Methods of theoretical knowledge are abstraction, analysis and synthesis, induction and deduction, idealization, analogy, formalization, modeling, hypothesis methods and axiomatic, systemic method and approach, etc.
Abstraction . The essence of abstraction consists in mental abstraction from non-essential properties, relationships and connections in an object and between them while simultaneously fixing individual sides, aspects of these objects in accordance with the goals of cognition and the tasks of research, design and transformation. The result of the abstraction process will be abstractions - concepts of natural language and concepts of science.
The abstraction method involves two points. First, the essential is separated from the unimportant, important from unimportant in a cognitive task. Then an assessment is made various aspects object, operating factors, conditions, the presence of something in common is established, membership in certain classes of phenomena, objects, etc. A necessary side of abstraction is the establishment of independence or negligible dependence on certain factors. Next, some object of an ideal or material nature being studied is replaced by another, less rich in properties, having a limited number of parameters and characteristics. The resulting object acts as models first.
It should be noted that the abstraction operation can be applied to both real and abstract objects, which themselves were already the result of a previous abstraction. At the same time, we seem to be moving away from the concreteness and richness of the properties of the original object, impoverishing it, but otherwise we would not be able to cover wide classes of objects and their general essence, interconnection, form, structure, etc. The role of the resulting abstraction is that , that it allows in knowledge to name objects that previously seemed different with one name, to replace complex things with simple ones, to classify diversity according to common features, i.e., ultimately reach a generalization, and therefore a law.
Analysis - this is the mental division of an object or its aspects of interest to us into separate parts for the purpose of their systematic study. Their role can be played by individual material or ideal elements, properties, relationships, etc.
Synthesis – mental combination of previously studied elements into a single whole.
From the above definitions it is already clear that these are mutually presupposing and complementary methods. Depending on the degree of research, the depth of penetration into the essence of the object or its aspects, analysis and synthesis of various kinds or types are used: direct, or empirical, analysis and synthesis, which are suitable for stage one, still a superficial acquaintance with the object of research and its aspects, especially when studying a complex object; recurrent, or elementary theoretical, analysis and synthesis, which are suitable for comprehending moments, sides, aspects of the essence, mastering certain cause-and-effect dependencies; structural genetic analysis and synthesis, which make it possible to identify the most important, central, decisive thing in the object of study, leading to the development of the object into a whole; they cover genetic connections and mediation; their entire chains lead to the completeness of coverage of parts and their content or to a systemic vision and description of the object.
Induction and deduction – the next two methods are, like the previous ones, paired and complementary. They occupy a special position in the system scientific methods and include the application of purely formal logical rules of inference and inference - deductive and inductive. Let's start by explaining the meaning of induction.
Induction is understood as inference from the particular to the general, when, based on knowledge about some objects, a conclusion is made about the properties of the entire class as a whole. In this case, the following types of induction can be distinguished. Full induction, when a conclusion is made about the properties of a given object based on enumerating all objects of a given class. This is completely reliable knowledge. Every science strives to obtain it and uses it as evidence of the reliability of its conclusions, their irrefutability.
Incomplete induction when a general conclusion is drawn from premises that do not cover all objects or aspects of a given class. Thus, there is a moment of hypothesis in it. Its evidence is weaker than the previous one, because there are no rules without exceptions.
Historically, the first was the so-called enumerative (or popular) induction. It is used when some kind of regularity or repeatability is noticed in experience, about which a judgment is formulated. If there are no refuting examples, then a general conclusion is drawn in the form of an inference. This type of induction is considered complete. Complete induction is otherwise called scientific, since it gives not only a formal result, but also a proof of the non-randomness of the found regularity. Such induction also makes it possible to capture cause-and-effect relationships. Example full induction: successively tested metals - one, another, the third, etc. - have electrical conductivity, from which it follows that all metals are electrically conductive, etc. An example of incomplete induction: every even number is divided by two, and although there are infinitely many of them set, we still draw a conclusion about the multiplicity of all even two numbers, and so on.
Deductive inference is an inference in which a conclusion about the properties of an object and about itself is made on the basis of knowledge of the general properties and characteristics of the entire set. The role of deduction in modern scientific knowledge and knowledge has increased dramatically. This is due to the fact that modern science and engineering practice are faced with objects inaccessible to ordinary sensory perception (microworld, the Universe, the past of humanity, its future, very complex systems of various kinds, etc.), so more and more often we have to turn to thoughts rather than to observations and experiments. Deduction is of particular importance for the formalization and axiomatization of knowledge, the construction of hypotheses in mathematics, theoretical physics, management theory and decision making, economics, computer science, ecology, etc. Classical mathematics is a typically deductive science. Deduction differs from other methods in that if the initial knowledge is true, it gives true inferential knowledge. However, the power of deduction cannot be overestimated. Before applying it, it is necessary to obtain true initial knowledge, general premises, and therefore special meaning remains up to the methods of obtaining such knowledge discussed above.
Idealization . For the purposes of scientific knowledge, construction, design and transformation, so-called “ideal objects” are widely used. They do not exist in reality and are fundamentally not implemented in practice, but without them theoretical knowledge and its applications are impossible. These include point, line, number, absolute solid, point electric charge, charge in general, ideal gas, absolutely black body and many others. Science cannot be imagined without them. The mental construction of such objects is called idealization.
For idealization to proceed successfully, the subject's abstracting activity is necessary, as well as other mental operations: induction, synthesis, etc. At the same time, we set ourselves the following tasks: mentally deprive real objects of certain properties; We mentally endow these objects with certain unreal ultimate properties; we name the resulting object. To accomplish these tasks, multi-stage abstraction is used. For example, abstracting from the thickness of a real object, a plane is obtained; depriving the plane of one dimension, they get a line; depriving a line of its only dimension, they get a point, etc. But how to move to the limiting property? Let us, for example, arrange the bodies known to us in a row in accordance with the increase in their hardness. Then, in the limit, we get an absolutely rigid body. The examples can easily be continued. Such an ideal object as incompressibility is constructed theoretically when the compressibility property is accepted equal to zero. We get an absolutely black body if we attribute to it the complete absorption of incoming energy.
Note that abstraction from any of the properties is necessarily the attribution to it opposite property, and the former is discarded, otherwise we will not get an ideal object.
Analogy . This is one of the methods of cognition when, from the similarity of some features and aspects of two or more objects, a conclusion is drawn about the similarity of other features and properties of these objects.
