinement of the equations of the theory, their experimental confirmation and correction lead to a refinement of the idealized object or even to its change. Replacing the idealized object of the theory means reinterpreting the basic equations of the theory. No scientific theory can be guaranteed that its equations will not be reinterpreted sooner or later. In some cases, this happens relatively quickly, in others - after a long time. So, for example, in the theory of heat, the original idealized object - caloric - was replaced by another - a set of randomly moving material points. Sometimes a modification or replacement of an idealized object of a theory does not significantly change the form of its fundamental equations. In this case, it is often said that the theory is preserved, but its interpretation changes. It is clear that one can say this only with a formalistic understanding of scientific theory. If by theory we understand not only certain mathematical formulas, but also a certain interpretation of these formulas, then the change of the idealized object should be considered as a transition to a new theory.

b) ways to construct an idealized object a

What are the ways of forming an idealized object. In the methodology of scientific research, there are at least three of them:

1. It is possible to abstract from some properties of real objects, while at the same time retaining their other properties and introducing an object that has only these remaining properties. So, for example, in Newtonian celestial mechanics we abstract from all the properties of the Sun and planets and represent them as moving material points with only gravitational mass. We are not interested in their size, structure, chemical composition, etc. The sun and planets act here only as carriers of certain gravitational masses, i.e. as idealized objects.

2. Sometimes it turns out to be useful to abstract from certain relations of the studied objects to each other. With the help of such an abstraction, for example, the concept of an ideal gas is formed. In real gases, there is always a certain interaction between molecules. Abstracting from this interaction and considering gas particles as possessing only kinetic energy and interacting only upon collision, we obtain an idealized object - an ideal gas. In the social sciences, when studying certain aspects of the life of society, certain social phenomena and institutions, social groups etc. we can abstract from the relationship of these parties, phenomena, groups with other elements of the life of society.

3. We can also attribute to real objects the properties that they lack or think of their inherent properties in some limiting value. Thus, for example, special idealized objects are formed in optics - an absolutely black body and an ideal mirror. It is known that all bodies, to a greater or lesser extent, have both the property of reflecting a certain part of the energy incident on its surface, and the property of absorbing a part of this energy. When we push the reflection property to the limit, we get a perfect mirror—an idealized object whose surface reflects all the energy that falls on it. Strengthening the absorption property, in the limiting case we get a completely black body - an idealized object that absorbs all the energy incident on it.

An idealized object can be any real object that is conceived in non-existent, ideal conditions. This is how the concept of inertia arises. Suppose we are pushing a cart along the road. For some time after the push, the cart moves and then stops. There are many ways to lengthen the path traveled by a cart after a push, such as lubricating the wheels, making the road smoother, and the like. The easier the wheels turn, and the smoother the road, the longer the cart will move. Through experiments, it is established that the less external influences on a moving body (in this case, friction), the longer the path traveled by this body. It is clear that all external influences on the moving body cannot be eliminated. In real situations, a moving body will inevitably be subjected to some influences from other bodies. However, it is not difficult to imagine a situation in which all influences are excluded. We can conclude that under such ideal conditions a moving body will move indefinitely and at the same time uniformly and rectilinearly.

c) Formalization and mathematical modeling

The most important means of constructing and studying an idealized theoretical object is formalization. Formalization in the broad sense of the word is understood as a method of studying a wide variety of objects by displaying their content and structure in a sign form, using a wide variety of artificial languages.

Operations on formalized objects mean operations on symbols. As a result of formalization, symbols can be treated as specific physical objects. The use of symbols provides a complete overview of a certain area of problems, brevity and clarity of knowledge fixation, and avoids the ambiguity of terms.

