Comparison and measurement

BASIC RESEARCH METHODS

In accordance with two interrelated levels of scientific knowledge (empirical and theoretical), there are empirical methods of scientific research (observation, description, comparison, measurement, experiment, induction, etc.), with the help of which the accumulation, fixation, generalization and systematization of experimental data, their statistical processing, and theoretical (analysis and synthesis, analogy and modeling, idealization, deduction, etc.); with their help, the laws of science and theory are formed.

In the process of scientific research, it is advisable to use a variety of methods, and not be limited to any one.

Observation

Observation- this is a purposeful systematic perception of an object that provides primary material for scientific research. Observation is a method of cognition in which an object is studied without interfering with it. Purposefulness - the most important characteristic observations. Observation is also characterized by systematicity, which is expressed in the perception of the object repeatedly and in different conditions, regularity, excluding gaps in observation, and the activity of the observer, his ability to select the necessary information, determined by the purpose of the study.

Direct observations in the history of science were gradually replaced by observations with the help of more and more advanced instruments - telescopes, microscopes, cameras, etc. Then came an even more indirect method of observation. It allowed not only to zoom in, enlarge or capture the object under study, but also to transform information that is inaccessible to our senses into an accessible form for them. In this case, the intermediary device plays the role of not only a "messenger", but also a "translator". So, for example, radars transform the captured radio beams into light pulses that our eyes can see.

As a method of scientific research, observation provides initial information about an object necessary for its further research.

Comparison and measurement

Comparison and measurement play an important role in scientific research. Comparison is a method of comparing objects in order to identify similarities or differences between them. Comparison - it is an operation of thinking by means of which the content of reality is classified, ordered and evaluated. When comparing, a pairwise comparison of objects is performed in order to identify their relationships, similar or hallmarks. Comparison makes sense only in relation to a set of homogeneous objects that form a class.

Measurement - this finding physical quantity experimentally with the help of special technical means.

The purpose of the measurement is to obtain information about the object under study.

Measurement can be carried out in the following cases:

- in purely cognitive tasks, in which a comprehensive study of the object is carried out, without clearly formulated ideas on the application of the results obtained in applied activities;

- in applied tasks related to the identification of certain properties of an object that are essential for a very specific application.

Metrology deals with the theory and practice of measurement - the science of measurements, methods and means of ensuring their unity and ways to achieve the required accuracy.

The exact sciences are characterized by an organic connection between observations and experiments with finding the numerical values ​​of the characteristics of the objects under study. According to the figurative expression of D. I. Mendeleev, “science begins as soon as they begin to measure.

Any measurement can be carried out if the following elements are present: measurement object, the property or state of which characterizes measurand; unit; measurement method; technical means of measurement, graduated in selected units; observer or recorder that accepts the result.

There are direct and indirect measurements. With the first of them, the result is obtained directly from the measurement (for example, measuring the length with a ruler, mass with the help of weights). Indirect measurements are based on the use of a known relationship between the desired value of a quantity and the values ​​of directly measured quantities.

Measuring instruments include measuring instruments, measuring devices and installations. Measuring tools are divided into exemplary and technical.

Exemplary means are standards. They are intended for testing to test technical, i.e. working means.

The transfer of unit sizes from standards or exemplary measuring instruments to working instruments is carried out by state and departmental metrological bodies that make up the domestic metrological service, their activities ensure the unity of measurements and the uniformity of measuring instruments in the country. The founder of the metrological service and metrology as a science in Russia was the great Russian scientist D. I. Mendeleev, who in 1893 created the Main Chamber of Weights and Measures, which carried out, in particular, a lot of work on the introduction of the metric system in the country (1918 - 1927).

One of the most important tasks in carrying out measurements is to establish their accuracy, i.e., the determination of errors (errors). Measurement uncertainty or error called the deviation of the measurement result of a physical quantity from its true value.

If the error is small, then it can be neglected. However, two questions inevitably arise: firstly, what is meant by a small error, and, secondly, how to estimate the magnitude of the error.