Let's build an analogy. It is known that the Sun is an ordinary star in our Galaxy, which contains about 100 billion such stars. These luminaries have a lot in common: huge masses, high temperatures, a certain luminosity, radiation spectrum, etc. They have satellites - planets. By analogy with our Solar system, scientists conclude that besides ours, there are also inhabited worlds in the galaxy, that we are not alone in the Universe. An analogy does not provide absolute certainty for a conclusion: it always has an element of conjecture, assumption, and only experience and practice can make a final verdict on this or that analogy.
Formalization . This term itself is ambiguous and is used in different meanings. The first is as a method for solving special problems in mathematics and logic. For example, proof of the consistency of mathematical theories, the independence of axioms, etc. Questions of this kind are solved by using special symbols, which makes it possible to operate not with the statements of the theory in their meaningful form, but with a set of symbols and formulas of various kinds. Secondly, in a broad sense, formalization is understood as a method of studying various problems by displaying their content, structure, relationships and functions using various artificial languages: mathematics, formal logic and other sciences.
What is the role of formalization in science? First of all, formalization ensures a complete overview of certain problems and a generalized approach to them. Further, thanks to symbolism, with which formalization is inevitably associated, polysemy (polysemy) and vagueness of terms are eliminated ordinary language, as a result of which the reasoning becomes clear and rigorous, and the conclusions are evidential. And finally, formalization ensures the simplification of the objects being studied, replacing their study with the study of models: a kind of modeling arises based on symbolism and formalisms. This helps to more successfully solve various cognitive, design, engineering and other tasks. From the above it is clear that formalization is associated with modeling; it is also associated with abstraction, idealization and other methods.
Modeling . Modeling, as a powerful and effective method, is used empirically in the form of mock-ups and at the theoretical level in the form of symbolic constructions. There is a distinction between analogue modeling, when the original and the model are described by the same mathematical equations, formulas, diagrams, etc. Sign modeling is more complicated. Here, the role of models - substitutes for real objects - are numbers, diagrams, symbols, etc. Actually, a significant part of the technical project is expressed in exactly this way. But this type of modeling is further developed thanks to mathematics and logic in the form of logical-mathematical modeling. Here operations, actions with things, processes, phenomena, properties and relationships are replaced by sign constructions, the structure of their relationships, and the expression on this basis of the dynamics of objects and their functions.
Another step forward was the development of model representation of information on computers: computer modeling. The models constructed in this case are based on a discrete representation of information about objects. The opportunity opens up to simulate in real time and build virtual reality.
Axiomatic method – it is a method of organizing existing knowledge into a deductive system. It is widely used in mathematics and mathematized disciplines. When using this method, a number of simple ideas, previously proven or obvious, are introduced into the foundations of the theory in the form of initial provisions. In mathematics they are called axioms, in theoretical physics and chemistry - “beginnings” or principles. All other knowledge - all theorems, all laws and their consequences - are derived from them according to certain logical rules, i.e. deductively.
Statement axiomatic method in science it is associated with the appearance of the famous “Principles” of Euclid. Basic requirements for this method are as follows: consistency of axioms, i.e. in the system of axioms or principles there should not be simultaneously a certain statement and its negation; completeness, that is, there should be no axioms without consequences, and their number should give us all the consequences or their negations; independence, when any axiom should not be deduced from others. There is nothing to add to this system.
The advantages of the axiomatic method are that axiomatization requires a precise definition of the concepts used and rigor of reasoning. It organizes knowledge, excludes unnecessary elements from it, eliminates ambiguity and contradictions, and allows us to take a fresh look at previously achieved knowledge within the framework of a certain theoretical system. True, the application of this method is limited, and within the framework of mathematics it also has certain boundaries. In clarifying this issue, an outstanding role was played by the theorem proven by Kurt Gödel about the fundamental incompleteness of developed formal knowledge systems. Its essence is that within the framework of this system it is possible to formulate statements that can neither be proven nor disproved without leaving this axiomatized system into a metatheory. For all mathematics, arithmetic plays this role. Gödel's result led to the collapse of mathematicians' illusion about the universal axiomatization of mathematics.
- 23.78 KbSpecifics and basic methods of theoretical knowledge: abstraction, idealization, formalization, thought experiment.
1. Abstraction. Ascent from the abstract to the concrete.
The process of cognition always begins with the consideration of specific, sensory objects and phenomena, their external signs, properties, connections. 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 associated with the complex abstracting activity of thinking.
In the process of abstraction, there is a departure (ascent) from sensually perceived concrete objects (with all their properties, sides, etc.) to abstract ideas about them reproduced in thinking. In this case, sensually concrete perception, as it were, “...evaporates to the level of abstract definition” 1 . Abstraction, therefore, consists in mental abstraction from some - less significant - properties, aspects, signs of the object being studied with the simultaneous selection, formation of one or more essential aspects, properties, characteristics of this object. The result obtained in the process of abstraction is called abstraction (or the term “abstract” is used - as opposed to concrete).
In scientific knowledge, for example, abstractions of identification and isolating abstractions are widely used. Abstraction of identification is a concept that is obtained as a result of identifying a certain set of objects (while abstracting from a number of individual properties, characteristics of these objects) and combining them into a special group. An example is the grouping of the entire set of plants and animals living on our planet into special species, genera, orders, etc. Isolating abstraction is obtained by highlighting certain properties and relationships that are inextricably linked with objects 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 being studied and reveal its essence. In this case, the researcher first finds the main connection (relationship) of the object being studied, and then, step by step, tracing how it changes under different conditions, discovers new connections, establishes their interactions, and in this way reflects in its entirety the essence of the object being studied.
The process of transition from sensory-empirical, visual ideas about the phenomena being studied to the formation of certain abstract, theoretical structures that reflect the essence of these phenomena lies at the basis of the development of any science.
Since the concrete (i.e., real objects, processes of the material world) is a collection of many properties, aspects, internal and external connections and relationships, it is impossible to know it in all its diversity, remaining at the stage of sensory cognition and limiting ourselves to it. Therefore, there is a need for a theoretical understanding of the concrete, that is, an ascent from the sensory-concrete to the abstract.
But the formation of scientific abstractions and general theoretical positions is not the ultimate goal of knowledge, but is only a means of deeper, more versatile knowledge of the concrete. Therefore, further movement (ascent) of knowledge from the achieved abstract back to the concrete is necessary. The knowledge about the concrete obtained at this stage of research will be qualitatively different compared to that which was available at the stage of sensory cognition. In other words, the concrete at the beginning of the process of cognition (sensory-concrete, which is its starting point) and the concrete, comprehended at the end of the cognitive process (it is called logical-concrete, emphasizing the role of abstract thinking in its comprehension) are fundamentally different from each other.