The cognitive value of formalization lies in the fact that it is a means of systematizing and clarifying the logical structure of a theory. The reconstruction of a scientific theory in a formalized language allows us to trace the logical relationship between various provisions theory, to reveal the entire set of prerequisites and grounds on the basis of which it is deployed, which makes it possible to clarify ambiguities, uncertainties, and prevent paradoxical situations. The formalization of the theory also performs a kind of unifying and generalizing function, allowing a number of provisions of the theory to be extrapolated to entire classes of scientific theories and to apply a formal apparatus for the synthesis of previously unrelated theories. One of the most valuable advantages of formalization is its heuristic possibilities, in particular, the possibility of discovering and proving previously unknown properties of the objects under study.

There are two types of formalized theories: fully formalized and partially formalizedtheories. Fully formalized theories are built in an axiomatically deductive form with an explicit indication of the language of formalization and the use of clear logical means. In partially formalized theories, the language and logical means used to develop a given scientific discipline are not explicitly fixed. At the present stage of development of science, it is dominated by partially formalized theories.

The formalization method has great heuristic possibilities. In the process of formalization through the reconstruction of the language of scientific theory, a new type conceptual constructions that open up opportunities for obtaining new, sometimes the most unexpected consequences, through purely formalized actions. The formalization process is creative. Based on a certain level of generalization scientific facts, formalization transforms them, reveals in them such features that were not fixed at the content-intuitive level. Yu.L. Ershov, in his works devoted to the use of formalized languages, cites a number of criteria confirming that with the help of formalization of the theory, non-trivial consequences can be obtained, which were not even suspected, as long as they were limited to a content-intuitive formulation of the theory in natural language. Thus, the formulation of the axiom of choice initially did not raise doubts. And only its use (in conjunction with other axioms) in a formal system that claims to be an axiomatization and formalization of set theory revealed that it leads to a number of paradoxical consequences, which cast doubt on the possibility of its use. In physics, when trying to axiomatize field theory, the selection of certain statements about the quality of its axioms led to a large number of consequences suitable for explaining experimental data.

The creation of formalized descriptions has not only its own cognitive value, but is a condition for use at a theoretical level.mathematical modeling. Mathematical modeling is a theoretical method for studying quantitative patterns based on the creation of a sign system consisting of a set of abstract objects (mathematical quantities, relations) thatallow different interpretations. Mathematical modeling as a theoretical method found its wide application in the late 1940s. in individual sciences and in interdisciplinary research. The basis of the method of mathematical modeling is the constructionmathematical model. A mathematical model is a formal structure consisting of a set of mathematical objects. Meaning mathematical method when developing a theory, it is determined by the fact that it, reflecting certain quantitative properties and relationships of the original, replaces it in a certain way, and manipulation with this model provides deeper and more complete information about the original.

In the simplest case, a separatemathematical object, that is, such a formal structure, with the help of which it is possible to pass from the empirically obtained values of some parameters of the material object under study to the value of others without resorting to experiment. For example, having measured the circumference of a spherical object, calculate the volume of this object using the formula.

The researchers found that in order for an object to be successfully studied using mathematical models, it must have a number of special properties. First, the relations in it must be well known; secondly, the properties essential for the object should be quantified (and their number should not be too large); and, thirdly, depending on the purpose of the study, the forms of the object's behavior (which is determined by laws, for example, physical, biological, social) must be known for a given set of relations.

In essence, any mathematical structure (or abstract system) acquires the status of a model only when it is possible to establish the fact of a structural, substratal or functional analogy between it and the object (or system) under study. In other words, there must be a certain consistency, obtained as a result of the selection and "mutual adjustment" of the model and the corresponding "fragment of reality." This consistency exists only within a certain interval of abstraction. In most cases, the analogy between an abstract and a real system is related to the isomorphism relation between them, defined within the framework of fixing the interval of abstraction. In order to investigate a real system, the researcher replaces it (up to isomorphism) with an abstract system with the same relations. Thus, the task of research becomes purely mathematical. For example, a drawing can serve as a model for displaying the geometric properties of a bridge, and a set of formulas underlying the calculation of the dimensions of the bridge, its strength, stresses arising in it, etc., can serve as a model for displaying the physical properties of the bridge.