The measurement error is usually unknown, as is the true value of the measured quantity (exceptions are measurements of known quantities carried out for the special purpose of studying measurement errors, for example, to determine the accuracy of measuring instruments). Therefore, one of the main tasks of mathematical processing of the results of the experiment is precisely the assessment of the true value of the measured quantity according to the results obtained.

Consider the classification of measurement errors.

There are systematic and random measurement errors.

Systematic error remains constant (or regularly changing) during repeated measurements of the same quantity. K permanently valid reasons This error includes the following: low-quality materials, components used for the manufacture of devices; unsatisfactory operation, inaccurate calibration of the sensor, use of measuring instruments of a low accuracy class, deviation of the thermal regime of the installation from the calculated (usually stationary), violation of the assumptions under which the calculated equations are valid, etc. Such errors are easily eliminated when debugging the measuring equipment or by introducing special corrections to the value of the measured quantity.

random error changes randomly during repeated measurements and is due to the chaotic action of many weak, and therefore difficult to detect, causes. An example of one of these causes is the reading of a pointer gauge - the result depends in an unpredictable way on the angle of view of the operator. It is possible to estimate a random measurement error only by methods of probability theory and mathematical statistics. If the error in the experiment significantly exceeds the expected one, then it is called a gross error (miss), the measurement result in this case is discarded. Gross errors arise due to violation of the basic conditions of measurement or as a result of an oversight by the experimenter (for example, in poor lighting, instead of 3, write 8). If a gross error is detected, the measurement result should be discarded immediately, and the measurement itself should be repeated (if possible). external sign a result containing a gross error is its sharp difference in magnitude from the results of other measurements.

Another classification of errors is their division into methodological and instrumental errors. Methodological errors due to theoretical errors of the chosen measurement method: deviation of the thermal regime of the installation from the calculated (stationary), violation of the conditions under which the calculated equations are valid, etc. Instrumental errors are caused by inaccurate calibration of sensors, errors of measuring instruments, etc. If methodological errors in a carefully designed experiment can be reduced to zero or taken into account by introducing corrections, then instrumental errors cannot be eliminated in principle - replacing one device with another of the same type changes the measurement result.

Thus, the most difficult errors to eliminate in the experiment are random and systematic instrumental errors.

If measurements are carried out repeatedly under the same conditions, then the results of individual measurements are equally reliable. Such a set of measurements x 1 , x 2 ...x n is called equal measurements.

With multiple (equally accurate) measurements of the same value x, random errors lead to a scatter of the obtained values ​​x i , which are grouped near the true value of the measured value. If we analyze a sufficiently large series of equally accurate measurements and the corresponding random measurement errors, then four properties of random errors can be distinguished:

1) the number of positive errors is almost equal to the number of negative ones;

2) small errors are more common than large ones;

3) the magnitude of the largest errors does not exceed a certain certain limit, which depends on the accuracy of the measurement;

4) the quotient of dividing the algebraic sum of all random errors by their total number is close to zero, i.e.

On the basis of the listed properties, taking into account some assumptions, the law of distribution of random errors is mathematically quite rigorously derived, which is described by next function:

The law of distribution of random errors is the main one in mathematical theory errors. Otherwise, it is called the normal law of distribution of measured data (Gaussian distribution). This law is shown graphically in Fig. 2

Rice. 2. Characteristics of the normal distribution law

p(x) is the probability density of obtaining individual values ​​x i (the probability itself is represented by the area under the curve);

m is the mathematical expectation, the most probable value of the measured value x (corresponding to the maximum of the graph), which, with an infinitely large number of measurements, tends to the unknown true value of x; , where n is the number of measurements. Thus, the mathematical expectation m is defined as the arithmetic mean of all values ​​x i ,

s is the standard deviation of the measured value x from the value m; (x i - m) – absolute deviation of x i from m,

The area under the curve of the graph in any interval of x values ​​is the probability of obtaining a random measurement result in this interval. For a normal distribution, 0.62 of all measurements taken fall into the interval ±s (relative to m); the wider interval ±2s already contains 0.95 of all measurements , and almost all measurement results (except for gross errors) fit within the ±3s interval.