The logical-concrete is the concrete, theoretically reproduced in the researcher’s thinking, in all the richness of its content.
It contains not only something sensually perceived, but also something hidden, inaccessible to sensory perception, something essential, natural, comprehended only with the help of theoretical thinking, with the help of certain abstractions.
The method of ascent from the abstract to the concrete is used in the construction of various scientific theories and can be used both in public and in natural sciences. For example, in the theory of gases, having identified the basic laws of an ideal gas - Clapeyron's equations, Avogadro's law, etc., the researcher goes to specific interactions and properties of real gases, characterizing their essential aspects and properties. As we delve deeper into the concrete, new abstractions are introduced, which act as a deeper reflection of the essence of the object. Thus, in the process of developing the theory of gases, it was found that the ideal gas laws characterize the behavior of real gases only at low pressures. This was due to the fact that the ideal gas abstraction neglects the forces of attraction between molecules. Taking these forces into account led to the formulation of Van der Waals' law. Compared to Clapeyron's law, this law expressed the essence of the behavior of gases more specifically and deeply.
2. Idealization. Thought experiment.
The mental activity of a researcher in the process of scientific knowledge includes a special type of abstraction, which is called idealization. Idealization is the mental introduction of certain changes to the object being studied in accordance with the goals of the research.
As a result of such changes, for example, some properties, aspects, or features of objects may be excluded from consideration. Thus, the widespread idealization in mechanics, called a material point, implies a body devoid of any dimensions. Such an abstract object, the dimensions of which are neglected, is convenient when describing the movement of a wide variety of material objects from atoms and molecules to the planets of the solar system.
Changes in an object, achieved in the process of idealization, can also be made by endowing it with some special properties that are not feasible in reality. An example is the abstraction introduced into physics through idealization, known as an absolutely black body (such a body is endowed with the property, which does not exist in nature, of absorbing absolutely all radiant energy falling on it, without reflecting anything or letting anything pass through it).
The advisability of using idealization is determined by the following circumstances:
Firstly, “idealization is appropriate 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 build and develop a theory that is effective in certain conditions and purposes.” , to describe the properties and behavior of these real objects. The latter, in essence, certifies the fruitfulness of idealization and distinguishes it from fruitless fantasy” 2.
Secondly, it is advisable to use idealization in cases where it is necessary to exclude certain properties and 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 makes it easier to study.
Thirdly, the use of idealization is advisable when the properties, aspects, and connections of the object being studied that are excluded from consideration do not affect its essence within the framework of this study. Wherein right choice the admissibility of such idealization plays a very important role.
It should be noted that the nature of idealization can be very different if there are different theoretical approaches to the study of a phenomenon. As an example, we can point to three different concepts of “ideal gas”, formed under the influence of different theoretical and physical concepts: Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac. However, all three idealization options obtained in this case turned out to be fruitful in the study of gas states of various natures: the Maxwell-Boltzmann ideal gas became the basis for studies of ordinary rarefied molecular gases located at fairly high temperatures; The Bose-Einstein ideal gas was used to study photonic gas, and the Fermi-Dirac ideal gas helped solve a number of electron gas problems.
Being a type of abstraction, idealization allows for an element of sensory clarity (the usual process of abstraction leads to the formation of mental abstractions that do not have any clarity). This feature of idealization is very important for the implementation of such a specific method of theoretical knowledge, which is a 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 and situations that make it possible to detect some important features of the object under study. This reveals a certain similarity between a mental (idealized) experiment and a real one. Moreover, every real experiment, before being carried out in practice, is first “played out” by the researcher mentally in the process of thinking and 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 independent role in science. At the same time, while maintaining similarities with the real experiment, it is at the same time significantly different from it.
In scientific knowledge, there may be cases when, when studying certain phenomena and situations, conducting real experiments turns out to be completely impossible. This gap in knowledge can only be filled by a thought experiment.
The scientific activity of Galileo, Newton, Maxwell, Carnot, Einstein and other scientists who laid the foundations of modern natural science testifies to the significant role of thought experiments in the formation of theoretical ideas. The history of the development of physics is rich in facts about the use of thought experiments. An example is Galileo's thought experiments, which led to the discovery of the law of inertia. “...The law of inertia,” wrote A. Einstein and L. Infeld, “cannot be deduced directly from experiment; it can be deduced speculatively - by thinking associated with observation. This experiment can never be performed in reality, although it leads to a deep understanding of actual experiments." 3
A thought experiment can have great heuristic value in helping to interpret new knowledge obtained purely mathematically. This is confirmed by many examples from the history of science.
The idealization method, which turns out to be very fruitful in many cases, at the same time has certain limitations. In addition, any idealization is limited to a specific area of phenomena and serves to solve only certain problems. This can be clearly seen from the example of the above-mentioned idealization of the “absolutely black body”.
The main positive significance of idealization as a method of scientific knowledge is that the theoretical constructions obtained on its basis then make it possible to effectively study real objects and phenomena. Simplifications achieved through idealization facilitate the creation of a theory that reveals the laws of the studied area of phenomena of the material world. If the theory as a whole correctly describes real phenomena, then the idealizations underlying it are also legitimate.
3. Formalization.
Formalization refers to a special approach in scientific knowledge, which consists in the use of special symbols, which allows one to escape from the study of real objects, from the content of the theoretical provisions describing them, and to operate instead with a certain set of symbols (signs).
This technique consists in constructing abstract mathematical models that reveal the essence of the processes of reality being studied. When formalizing, reasoning about objects is transferred to the plane of operating with signs (formulas). Relationships of signs replace statements about the properties and relationships of objects. In this way, a generalized sign model of some subject area, which makes it possible to detect the structure of various phenomena and processes while abstracting from the qualitative characteristics of the latter. The derivation of some formulas from others according to the strict rules of logic and mathematics represents a formal study of the main characteristics of the structure of various, sometimes very distant in nature, phenomena.
A striking example of formalization is the mathematical descriptions of various objects and phenomena widely used in science, based on relevant substantive theories. At the same time, the mathematical symbolism used not only helps to consolidate existing knowledge about the objects and phenomena being studied, but also acts as a kind of tool in the process of further knowledge of them.
To build any formal system it is necessary: a) specifying an alphabet, i.e., a certain set of characters; b) setting the rules by which “words” and “formulas” can be obtained from the initial characters of this alphabet; c) setting rules according to which one can move from some words and formulas of a given system to other words and formulas (the so-called rules of inference).
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 any object in a purely formal way (operating with signs) without directly addressing this object.
Another advantage of formalization is to ensure the brevity and clarity of recording scientific information, which opens up great opportunities for operating with it.