The use of mathematical models is an effective way of learning. The mere translation of any qualitative problem into a clear, unambiguous and rich in its possibilities language of mathematics makes it possible to see the research problem in a new light, to clarify its content. However, mathematics gives something more. Characteristic of mathematical knowledge is the use of the deductive method, i.e. manipulation with objects according to certain rules and thus obtaining new results.

According to Tarasov (pp. 91-94)

Idealization, abstraction- replacement of individual properties of an object or the entire object with a symbol or sign, a mental distraction from something in order to highlight something else. Ideal objects in science reflect stable connections and properties of objects: mass, speed, force, etc. But ideal objects may not have real prototypes in the objective world, i.e. as scientific knowledge develops, some abstractions can be formed from others without recourse to practice. Therefore, a distinction is made between empirical and ideal theoretical objects.

Idealization is a necessary preliminary condition for constructing a theory, since the system of idealized, abstract images determines the specifics of this theory. In the theory system, basic and derivative idealized concepts are distinguished. For example, in classical mechanics, the main idealized object is the mechanical system as the interaction of material points.

In general, idealization allows one to accurately outline the features of an object, to abstract from unimportant and vague properties. This provides a huge capacity for expressing thoughts. In this regard, special languages of science are being formed, which contributes to the construction of complex abstract theories and, in general, the process of cognition.

Formalization - operating with signs reduced to generalized models, abstract mathematical formulas. The derivation of some formulas from others is carried out according to strict rules logic and mathematics, which is a formal study of the main structural characteristics object under study.

Modeling . Model - a mental or material substitution of the most significant aspects of the object under study. A model is an object or system specially created by a person, a device that, in a certain respect, imitates, reproduces real-life objects or systems that are the object of scientific research.

Modeling is based on the analogy of properties and relationships between the original and the model. Having studied the relationships that exist between the quantities that describe the model, they are then transferred to the original and thus make a plausible conclusion about the behavior of the latter.

Modeling as a method of scientific knowledge is based on the ability of a person to abstract the studied features or properties of various objects, phenomena and establish certain relationships between them.

Although scientists have long used this method, only since the middle of the XIX century. simulation is gaining lasting, acceptance from scientists and engineers. In connection with the development of electronics and cybernetics, modeling is turning into an extremely effective research method.

Thanks to the use of modeling the patterns of reality, which in the original could be studied only through observation, they become accessible to experimental research. There is a possibility of repeated repetition in the model of phenomena corresponding to the unique processes of nature or social life.

If we consider the history of science and technology from the point of view of the application of certain models, then we can state that at the beginning of the development of science and technology, material, visual models were used. Subsequently, they gradually lost one after another the specific features of the original, their correspondence to the original acquired an increasingly abstract character. At present, the search for models based on logical foundations is becoming increasingly important. There are many options for classifying models. In our opinion, the most convincing next option:

a) natural models (existing in nature in their natural form). So far, none of the structures created by man can compete with natural structures in terms of the complexity of the tasks being solved. There is a science bionics , the purpose of which is to study unique natural models in order to further use the knowledge gained in the creation of artificial devices. It is known, for example, that the creators of the submarine shape model took the shape of the body of a dolphin as an analogue, when designing the first aircraft the wingspan model of birds was used, etc.;

b) material-technical models (in reduced or enlarged form, fully reproducing the original). At the same time, experts distinguish (88. P. 24-25): a) models created in order to reproduce the spatial properties of the object under study (models of houses, building districts, etc.); b) models that reproduce the dynamics of the objects under study, regular relationships, quantities, parameters (models of aircraft, ships, plane trees, etc.).

Finally, there is a third type of models - c) sign models, including mathematical ones. Sign-based modeling makes it possible to simplify the subject under study, to single out those structural relationships in it that are of most interest to the researcher. Losing to real-technical models in visualization, sign models win due to deeper penetration into the structure of the studied fragment of objective reality.