The standard deviation s characterizes the width of the normal distribution. If the measurement accuracy is increased, the scatter of the results will sharply decrease due to the decrease in s (distribution 2 in Fig. 4.3 b is narrower and sharper than curve 1).

The ultimate goal of the experiment is to determine the true value of x, which, in the presence of random errors, can only be approached by calculating the mathematical expectation m for an increasing number of experiments.

The spread of the values ​​of the mathematical expectation m calculated for a different number of measurements n is characterized by the value s m ; When compared with the formula for s, it can be seen that the scatter of m, as the arithmetic mean, in Ön is less than the scatter of individual measurements x i . The above expressions for s m and s reflect the law of increasing accuracy with an increase in the number of measurements. It follows from it that in order to increase the accuracy of measurements by a factor of 2, it is necessary to make four measurements instead of one; to increase the accuracy by a factor of 3, you need to increase the number of measurements by a factor of 9, and so on.

For a limited number of measurements, the value of m still differs from the true value of x, so along with calculating m, it is necessary to specify a confidence interval , in which the true value of x is found with a given probability. For technical measurements, a probability of 0.95 is considered sufficient, so the confidence interval for a normal distribution is ±2s m . The normal distribution is valid for the number of measurements n ³ 30.

In real conditions, a technical experiment is rarely carried out more than 5 - 7 times, so the lack of statistical information should be compensated by expanding the confidence interval. In this case, for (n< 30) доверительный интервал определяется как ± k s s m , где k s – коэффициент Стьюдента, определяемый по справочным таблицам

As the number of measurements n decreases, the coefficient k s increases, which widens the confidence interval, and as n increases, the value of k s tends to 2, which corresponds to the confidence interval of the normal distribution ± 2s m .

The end result of repeated measurements of a constant value always reduced to the form: m ± k s s m .

Thus, to estimate random errors, it is necessary to perform the following operations:

one). Record the results of x 1 , x 2 ...x n repeated measurements of n constant value;

2). Calculate the average value of n measurements - mathematical expectation;

3). Determine the errors of individual measurements x i -m;

four). Calculate the squared errors of individual measurements (х i -m) 2 ;

if several measurements differ sharply in their values ​​from the rest of the measurements, then you should check whether they are a miss (gross error). When excluding one or more measurements, p.p. 1...4 repeat;

5). The value s m is determined - the spread of the values ​​of the mathematical expectation m;

6). For the selected probability (usually 0.95) and the number of measurements taken, n is determined from the reference table Student's coefficient k s ;

The values ​​of the Student's coefficient k s depending on the number of measurements n for a confidence level of 0.95

7). The boundaries of the confidence interval ± k s s m are determined

eight). The final result m ± k s s m is recorded.

Instrumental errors cannot be eliminated in principle. All measuring instruments are based on a certain measurement method, the accuracy of which is finite.

Instrumental errors cannot be eliminated in principle. All measuring instruments are based on a certain measurement method, the accuracy of which is finite. The error of the device is determined by the accuracy of division of the scale of the device. So, for example, if the scale of the ruler is applied every 1 mm, then the reading accuracy (half of the division value of 0.5 mm) cannot be changed if a magnifying glass is used to view the scale.

There are absolute and relative measurement errors.

Absolute error D of the measured quantity x is equal to the difference between the measured and true values:

D = x - x

Relative error e is measured in fractions of the found value x:

For the simplest measuring instruments - measuring instruments, the absolute measurement error D is equal to half the division value. The relative error is determined by the formula.

a method of scientific research in pedagogy and other sciences, the essence of which is to fix the manifestations of behavior and obtain information about the subjective mental phenomena of the observed, manifested in his behavior.