Description of work
The process of cognition always begins with the consideration of specific, sensory objects and phenomena, their external signs, properties, and connections. 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 associated with the complex abstracting activity of thinking.
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. Modern hypothetico-deductive theory is based on a certain empirical basis - a set of facts that need explanation and make the creation of a theory necessary. It is the idealized object that makes possible creation theories. Scientific theories are primarily distinguished by the idealized objects they are based on.
QUESTION No. 25
Formalization, idealization and the role of modeling
According to Radugin (p. 123)
Methods for constructing and studying an idealized object
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 foundations and causes, to identify 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 knowledge 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 is various shapes, techniques and stages of indirect cognition of reality.
Methods and forms of cognition at the theoretical level, depending on the functions they perform, can be divided into two groups. The first group includes 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 if in a “pure” form. The second group is methods of constructing and justifying theoretical knowledge, which is given in the form of a hypothesis, which as a result acquires the status of a theory.
To methods of construction and research idealized object include: abstraction, idealization, formalization, thought experiment, mathematical modeling.
a) Abstraction and idealization. The concept of an idealized object
It is known that every 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, theory is forced to abstract itself from those aspects of the subjects it studies that do not interest it. In addition, theory is often forced to abstract from some differences in the objects it studies in certain respects. From a psychological point of viewthe process of mental abstraction from certain aspects, properties of the objects being studied, from certain relationships between them is called abstraction.Mentally identified properties and relationships appear in the foreground, appear as necessary for solving problems, and 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 complianceinterval of abstractions.The interval of abstractions is the limits of rational validity of a particular abstraction, the conditions of its “objective truth” and the limits of applicability, established on the basis of information obtained by empirical or logical means. The abstraction interval depends, firstly, onthe assigned cognitive task;secondly, what one is distracted from in the process of comprehending an object must be to outsiders (according to clearly defined criteria) for a specific object being abstracted; thirdly, the researcher must know to what extent a given abstraction has legal force.
The abstraction method involves performing a conceptual development and conceptual assembly of objects when studying complex objects.Conceptual developmentmeans displaying the same initial object of study in different mental planes (projections) and, accordingly, finding many intervals of abstractions for it. So, for example, in quantum mechanics, one and the same object (an elementary particle) can be alternately represented within two projections: one as a corpuscle (in some experimental conditions), then as a wave (in other conditions). These projections are logically incompatible with each other, but only taken together they exhaust the whole necessary information about the behavior of particles.
Conceptual buildrepresentation of an object in a multidimensional cognitive space by establishing logical connections and transitions between at different intervals, forming 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 "Galileo's rules of transformation" governing the ways of moving from one group of statements to another.
Abstraction as the most important technique cognitive activity human beings is widely used at all stages of scientific and cognitive activity, including at the level empirical knowledge. On its basis, empirical objects are created. As V.S. Stepin noted, empirical objects are abstractions that capture the characteristics of real objects of experience. They are certain schematizations of fragments of the real world. Any feature, the “carrier” of which is an empirical object, can be found in the corresponding real objects (but not vice versa, since an empirical object represents not all, but only some signs of real objects, abstracted from reality in accordance with the tasks of cognition and practice) . Empirical objects constitute the meaning of such terms in empirical language as “Earth,” “current-carrying wire,” “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 features that correspond to the properties and relationships of real objects, but also with features that no such object possesses. Theoretical objects form the meaning of such terms as “point”, “ideal gas”, “absolute black body”, etc.
In logical and methodological research, theoretical objects are sometimes called theoretical constructs, as well as abstract objects. Objects of this kind serve as the most important means of understanding real objects and the relationships between them.They are called idealized objects, and the process of their creation is called idealization. Thus, idealization is the process of creating mental objects, conditions, situations that do not exist in reality through mental abstraction from some properties of real objects and relationships between them or endowing objects and situations with those properties that they do not actually possess or cannot possess, with the goal 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 limit ourselves to only this, then we will not yet receive any integral object, but will simply destroy a real object or situation. After abstraction, we still need to highlight the properties that interest 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 as a result of usingidealization method.
Idealization helps the researcher to highlight pure form aspects of reality that interest him. As a result of idealization, an object acquires properties that are not required in empirical experience. Unlike ordinary abstraction, idealization places emphasis not on the operations of abstraction, but on the mechanism replenishment . Idealization gives an absolutely accurate construct,mental construct, in which this or that property, state is presented in extreme, most expressed form . Creative constructs, abstract objects act asideal model.
Why is it necessary to use abstract objects (theoretical constructs) in cognition? The fact is that a real object is always complex; significant and secondary properties for a given researcher are intertwined in it; necessary regular relationships are obscured by random ones. Constructs, ideal models, are objects endowed with a small number of specific and essential properties and having a relatively simple structure.
Researcher , based on a relatively simple idealized object, give a deeper and more complete description of these aspects. Cognition moves from concrete objects to theirabstract, ideal models, which, becoming more and more accurate, perfect and numerous, gradually give us an increasingly adequate image of specific objects. This widespread use of idealized objects is one of the most characteristic features of human cognition.
It should be noted that idealization is used both at the empirical and theoretical levels. The objects to which scientific statements refer are always idealized objects. Even in cases where we use empirical methods cognition - observation, measurement, experiment, the results of these procedures directly relate 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 real objects.
However, the role of idealization increases sharply in the transition from the empirical to the theoretical level of scientific knowledge. Modern hypothetico-deductive theory is based on a certain empirical basis - a set of facts that need explanation and make the creation of a theory necessary. But a theory is not a simple generalization of facts and cannot be logically deduced from them. In order to make it possible to create a special system of concepts and statements, called a theory, we first introducean idealized object, which is an abstract model of reality, endowed with a small amountproperties and having a relatively simple structure. This idealized object expresses the specificity and essential features of the field of phenomena being studied. It is the idealized object that makes the creation of a theory possible. Scientific theories are, first of all, distinguished by the idealized objects they are based on. IN special theory relativity, the 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 n-dimensional configuration space, the properties of which are associated with the quantum of action.