Thus, with the help of sign systems, it is possible to understand the essence of such complex phenomena as the device atomic nucleus, elementary particles, Universe. Therefore, the use of sign models is especially important in those areas of science and technology where they deal with the study of extremely general connections, relationships, structures.

The possibilities of sign modeling were especially expanded in connection with the advent of computers. Options for constructing complex sign-mathematical models have appeared that make it possible to choose the most optimal values for the values of complex real processes under study and to carry out long-term experiments on them.

In the course of research, it often becomes necessary to build various models of the processes under study, ranging from material to conceptual and mathematical models.

In general, “the construction of not only visual, but also conceptual, mathematical models accompanies the process of scientific research from its beginning to end, making it possible to cover the main features of the processes under study in a single system of visual and abstract images” (70, p. 96).

Method of historical and logical : the first reproduces the development of the object, taking into account all the factors acting on it, the second reproduces only the general, the main thing in the subject in the process of development. The logical method reproduces the history of the emergence, formation and development of an object, so to speak, in a "pure form", in essence, without considering the circumstances that contribute to it. That is, the logical method is a straightened, simplified (without loss of essence) version of the historical method.

In the process of cognition, one should be guided by the principle of the unity of historical and logical methods: one must begin the study of an object from those sides, relations that historically preceded others. Then, with the help of logical concepts, as it were, repeat the history of the development of this cognizable phenomenon.

Extrapolation - continuation into the future of trends, the patterns of which in the past and present are quite well known. It has always been believed that lessons can be learned from the past for the future, because the evolution of inanimate, living and social matter is based on quite definite rhythmic processes.

Modeling - representation of the object under study in a simplified, schematic form, convenient for obtaining predictive conclusions. An example is the periodic system of Mendeleev (see above for more details on modeling).

Expertise - forecasting based on an assessment of the opinions of specialists - (individuals, groups, organizations), based on an objective statement of the prospects of the relevant phenomenon.

The three methods mentioned above complement each other. Any extrapolation is, to a certain extent, a model and an estimate. Any predictive model is an estimate plus an extrapolation. Any predictive estimate implies extrapolation and mental modeling.

As well as other works that may interest you
46452.		The main steps in the formation of concepts	16.16KB
	The first stage is manifested in the behavior of a young child, the formation of an unformed and disordered set, the allocation of a heap of any objects that are allocated by the child without a sufficient internal basis. The first stage in the formation of a syncretic undivided image or a pile of objects. A group of new objects is taken by the child at random with the help of individual samples that replace each other when they are found to be inaccurate. The second stage is a syncretic image or a bunch of objects formed on the basis of...
46454.		The culture of speech is a necessary condition for professional activity	16.27KB
	Emotional culture includes the ability to regulate one's mental state, understand the emotional state of the interlocutor, manage one's emotions, relieve anxiety, overcome indecision to establish emotional contact. The culture of professional speech includes: possession of the terminology of this specialty; the ability to build a presentation on a professional topic; the ability to organize a professional dialogue and manage it; ability to communicate with non-specialists professional activity. Knowledge of terminology...
46456.		Analysis and diagnostics of enterprise costs	16.34KB
	The costs that form the cost of production are grouped in accordance with their environmental content according to the following elements: material costs; labor costs; deductions for social needs; depreciation of fixed assets; Material costs are the largest element of production costs. Their share in the total cost is 6080 only in the extractive industries, it is small. The composition of material costs is heterogeneous and includes the cost of raw materials minus the cost of returnable waste at the price of their ...
46457.		Phraseology as a branch of linguistics: types of phraseological phrases (fusion, unity, combinations) and principles for their selection	16.4KB
	Phraseology as a section of linguistics: types of phraseological phrases, merging, unity, combinations and principles for their selection. These words form free combinations. Other words have limited combination possibilities. Such combinations are called phraseological units.
46458.		USSR in the mid-60s - mid-80s. (neo-Stalinism, stagnation, crisis of the system)	16.42KB
	Economic reform, the development and implementation of which was associated with the name of the Chairman of the Council of Ministers of the USSR A. The dead end is dangerous because the gap between the developed economies of the world and the economy of the USSR was steadily increasing. Their ideological justification was the concept of developed socialism, according to which the slow, systematic gradual improvement of real socialism built in the USSR will completely and finally take an entire historical era. this concept was legally enshrined in the preamble of the new Constitution of the USSR.
46459.		Bankruptcy procedures	16.43KB
	Supervision is a procedure aimed at ensuring the safety of the debtor's property and conducting a thorough analysis of its financial condition in order to search for the possibility of restoring the solvency of the enterprise. This procedure is introduced from the moment the Arbitration Court accepts an application for declaring a debtor bankrupt for a period of up to 7 months. executive documents issued on the basis of court decisions; the payment of dividends is prohibited; it is not allowed to terminate the debtor's monetary obligations by offsetting a counter ...
46460.		Elkonin. Psychology of teaching a younger student	16.45KB
	Psychology of teaching a younger student Introduction Primary school sets itself the task of forming the ability to assimilate the system scientific knowledge turns into a preparatory stage organically linked with all other higher levels of education. The main result of the research is the experimentally confirmed possibility of forming significantly higher levels under certain learning conditions. mental development at primary school age. The determining factors in this are the content of training and organically with it...