Great Definition

Incomplete definition ↓

Observation

the main method of human cognition of reality, the essence of which is the deliberately organized perception by the senses of objects and phenomena of the surrounding world. At the same time, the observer does not interfere in the natural course of events and perceives the object as if from the outside. Observation is used in everyday life for the purpose of knowledge, in science - as a method of research. The following types of observations are distinguished: direct and indirect, i.e. mediated and hidden; continuous and elective; simple (ordinary) and included, i.e. participating in events. The types of observations also include direct analysis of the interaction of something and the evaluation of perceived phenomena. To observe is to note, highlight, notice some aspects, signs of the “behavior” of an object. Observation is characterized by systematicity, controllability, planning. In scientific observation, diaries, chronocards, timekeeping, etc. are used to fix the noticed signs. This method of cognition of reality is the most common. It is simple, accessible to everyone, but it is also subjective, dependent on the observer, it cannot be used to open internal causes object behavior. It can also harm the observer, who is able to identify himself with the object of his knowledge: empathize, imitate, show passions, etc. Self-observation is a special kind of observation.

Great Definition

Incomplete definition ↓

Other methods of scientific knowledge

Private scientific methods - a set of methods, principles of cognition, research techniques and procedures used in a particular branch of science, corresponding to a given basic form of the movement of matter. These are the methods of mechanics, physics, chemistry, biology and the humanities (social) sciences.

Disciplinary methods are systems of techniques used in a particular discipline that is part of some branch of science or that has arisen at the intersection of sciences. Each fundamental science is a complex of disciplines that have their own specific subject and their own unique research methods.

Methods of interdisciplinary research are a set of a number of synthetic, integrative methods (resulting from a combination of elements of different levels of methodology), aimed mainly at the intersections of scientific disciplines.

empirical knowledge is a set of statements about real, empirical objects. empirical knowledge based on sensory knowledge . The rational moment and its forms (judgments, concepts, etc.) are present here, but have a subordinate meaning. Therefore, the researched the object is reflected mainly from the side of its external relations and manifestations accessible to contemplation and expressing internal relations. empirical, experimental research is directed without intermediate links to its object. It masters it with the help of such techniques and means as description, comparison, measurement, observation, experiment, analysis, induction (from the particular to the general), and its most important element is the fact (from Latin factum - done, accomplished).

1. Observation - this is a deliberate and directed perception of the object of knowledge in order to obtain information about its form, properties and relationships. The process of observation is not passive contemplation. This is an active, directed form of the epistemological relationship of the subject in relation to the object, enhanced by additional means of observation, fixing information and its translation. The following requirements are imposed on observation: the purpose of observation; choice of methodology; observation plan; control over the correctness and reliability of the results obtained; processing, comprehension and interpretation of the received information.

2. Measurement - this is a technique in cognition, with the help of which a quantitative comparison of quantities of the same quality is carried out. The qualitative characteristics of an object, as a rule, are fixed by instruments, the quantitative specificity of an object is established by means of measurements.

3. Experiment- (from lat. experimentum - test, experience), a method of cognition, with the help of which phenomena of reality are studied under controlled and controlled conditions. Differing from observation in active operation of the object under study, E. is carried out on the basis of a theory that determines the formulation of problems and the interpretation of its results.

4 Comparison is a method of comparing objects in order to identify similarities or differences between them. If objects are compared with an object that acts as a reference, then this is called a comparison by measurement.

Methods of empirical research

Observation

¨ comparison

¨ dimension

¨ experiment

Observation

Observation is a purposeful perception of an object, due to the task of activity. Basic condition scientific observation- objectivity, i.e. the possibility of control by either repeated observation or the use of other research methods (for example, experiment). This is the most elementary method, one of many other empirical methods.

Comparison

This is one of the most common and versatile research methods. The well-known aphorism "everything is known in comparison" - the best of that proof.

Comparison is the ratio between two integers a and b, meaning that the difference (a - b) of these numbers is divisible by a given integer m, called the modulus C; written a = b (mod, t).

In the study, comparison is the establishment of similarities and differences between objects and phenomena of reality. As a result of comparison, the general that is inherent in two or more objects is established, and the identification of the general, which is repeated in phenomena, as you know, is a step on the way to the knowledge of the law.