The concepts and statements of a theory are introduced and formulated precisely as characteristics of its idealized object. The basic properties of an idealized object are described by a system of fundamental equations of the theory. The difference in idealized objects of theories leads to the fact that each hypothetico-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 provides an interpretation of the concepts and equations of the theory. Clarification of the theory equations, their experimental confirmation and correction lead to clarification of the idealized object or even to its change. Replacing the idealized object of a theory means reinterpreting the basic equations of the theory. No scientific theory can be guaranteed that its equations will not sooner or later be subject to reinterpretation. In some cases this happens relatively quickly, in others it happens later. long time. So, for example, in the doctrine of heat, the original idealized object - caloric - was replaced by another - a collection of randomly moving material points. Sometimes modification or replacement of the 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 remains the same, but its interpretation changes. It is clear that this can be said only with a formalistic understanding scientific theory. If by theory we mean not only certain mathematical formulas, but also a certain interpretation of these formulas, then a change in 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 methodology 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 imagine them as moving material points that have 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. in the form of idealized objects.
2. Sometimes it turns out to be useful to abstract from some relationships of the objects being studied to each other. With the help of such 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 having only kinetic energy and interacting only upon collision, we obtain an idealized object - an ideal gas. IN social sciences when studying individual aspects of the life of society, individual social phenomena and institutions, social groups, etc. we can abstract from the relationships of these parties, phenomena, groups with other elements of social life.
3. We can also attribute properties to real objects that they do not have, or we can think of the properties inherent in them in some limiting value. Thus, for example, in optics special idealized objects are formed - 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 some part of the energy incident on its surface and the property of absorbing part of this energy. When we enhance the reflection property to its maximum value, we get an ideal mirror - an idealized object whose surface reflects all the energy incident on it. By enhancing the absorption property, in the limiting case we obtain an absolutely 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. Let's say that we are pushing a cart along the road. The cart moves for some time after the push and then stops. There are many ways to lengthen the path covered by a cart after a push, for example, lubricating the wheels, creating a smoother road, etc. 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 traversed by this body. It is clear that it is impossible to eliminate all external influences on the moving body. In real situations, a moving body will inevitably be subject to some kind of influence 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 construction and research of 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 symbolic form, using a wide variety of artificial languages.
Operations with formalized objects mean operations with symbols. As a result of formalization, symbols can be treated as concrete physical objects. The use of symbolism ensures a complete overview of a certain area of problems, brevity and clarity of knowledge recording, 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. Reconstruction of a scientific theory in a formalized language makes it possible to trace the logical relationship between various provisions of the theory, to identify the entire set of prerequisites and foundations on the basis of which it is developed, which makes it possible to clarify ambiguities and uncertainties, and to prevent paradoxical situations. The formalization of a theory also performs a kind of unifying and generalizing function, allowing a number of theoretical provisions to be extrapolated to entire classes of scientific theories and to use a formal apparatus for the synthesis of previously unrelated theories. One of the most valuable advantages of formalization is its heuristic capabilities, in particular the ability to detect and prove previously unknown properties of the objects being studied.
There are two types of formalized theories: fully formalized and partially formalizedtheories. Fully formalized theories are constructed in an axiomatically deductive form with an explicit indication of the formalization language and the use of clear logical means. In partially formalized theories, language and logical means, used for the development of this scientific discipline, are not explicitly recorded. On modern stage development of science, it is dominated by partially formalized theories.
The formalization method contains 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 most unexpected consequences, through purely formalized actions. The formalization process is creative. Starting from a certain level generalizations scientific facts, formalization transforms them, reveals in them such features that were not recorded at the content-intuitive level. Y.L. Ershov, in his works devoted to the use of formalized languages, provides a number of criteria confirming that with the help of formalizing a theory, non-trivial consequences can be obtained, which were not even suspected until they were limited to the content-intuitive formulation of the theory in natural language. Thus, the formulation of the axiom of choice was initially not in doubt. And only its use (in conjunction with other axioms) in a formal system that claims to axiomatize and formalize set theory revealed that it leads to a number of paradoxical consequences, which cast doubt on the possibilities of its use. In physics, when trying to axiomatize field theory, isolating certain statements about the quality of its axioms led to obtaining large number consequences suitable for explaining experimental data.
The creation of formalized descriptions has not only cognitive value itself, but is a condition for use at the theoretical levelmathematical 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, relationships) thatallow different interpretations . Mathematical modeling as a theoretical method found its wide application in the late 40s of the twentieth century. in individual sciences and in interdisciplinary research. The basis of the mathematical modeling method is the constructionmathematical model. A mathematical model is a formal structure consisting of a set of mathematical objects. The significance of the mathematical method in developing a theory is determined by the fact that, while displaying certain quantitative properties and relationships of the original, it replaces it in a certain way, and manipulation with this model provides deeper and more complete information about the original.
In the simplest case, the model is a separatemathematical object, that is, such a formal structure with the help of which it is possible from empirically obtained values of some parameters of the studied material object move on to the meaning of others without recourse to experiment. For example, by measuring the circumference of a spherical object, use the formula to calculate the volume of this object.
Researchers have established that in order for an object to be successfully studied using mathematical models, it must have a number of special properties. First, the relationships within it must be well known; secondly, the properties essential for the object must be quantified (and their number should not be too large); and, thirdly, depending on the purpose of the study, the forms of behavior of the object (which is determined by laws, for example, physical, biological, social) must be known for a given set of relationships.
Essentially any mathematical structure(or abstract system) acquires the status of a model only when it is possible to establish the fact of an analogy of a structural, substrate or functional nature 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 associated with the relation of isomorphism between them, defined within the framework of fixing the interval of abstraction. In order to study a real system, the researcher replaces it (up to isomorphism) with an abstract system with the same relations. Thus, the research problem 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 that form the basis for calculating the size of the bridge, its strength, the 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. Just one translation qualitative task the clear, unambiguous and rich in its capabilities language of mathematics allows you to see the research problem in a new light and clarify its content. However, mathematics also reveals something more. Characteristic of mathematical knowledge is the use of the deductive method, i.e. manipulating objects according to certain rules and thus obtaining new results.
According to Tarasov (pp. 91-94)
Idealization, abstraction- replacement individual properties an object or an entire object with a symbol or sign, 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 the scientific knowledge 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 precondition for constructing a theory, since the system of idealized, abstract images determines the specifics of a given theory. The theory system distinguishes between basic and derived idealized concepts. For example, in classical mechanics such a main idealized object is mechanical system as the interaction of material points.
In general, idealization allows you to accurately outline the characteristics of an object and 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 the process of cognition in general.
Formalization - operating with signs reduced to generalized models, abstract mathematical formulas. The derivation of some formulas from others is carried out according to the strict rules of logic and mathematics, which is formal research the main structural characteristics of the object being studied.
Modeling . A model is a mental or material replacement of the most significant aspects of the object being studied. A model is a specially created human object or system, a device that in a certain respect imitates and reproduces real-life objects or systems that are the object of scientific research.