The theoretical level of scientific research is a rational (logical) stage of knowledge. At the theoretical level, with the help of thinking, there is a transition from a sensory-concrete idea of the object of study to a logical-concrete one. The logically concrete is the theoretically reproduced in the thinking of the researcher a concrete idea of the object in all the richness of its content. At the theoretical level, the following methods of cognition are used: abstraction, idealization, thought experiment, induction, deduction, analysis, synthesis, analogy, modeling.

Abstraction- this is a mental distraction from some less significant properties, aspects, features of the object or phenomenon being studied with the simultaneous selection, formation of one or more essential aspects, properties, features. The result obtained in the process of abstraction is called abstraction.

Idealization- this is a special kind of abstraction, the mental introduction of certain changes in the object under study in accordance with the objectives of the research. We give examples of idealization.

Material point- a body devoid of any dimensions. This is an abstract object, the dimensions of which are neglected, it is convenient in describing the movement.

Completely black body- is endowed with a property that does not exist in nature to absorb absolutely all the radiant energy that falls on it, reflecting nothing and not passing through itself. The emission spectrum of a blackbody is an ideal case, since it is not affected by the nature of the substance of the emitter or the state of its surface.

thought experiment is a method of theoretical knowledge, which involves operating with an ideal object. This is a mental selection of positions, situations that allow you to detect important features of the object under study. In this it resembles a real experiment. In addition, it precedes the real experiment in the form of a planning procedure.

Formalization- this is a method of theoretical knowledge, which consists in the use of special symbolism, which allows you to abstract from the study of real objects, from the content of the theoretical provisions that describe them, and instead operate with a certain set of symbols, signs.

To build any formal system, it is necessary:

1. setting the alphabet, i.e. a certain set of characters;

2. setting the rules by which "words", "formulas" can be obtained from the initial characters of this alphabet;

3. setting the rules by which one can move from one word, formula of a given system to other words and formulas.

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

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

Induction- (from Latin induction - guidance, motivation) is a method of cognition based on a formal logical conclusion, which leads to a general conclusion based on particular premises. In other words, it is the movement of our thinking from the particular, the individual to the general. Finding similar features, properties in many objects of a certain class, the researcher concludes that these features, properties are inherent in all objects of this class.

The popularizer of the classical inductive method of cognition was Francis Bacon. But he interpreted induction too broadly, considered it the most important method of discovering new truths in science, the main means of scientific knowledge of nature. In fact, the above methods of scientific induction serve mainly to find empirical relationships between the experimentally observed properties of objects and phenomena. They systematize the simplest formal logical techniques that were spontaneously used by natural scientists in any empirical study.