In order for a comparison to be fruitful, it must satisfy two basic requirements.

1. Only such phenomena should be compared between which a certain objective commonality can exist. You can not compare obviously incomparable things - it does not give anything. At best, only superficial and therefore fruitless analogies are possible here.

2. Comparison should be carried out according to the most important features Comparison based on non-essential features can easily lead to confusion.

So, formally comparing the work of enterprises producing the same type of product, one can find a lot in common in their activities. If this omits a comparison according to such the most important parameters, as the level of production, the cost of production, various conditions where the enterprises being compared operate, it is easy to come up with a methodological error leading to one-sided conclusions. If, however, these parameters are taken into account, it becomes clear what is the reason and where the real sources of the methodological error lie. Such a comparison will already give a true idea of ​​the phenomena under consideration, corresponding to the real state of affairs.

Various objects of interest to the researcher can be compared directly or indirectly - by comparing them with some third object. In the first case, qualitative results are usually obtained (more - less; lighter - darker; higher - lower, etc.). However, even with such a comparison, it is possible to obtain the simplest quantitative characteristics that express quantitative differences between objects in numerical form (more than 2 times, more than 3 times, etc.).

When objects are compared with some third object that acts as a standard, quantitative characteristics acquire special value, since they describe objects without regard to each other, provide a deeper and detailed knowledge about them (for example, to know that one car weighs 1 ton and the other 5 tons means to know much more about them than what is contained in the sentence: "the first car is 5 times lighter than the second." Such a comparison is called measurement. It will be discussed in detail below.

With comparison, information about an object can be obtained in two different ways.

First, it very often acts as a direct result of comparison. For example, the establishment of any relationship between objects, the discovery of differences or similarities between them is information obtained directly by comparison. This information can be called primary.

Secondly, very often obtaining primary information does not act as the main goal of comparison, this goal is to obtain secondary or derivative information that is the result of processing primary data. The most common and most important way such processing is inference by analogy. This conclusion was discovered and investigated (under the name "paradeigma") by Aristotle.

Its essence boils down to the following: if, as a result of comparison, several identical features are found out of two objects, but some additional feature is found in one of them, then it is assumed that this feature should also be inherent in the other object. In a nutshell, the analogy can be summarized as follows:

A has features X1, X2, X3, ..., Xn, Xn+,.

B has features X1, X2, X3, ..., Xn.

Conclusion: "Probably, B has the attribute Xn +1". The conclusion based on analogy is probabilistic in nature, it can lead not only to truth, but also to error. In order to increase the probability of obtaining true knowledge about an object, the following should be kept in mind:

¨ inference by analogy gives the more true value, the more similar features we find in the compared objects;

¨ the truth of the conclusion by analogy is directly dependent on the significance of similar features of objects, even a large number of similar, but not essential features, can lead to a false conclusion;

¨ the deeper the relationship of the features found in the object, the higher the probability of a false conclusion;

¨ the general similarity of two objects is not a basis for inference by analogy, if one of them, regarding which the conclusion is made, has a feature that is incompatible with the transferred feature. In other words, in order to obtain a true conclusion, it is necessary to take into account not only the nature of the similarity, but also the nature of the difference between objects.

Measurement

Measurement has historically evolved from the comparison operation, which is its basis. However, unlike comparison, measurement is more powerful and universal. cognitive tool.

Measurement - a set of actions performed using measuring instruments in order to find the numerical value of the measured quantity in the accepted units of measurement. There are direct measurements (for example, measuring the length with a graduated ruler) and indirect measurements based on a known relationship between the desired value and directly measured values.

The measurement assumes the presence of the following main elements:

measurement object;

units of measurement, i.e. reference object;

measuring instrument(s);

measurement method;

observer (researcher).

With direct measurement, the result is obtained directly from the measurement process itself (for example, in sports competitions, measuring the length of a jump with a tape measure, measuring the length of carpets in a store, etc.).