Modeling relies on analogies of properties and relationships between the original and the model. Having studied the relationships that exist between the quantities describing 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 a person’s ability to abstract the studied signs or properties of various items, phenomena and establish certain relationships between them.
Although scientists have long used this method, it was only from the middle of the 19th century. modeling is gaining strong recognition among scientists and engineers. In connection with the development of electronics and cybernetics, modeling is becoming an extremely effective research method.
Thanks to the use of modeling the patterns of reality, which in the original could only be studied through observation, they become accessible to experimental research. An opportunity arises 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 use of certain models, then we can state that in the early stages of the development of science and technology, material, visual models were used. Subsequently, they gradually lost, one after another, the concrete features of the original, and their correspondence with the original acquired an increasingly abstract character. Currently, 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 option is the following:
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 problems they solve. There is science bionics , the purpose of which is to study unique natural models with the aim of further using the acquired knowledge in the creation of artificial devices. It is known, for example, that the creators of the model of the shape of a submarine took the body shape of a dolphin as an analogue; when designing the first aircraft, a model of the wingspan of birds was used, etc.;
b) material-technical models (in a reduced or enlarged form, completely 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 being studied (models of houses, district buildings, etc.); b) models that reproduce the dynamics of the objects being studied, regular relationships, quantities, parameters (models of airplanes, ships, plane trees, etc.).
Finally, there is a third type of models - c) symbolic models, including mathematical ones. Sign modeling makes it possible to simplify the subject being studied and to highlight in it those structural relationships that most interest the researcher. While losing to material-technical models in terms of clarity, iconic models gain due to deeper penetration into the structure of the fragment of objective reality being studied.
Thus, with the help of sign systems it is possible to understand the essence of such complex phenomena like a device atomic nucleus, elementary particles, Universe. Therefore the application iconic models is especially important in those areas of science and technology where they deal with the study of extremely common connections, relationships, structures.
The possibilities of symbolic modeling have especially expanded due to the advent of computers. Options have appeared for constructing complex sign-mathematical models that make it possible to select the most optimal values of quantities of complex studied real processes and carry out long-term experiments on them.
In the course of research, the need often arises to construct various models of the processes being studied, ranging from real ones to conceptual and mathematical models.
In general, “the construction of not only visual, but also conceptual and mathematical models accompanies the process scientific research from its beginning to the 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 an 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 origin, formation and development of an object, so to speak, in its “pure form,” essentially, without considering the circumstances that contribute to it. That is, the logical method is a straightened, simplified (without losing the essence) version of the historical method.
In the process of cognition, one should be guided by the principle of unity of historical and logical methods: it is necessary to begin the study of the object from those aspects, relationships that historically preceded others. Then, with the help of logical concepts, it is as if to 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 evolution is based on inanimate, living and social matter quite definite rhythmic processes lie.
Modeling - representation of the object under study in a simplified, schematic form, convenient for obtaining predictive conclusions. Example - periodic table Mendeleev (see above for more details on modeling).
Expertise - forecasting based on the assessment of expert opinion - ( individuals, groups, organizations), based on an objective statement of the prospects of the corresponding phenomenon.
The three listed methods seem to complement each other. Any extrapolation is to a certain extent a model and an estimate. Any predictive model is an estimate plus extrapolation. Any predictive assessment implies extrapolation and mental simulation.
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Theoretical methods-operations have a wide field of application, both in scientific research and in practical activities.
Theoretical methods - operations are defined (considered) by 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 identification of individual signs and qualities of a phenomenon, process or relationships of phenomena, processes. Analysis procedures are an organic component of any scientific research and usually form its first phase, when the researcher moves from an undifferentiated description of the object under study to the identification of its structure, composition, its properties and characteristics.
The same phenomenon, process can be analyzed in many aspects. A comprehensive analysis of the phenomenon allows us to examine it in more depth.
Synthesis – connection of various elements, sides of an object into a single whole (system). Synthesis is not a simple summation, but a semantic connection. If you simply connect phenomena, no system of connections will arise between them; only a chaotic accumulation of individual facts will form. Synthesis is the opposite of analysis, with which it is inextricably linked. Synthesis as a cognitive operation appears in various functions of theoretical research. Any process of concept formation 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 interconnection of theories related to one subject area, as well as as a function of combining competing theories (for example, the synthesis of corpuscular and wave concepts in physics).
Synthesis also plays a significant 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 essential details for the study will not be noticed, which can be of great importance for understanding the phenomenon as a whole.
Comparison is a cognitive operation that underlies judgments about the similarity or difference of objects. With the help of comparison, the quantitative and qualitative characteristics of objects are identified, their classification, ordering and evaluation are carried out. Comparison is comparing one thing to another. Wherein important role play grounds, or signs of comparison, that determine 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 principles that are essential for this consideration. Moreover, objects that are comparable on one basis may not be comparable on other characteristics. The more accurately the characteristics are assessed, the more thoroughly the comparison of phenomena is possible. An integral part comparison is always analysis, since for any comparison in phenomena it is necessary to isolate the corresponding characteristics of comparison. Since comparison is the establishment of certain relationships between phenomena, then, naturally, synthesis is also used during the comparison.
Abstraction- one of the main mental operations that allows you to mentally isolate and turn into an independent object of consideration individual aspects, properties or states of an 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 in themselves and independently of it. Such isolation is possible only in the mental plane - in abstraction. Thus, the geometric figure of a body in itself does not really exist and cannot be separated from the body. But thanks to abstraction, it is mentally isolated, 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 to fix these properties, for example, through concepts.
Specification– a process opposite to abstraction, that is, finding the 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 knowledge of the concrete. Therefore, dialectics distinguishes two processes of ascent in the process of cognition in the coordinates “abstraction - concretization”: the ascent from the concrete to the abstract and then the process of ascent from the abstract to the new concrete (G. Hegel). The dialectics of theoretical thinking consists in the unity of abstraction, the creation of various abstractions and concretization, movement towards the concrete and its reproduction.
Generalization– one of the main cognitive mental operations, consisting of isolating and fixing 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, identifies and labels them as identical, general properties, which can become the content of the concept of this group, class of objects. Separating general properties from private ones and denoting them with a word allows you to cover the entire variety of objects in an abbreviated, condensed form, reduce them into certain classes, and then, through abstractions, operate with concepts without directly referring to individual objects. The same real object can be included in both narrow and broad classes, for which scales of generality of characteristics are built on the principle of genus-species relations. The function of generalization is to organize the variety of objects and their classification.