Deduction- (from lat. deduction - derivation) is the receipt of private conclusions based on the knowledge of some general provisions. In other words, it is the movement of our thinking from the general to the particular.

However, despite the attempts that have taken place in the history of science and philosophy to separate induction from deduction, to oppose them, in the real process of scientific knowledge, both of these two methods are used at the corresponding stage of the cognitive process. Moreover, in the process of using the inductive method, deduction is often “hidden” as well. Generalizing the facts in accordance with some ideas, we indirectly derive the generalizations we receive from these ideas, and we are not always aware of this. It seems that our thought moves directly from facts to generalizations, that is, that there is pure induction here. In fact, in accordance with some ideas, implicitly guided by them in the process of generalizing facts, our thought indirectly goes from ideas to these generalizations, and, consequently, deduction also takes place here ... We can say that in all cases, when we generalize according to some philosophical propositions, our conclusions are not only induction, but also hidden deduction.

Analysis and synthesis. Under analysis understand the division of an object into constituent particles for the purpose of studying them separately. Such parts may be some material elements of the object or its properties, features, relationships, etc. Analysis is a necessary and important stage in the cognition of an object. But it is only the first stage of the process of cognition. To comprehend an object as a single whole, one cannot limit oneself to studying only its constituent parts. In the process of cognition, it is necessary to reveal the objectively existing connections between them, to consider them together, in unity. To carry out this second stage in the process of cognition - to move from the study of individual component parts of an object to the study of it as a single connected whole - is possible only if the method of analysis is supplemented by another method - synthesis. During synthesis the component parts of the object under study, dissected as a result of the analysis, are joined together. On this basis, further study of the object takes place, but already as a single whole. At the same time, synthesis does not mean a simple mechanical connection of disconnected elements into a single system. It reveals the place and role of each element in the system of the whole, establishes their interrelation and interdependence.

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

Analogy and modeling. Under analogy similarity, the similarity of some properties, features or relationships of objects that are generally different is understood. Establishing similarities (or differences) between objects is carried out as a result of comparison. Thus, comparison underlies the method of analogy.

The analogy method is used in various fields of science: in mathematics, physics, chemistry, cybernetics, in the humanities, etc. There are various types of conclusions by analogy. But what they have in common is that in all cases one object is directly investigated, and a conclusion is made about another object. Therefore, inference by analogy in the most general sense can be defined as the transfer of information from one object to another. In this case, the first object, which is actually being studied, is called a model, and the other object, to which the information obtained as a result of the study of the first object (model) is transferred, is called the original (sometimes a prototype, sample, etc.). Thus, the model always acts as an analogy, i.e., the model and the object (original) displayed with its help are in a certain similarity (similarity).

The limits of the scientific method.

The limitations of the scientific method are mainly associated with the presence of a subjective element in cognition and are due to the following reasons.

Human experience, which is the source and means of cognition of the surrounding world, is limited. Man's senses allow him only limited orientation in the world around him. The possibilities of experiential knowledge of the surrounding world by a person are limited. The mental capabilities of man are great, but also limited.

The dominant paradigm, religion, philosophy, social conditions and other elements of culture inevitably influence the worldview of scientists, and consequently, the scientific result.

The Christian worldview proceeds from the fact that the fullness of knowledge is revealed by the Creator and man is given the opportunity to possess it, but the damaged state of human nature limits his ability to know. Nevertheless, a person is capable of knowing God, that is, he can know himself and the world around him, see the manifestation of the Creator's features in himself and in the world around him. It should not be forgotten that scientific method is only an instrument of knowledge and, depending on whose hands it is, it can bring benefit or harm.

Specificity and basic methods of theoretical knowledge: abstraction, idealization, formalization, thought experiment. Special theoretical methods of scientific knowledge abstraction, idealization, formal

A) Abstraction and idealization. The concept of an idealized object

Methods for constructing and studying an idealized object

As well as other works that may interest you

Report a typo

Text to be sent to our editors:

Your comment (optional):