With indirect measurement, the desired value is determined mathematically based on the knowledge of other quantities obtained by direct measurement. For example, knowing the size and weight of building bricks, it is possible to measure the specific pressure (with appropriate calculations) that a brick must withstand when building multi-storey buildings.

The value of measurements is evident even from the fact that they provide accurate, quantitatively defined information about the surrounding reality. As a result of measurements, such facts can be established, such empirical discoveries can be made that lead to a radical break in the ideas that have been established in science. This applies primarily to unique, outstanding measurements, which are very important milestones in the history of science. A similar role was played in the development of physics, for example, by A. Michelson's famous measurements of the speed of light.

The most important indicator of the quality of measurement, its scientific value is accuracy. It was the high accuracy of T. Brahe's measurements, multiplied by the extraordinary diligence of I. Kepler (he repeated his calculations 70 times), that made it possible to establish the exact laws of planetary motion. Practice shows that the main ways to improve the accuracy of measurements should be considered:

improving the quality of measuring instruments, operating on the basis of certain established principles;

creation of devices operating on the basis of the latest scientific discoveries. For example, now time is measured using molecular generators with an accuracy of up to 11 digits.

Among the empirical methods of research, measurement occupies approximately the same place as observation and comparison. It is a relatively elementary method, one of the components of the experiment - the most complex and significant method of empirical research.

Experiment

Experiment - the study of any phenomena by actively influencing them by creating new conditions that correspond to the goals of the study, or by changing the course of the process in the right direction. This is the most complex and effective method empirical research It involves the use of the simplest empirical methods - observation, comparison and measurement. However, its essence is not in particular complexity, "syntheticity", but in a purposeful, deliberate transformation of the phenomena under study, in the intervention of the experimenter in accordance with his goals during natural processes.

It should be noted that the establishment of the experimental method in science is a long process that took place in the acute struggle of the advanced scientists of the New Age against ancient speculation and medieval scholasticism. (For example, the English materialist philosopher F. Bacon was one of the first to oppose experiment in science, although he advocated experience.)

Galileo Galilei (1564-1642), who considered experience as the basis of knowledge, is rightfully considered the founder of experimental science. Some of his studies are the basis of modern mechanics: he established the laws of inertia, free fall and the movement of bodies on an inclined plane, the addition of movements, discovered the isochronism of the pendulum oscillation. He himself built a telescope with a 32-fold magnification and discovered mountains on the Moon, four satellites of Jupiter, phases near Venus, spots on the Sun. In 1657, after his death, the Florentine Academy of Experience arose, which worked according to his plans and aimed primarily at conducting experimental research. Scientific and technological progress requires an ever wider application of the experiment. As for modern science, its development is simply unthinkable without experiment. At present, experimental research has become so important that it is considered as one of the main forms of practical activities researchers.

Benefits of experiment over observation

1. During the experiment, it becomes possible to study this or that phenomenon in a "pure" form. This means that any kind of "skirt" factors obscuring the main process can be eliminated, and the researcher obtains accurate knowledge about the phenomenon of interest to us.

2. The experiment makes it possible to investigate the properties of objects of reality in extreme conditions:

at ultra-low and ultra-high temperatures;

at highest pressures:

at huge intensities of electric and magnetic fields, etc.

Working under these conditions can lead to the discovery of the most unexpected and amazing properties in ordinary things and thus allows you to penetrate much deeper into their essence. Superconductivity can serve as an example of this kind of "strange" phenomena discovered under extreme conditions relating to the field of control.

3. The most important advantage of the experiment is its repeatability. During the experiment, the necessary observations, comparisons and measurements can be carried out, as a rule, as many times as necessary to obtain reliable data. This feature of the experimental method makes it very valuable in research.

All the advantages of the experiment will be considered in more detail below, when presenting some specific types of experiment.

situations requiring pilot study

1. A situation when it is necessary to detect previously unknown properties of an object. The result of such an experiment are statements that do not follow from the existing knowledge about the object.