Formalization– displaying the results of thinking in precise concepts or statements. It is, as it were, a “second order” mental operation. Formalization is opposed to intuitive thinking. In mathematics and formal logic, formalization is understood as the display of meaningful knowledge in a symbolic 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 a significant role in the development of scientific knowledge, since intuitive concepts, although they seem clearer from the point of view of ordinary consciousness, are of little use for science: in scientific knowledge it is often impossible not only to resolve, 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, proceeding in a logical linguistic form through concepts, judgments and conclusions.
In scientific judgments, connections are established between objects, phenomena or between them. certain signs. In scientific conclusions, one judgment comes from another, and a new one is made on the basis of existing conclusions. There are two main types of inferences: inductive (induction) and deductive (deduction).
Induction- this is an inference from particular objects, phenomena to a general conclusion, from individual facts to generalizations.
Deduction- this is an inference 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 realizable 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 relationships inherent in the objects of reality and the introduction into the content of the concepts being formed 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 “point”, “straight line”; in physics – “material point”, “absolutely black body”, “ideal gas”, etc.
Concepts that are the result of idealization are said to represent idealized (or ideal) objects. Having formed concepts of this kind about objects through idealization, one can subsequently operate with them in reasoning as with really existing objects and build abstract diagrams 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 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 a prototype, original. This 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 (construction and research of models). The difference between analogy and modeling is 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 - an action method.
Model is an auxiliary object, selected or transformed for cognitive purposes, providing new information about the main object. The forms of modeling are varied and depend on the models used and the scope of their application. According to the nature of the models, subject and sign (information) modeling are distinguished.
Subject modeling is carried out on a model that reproduces certain geometric, physical, dynamic, or functional characteristics modeling object - the original; in a particular case - analogue modeling, when the behavior of the original and the model is described by unified mathematical relationships, for example, unified differential equations. In symbolic modeling, models are diagrams, drawings, formulas, etc. The most important type of such modeling is mathematical modeling.
Modeling is always used together with other research methods; it is especially closely related to experiment. The study of a phenomenon using its model is a special type of experiment - a model experiment, which differs from a regular experiment in that in the process of cognition an “intermediate link” is included - a model, which is both a means and an object of experimental research, replacing the original.
A special type 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 simulating the movement and situations that could take place in a real experiment. At the same time, ideal models and objects help to identify “in their purest form” the most important, essential connections and relationships, mentally play out possible situations, and weed out unnecessary options.
Modeling also serves as a way to construct something new that does not previously exist in practice. The researcher, having studied the characteristic features of real processes and their trends, searches for their new combinations based on the leading idea, makes their mental reconstruction, that is, models the required state of the system being studied (just like any person and even an animal, builds his activity based on the initially formed “model of the required future” - according to N.A. Bernstein). In this case, hypothetical models are created that reveal the mechanisms of connection between the components of what is being studied, which are then tested in practice. In this understanding, modeling in Lately has become widespread in the social sciences and humanities - in economics, pedagogy, etc., when different authors propose different models of firms, industries, educational systems, etc.
Along with the operations of logical thinking, theoretical methods-operations can also include (perhaps conditionally) imagination as a mental process for creating new ideas and images with its specific forms of fantasy (creating implausible, paradoxical images and concepts) and dreams (as creating images of what is 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 poor in content forms to dissected and richer in content, to a system of concepts that allows us to comprehend the subject 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 knowledge. Finally, dialectics is oriented in knowledge towards the disclosure and ways of resolving contradictions.
Laws of dialectics: the transition of quantitative changes into qualitative ones, unity and struggle of opposites, etc.; analysis of paired dialectical categories: historical and logical, phenomenon and essence, general (universal) and individual, etc. are integral components of any well-constructed scientific research.
Scientific theories tested by practice: any such theory, essentially, acts as a method in constructing new theories in this or even other areas of scientific knowledge, as well as as a method that determines the content and sequence of the researcher’s experimental activities. Therefore, the difference between scientific theory as a form of scientific knowledge and as a method of cognition in this case is functional in nature: being formed as a theoretical result of past research, the method acts as the starting point and condition for subsequent research.
Proof - a method - a theoretical (logical) action, during which the truth of a thought is substantiated with the help of other thoughts. Any proof consists of three parts: thesis, arguments (arguments) and demonstration. According to the method of conducting evidence, there are direct and indirect, and according to the form of inference - inductive and deductive. Rules of evidence:
1. The thesis and arguments must be clear and precisely defined.
2. The thesis must remain identical throughout the entire proof.
3. The thesis should not contain a logical contradiction.
4. The arguments given in support of the thesis must themselves be true, beyond 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, the properties of which influence 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 clearly 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 being studied. In it, only a certain, historically specific part of such content always receives description and explanation.
Method of analysis scientific systems knowledge 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 justifying the equivalence or priority of using certain mathematical tools in various theories related to the same subject area; when exploring 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 and popularization; for coordination with other knowledge systems, etc.
- deductive method (synonym - axiomatic method) - a method of constructing a scientific theory in which it is based on some initial provisions of the axiom (synonym - postulates), from which all other provisions of this theory (theorem) are deduced in a purely logical way through proof. The construction of a theory based on the axiomatic method is usually called deductive. All concepts of deductive theory, except for a fixed number of initial ones (such initial concepts in geometry, for example, are: point, straight line, plane) are introduced through definitions that express them through previously introduced or derived concepts. Classic example The deductive theory is Euclid's geometry. The deductive method is used to build theories in mathematics, mathematical logic, and theoretical physics;
– the second method has not received a name in the literature, but it certainly exists, since in all other sciences, except those listed above, theories are built using a method that 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 resulting generalizations can be extended to all objects and phenomena covered by a given theory (deduction). Most theories in the sciences about nature, society and man are constructed using the inductive-deductive method: 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, constructing 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.
TO special methods Scientific knowledge includes procedures of abstraction and idealization, during which scientific concepts are formed.
Abstraction- mental distraction from all the properties, connections and relationships of the object being studied, which seem unimportant for this theory.
The result of the abstraction process is called abstraction. An example of abstractions are concepts such as point, line, set, etc.
Idealization- this is the operation of mentally highlighting any one property or relationship that is important for a given theory (it is not necessary that this property really exists), and mentally constructing an object endowed with this property.
It is through idealization that such concepts as “absolutely black body”, “ideal gas”, “atom” in classical physics, etc. are formed. The ideal objects obtained in this way do not actually exist, since in nature there cannot be objects and phenomena that have only one property or quality. This is the main difference between ideal objects and abstract ones.
Formalization- use of special symbols instead of real objects.
A striking example of formalization is wide use mathematical symbolism and mathematical methods in natural science. Formalization makes it possible to examine an object without directly addressing it and record the results obtained in a concise and clear form.