A classic example is the experiment of E. Rutherford on the scattering of X-particles, as a result of which the planetary structure of the atom was established. Such experiments are called research.

2. The situation when it is necessary to check the correctness of certain statements or theoretical constructions.
15. Methods theoretical research. Axiomatic method, abstraction, idealization, formalization, deduction, analysis, synthesis, analogy.

characteristic feature theoretical knowledge is that the subject of knowledge deals with abstract objects. Theoretical knowledge is characterized by consistency. If individual empirical facts can be accepted or refuted without changing the totality of empirical knowledge, then in theoretical knowledge, a change in individual elements of knowledge entails a change in the entire system of knowledge. Theoretical knowledge also requires its own techniques (methods) of cognition, focused on testing hypotheses, substantiating principles, and building a theory.

Idealization- epistemological relation, where the subject mentally constructs an object, the prototype of which is in the real world. And it is characterized by the introduction into the object of such features that are absent in its real prototype, and the exclusion of the properties inherent in this prototype. As a result of these operations, concepts were developed - "point", "circle", "straight line", "ideal gas", "absolutely black body" - idealized objects. Having formed an object, the subject gets the opportunity to operate with it as with a real-life object - to build abstract schemes of real processes, to find ways to penetrate into their essence. I. has the limit of its capabilities. I. is created to solve a specific problem. It is not always possible to ensure the transition from the ideal. object to empirical.

Formalization- construction of abstract models for the study of real objects. F. provides the ability to operate with signs, formulas. The derivation of some formulas from others according to the rules of logic and mathematics makes it possible to establish theoretical patterns without empiricism. Ф plays an important role in the analysis and refinement of scientific concepts. In scientific knowledge, sometimes it is impossible not only to solve, but even to formulate a problem until the concepts related to it are clarified.

Generalization and abstraction- two logical reception almost always used together in the process of cognition. Generalization is a mental selection, fixation of some common essential properties that belong only to a given class of objects or relations. abstraction- this is a mental abstraction, the separation of general, essential properties, identified as a result of generalization, from other non-essential or non-general properties of the objects or relations under consideration and the rejection (within the framework of our study) of the latter. Abstraction cannot be carried out without generalization, without highlighting the general, essential that is subject to abstraction. Generalization and abstraction are invariably used in the process of concept formation, in the transition from representations to concepts, and, together with induction, as a heuristic method.

Cognition is a specific type of human activity aimed at comprehending the surrounding world and oneself in this world. "Cognition is, primarily due to socio-historical practice, the process of acquiring and developing knowledge, its constant deepening, expansion, and improvement."

Theoretical knowledge is, first of all, an explanation of the causes of phenomena. This presupposes the clarification of the internal contradictions of things, the prediction of the probable and necessary occurrence of events and the tendencies of their development.

The concept of method (from the Greek word "methodos" - the path to something) means a set of techniques and operations for the practical and theoretical development of reality.

The theoretical level of scientific knowledge is characterized by the predominance of the rational moment - concepts, theories, laws and other forms and "mental operations". The theoretical level is a higher level in scientific knowledge. "The theoretical level of knowledge is aimed at the formation of theoretical laws that meet the requirements of universality and necessity, i.e. act everywhere and always." The results of theoretical knowledge are hypotheses, theories, laws.

Empirical and theoretical levels of knowledge are interconnected. The empirical level acts as the basis, the foundation of the theoretical one. Hypotheses and theories are formed in the process of theoretical understanding scientific facts, statistical data obtained at the empirical level. In addition, theoretical thinking inevitably relies on sensory-visual images (including diagrams, graphs, etc.) with which the empirical level of research deals.