Induction
Induction- a method of scientific knowledge, which is the formulation of a logical conclusion by summarizing observational and experimental data, obtaining a general conclusion based on particular premises, moving from the particular to the general.
A distinction is made between complete and incomplete induction. Full induction builds a general conclusion based on the study of all objects or phenomena of a given class. As a result of complete induction, the resulting conclusion has the character of a reliable conclusion. But in the world around us there are not many similar objects of the same class, the number of which is so limited that a researcher can study each of them.
Therefore, scientists much more often resort to incomplete induction, which builds a general conclusion based on the observation of a limited number of facts, unless among them there are those that contradict the inductive inference. For example, if a scientist observes the same fact on a hundred or more occasions, he can conclude that this effect will appear in other similar circumstances. Naturally, the truth obtained in this way is incomplete; the knowledge obtained is probabilistic in nature and requires additional confirmation.
Deduction
Induction cannot exist in isolation from deduction.
Deduction- a method of scientific knowledge, which is the obtaining of particular conclusions based on general knowledge, a conclusion from the general to the particular.
Deductive inference is constructed according to the following scheme: all items in the class A have the property IN, item A belongs to the class A; hence, A has the property IN. For example: “All people are mortal”; “Ivan is a man”; therefore, “Ivan is mortal.”
Deduction as a method of cognition is based on already known laws and principles. Therefore, the deduction method does not allow us to obtain meaningful new knowledge. Deduction is only a way of logical development of a system of propositions based on initial knowledge, a way of identifying the specific content of generally accepted premises. Therefore, it cannot exist in isolation from induction. Both induction and deduction are indispensable in the process of scientific knowledge.
Hypothesis
The solution to any scientific problem involves putting forward various guesses, assumptions, and most often more or less substantiated hypotheses, with the help of which the researcher tries to explain facts that do not fit into old theories.
Hypothesis is any assumption, guess or prediction put forward to eliminate a situation of uncertainty in scientific research.
Therefore, a hypothesis is not reliable, but probable knowledge, the truth or falsity of which has not yet been established.
Special universal methods of scientific knowledge
Universal methods of scientific knowledge include analogy, modeling, analysis and synthesis.
Analogy
Analogy- a method of cognition in which the transfer of knowledge obtained by examining any one object occurs to another, less studied, but similar to the first object in some essential properties.
The analogy method is based on the similarity of objects according to a number of characteristics, and the similarity is established as a result
comparing objects with each other. Thus, the basis of the analogy method is the comparison method.
The use of the analogy method in scientific knowledge requires some caution. The fact is that one can mistake a purely external, random similarity between two objects for an internal, significant one, and on this basis draw a conclusion about a similarity that in fact does not exist. Thus, although both the horse and the car are used as vehicles, it would be wrong to transfer knowledge about the structure of a machine to the anatomy and physiology of a horse. This analogy will be wrong.
However, the method of analogy occupies a much more significant place in cognition than it might seem at first glance. After all, analogy does not simply outline connections between phenomena. The most important feature of human cognitive activity is that our consciousness is not capable of perceiving completely new knowledge if it does not have points of contact with knowledge already known to us. That is why, when explaining new material in the classroom, they always resort to examples, which should draw an analogy between known and unknown knowledge.
Modeling
The analogy method is closely related to the modeling method.
Simulation method involves the study of any objects through their models with further transfer of the obtained data to the original.
This method is based on the significant similarity of the original object and its model. Modeling should be treated with the same caution as analogy, and the limits and boundaries of simplifications permissible in modeling should be strictly indicated.
Modern science Several types of modeling are known: subject, mental, symbolic and computer.
Subject modeling is the use of models that reproduce certain geometric, physical, dynamic or functional characteristics of the prototype. Thus, the aerodynamic qualities of airplanes and other machines are studied using models, and various structures (dams, power plants, etc.) are being developed.
Mental simulation - it is the use of various mental representations in the form of imaginary models. The ideal planetary model of the atom by E. Rutherford is widely known, reminiscent of the Solar system: there is a positively charged environment around
negatively charged electrons (planets) rotated from the core (the Sun).
Sign (symbolic) modeling uses diagrams, drawings, and formulas as models. They reflect some properties of the original in a symbolic form. A type of symbolic is mathematical modeling, carried out by means of mathematics and logic. The language of mathematics allows you to express any properties of objects and phenomena, describe their functioning or interaction with other objects using a system of equations. This is how it is created mathematical model phenomena. Often mathematical modeling is combined with subject modeling.
Computer modelling received wide use last time. In this case, the computer is both a means and an object experimental research, replacing the original. The model in this case is computer program(algorithm).
Analysis
Analysis- a method of scientific knowledge, which is based on the procedure of mental or real division of an object into its constituent parts and their separate study.
This procedure aims to move from the study of the whole to the study of its parts and is carried out by abstracting from the connection of these parts with each other.
Analysis is an organic component of any scientific research, which is usually its first stage, when the researcher moves from describing the undivided object under study to identifying its structure, composition, as well as properties and characteristics. To comprehend an object as a whole, it is not enough to know what it consists of. It is important to understand how the component parts of an object are related to each other, and this can only be done by studying them in unity. For this purpose, analysis is complemented by synthesis.
Synthesis
Synthesis- a method of scientific knowledge, which is based on the connection procedure various elements a subject into a single whole, a system, without which truly scientific knowledge of this subject is impossible.
Synthesis acts not as a method of constructing the whole, but as a method of representing the whole in the form of a unity of knowledge obtained through analysis. It is important to understand that synthesis is not at all a simple mechanical connection of disconnected elements into a single system. It shows the place and role of each element in this system, its connection with others components systems. Thus, during synthesis there is not just a unification, but a generalization of the analytically identified and studied features of the object.
Synthesis is the same necessary part of scientific knowledge as analysis, and comes after it. Analysis and synthesis are two sides of a single analytical-synthetic method of cognition that do not exist without each other.
Classification
Classification- a method of scientific knowledge that allows you to combine into one class objects that are as similar as possible to each other in essential characteristics.
Classification makes it possible to reduce the accumulated diverse material to a relatively small number of classes, types and forms, to identify the initial units of analysis, and to discover stable characteristics and relationships. Typically, classifications are expressed in the form of natural language texts, diagrams and tables.
The variety of methods of scientific knowledge creates difficulties in their use and understanding of their significance. These problems are solved by a special field of knowledge - methodology, i.e. teaching about methods. The most important task of methodology is to study the origin, essence, effectiveness and other characteristics of methods of cognition.