Formalization and axiomatization"

The scientific methods of the theoretical level of research include:

Formalization - displaying the results of thinking in exact terms or statements, i.e., the construction of abstract mathematical models that reveal the essence of the studied processes of reality. It is inextricably linked with the construction of artificial or formalized scientific laws. Formalization is the display of meaningful knowledge in sign formalism (formalized language). The latter is created for the exact expression of thoughts in order to exclude the possibility of ambiguous understanding. When formalizing, reasoning about objects is transferred to the plane of operating with signs (formulas). The relations of signs replace statements about the properties and relations of objects. Formalization plays an important role in the analysis, clarification and explication of scientific concepts. Formalization is especially widely used in mathematics, logic and modern linguistics.

Abstraction, idealization

Each object under study is characterized by many properties and is connected by many threads with other objects. In the process of natural science knowledge, it becomes necessary to focus on one side or property of the object under study and abstract from a number of its other qualities or properties.

Abstraction is the mental selection of an object, in abstraction from its connections with other objects, any property of an object in abstraction from its other properties, any relation of objects in abstraction from the objects themselves.

Initially, abstraction was expressed in the selection of some objects with hands, eyes, tools and distraction from others. This is evidenced by the origin of the word "abstract" itself - from lat. abstractio - removal, distraction. Yes and Russian word"distracted" comes from the verb "to drag".

Abstraction makes up necessary condition the emergence and development of any science and human knowledge in general. The question is what is in objective reality is distinguished by the abstracting work of thinking and from which thinking is distracted, in each specific case it is solved in direct proportion to the nature of the object being studied and the tasks that are put before the researcher. For example, in mathematics, many problems are solved using equations without considering the specific objects behind them - whether they are people or animals, plants or minerals. This is what it consists great power mathematics, and at the same time its limitations.

For mechanics, which studies the movement of bodies in space, the physical and kinetic properties of bodies, except for mass, are indifferent. I. Kepler did not care about the reddish color of Mars or the temperature of the Sun to establish the laws of planetary circulation. When Louis de Broglie (1892-1987) was looking for a connection between the properties of the electron as a particle and as a wave, he had the right not to be interested in any other characteristics of this particle.

Abstraction is the movement of thought deep into the subject, the selection of its essential elements. For example, in order for a given property of an object to be regarded as chemical, a distraction, an abstraction, is necessary. Indeed, to chemical properties substance does not include a change in its shape, so the chemist examines copper, distracting from what exactly is made of it.

In the living fabric of logical thinking, abstractions make it possible to reproduce a deeper and more accurate picture of the world than can be done with the help of perception.

An important method of natural science knowledge of the world is idealization as a specific type of abstraction.

Idealization is the mental formation of abstract objects that do not exist and are not feasible in reality, but for which there are prototypes in the real world.

Idealization is the process of forming concepts, the real prototypes of which can only be indicated with varying degrees of approximation. Examples of idealized concepts: "point", i.e. an object that has neither length, nor height, nor width; "straight line", "circle", "point electric charge", "ideal gas", "absolutely black body", etc.

Introduction to the natural science process of studying idealized objects makes it possible to construct abstract schemes of real processes, which is necessary for deeper penetration into the laws of their course.

Indeed, nowhere in nature is there a "geometric point" (without dimensions), but an attempt to construct a geometry that does not use this abstraction does not lead to success. Similarly, it is impossible to develop geometry without such idealized concepts as "straight line", "plane". "ball", etc. All real prototypes of the ball have potholes and irregularities on their surface, and some deviate somewhat from the "ideal" shape of the ball (like the earth), but if geometers began to deal with such potholes, bumps and deviations , they could never get the formula for the volume of a sphere. Therefore, we study the "idealized" shape of the ball, and although the resulting formula, when applied to real figures that only look like a ball, gives some error, the resulting approximate answer is sufficient for practical needs.

The methods of empirical and theoretical knowledge were used in the work. Among the methods of theoretical knowledge were used: problem statement, hypothesis statement, analysis and synthesis. Among the methods of empirical knowledge were used survey, observation, measurement, questioning, testing, comparison, description and modeling.

1. Observation is a deliberate and purposeful perception of phenomena and processes without direct intervention, subject to the tasks of scientific research.

Basic requirements for scientific observation:

• 1) Unambiguity of purpose and design
• 2) Objectivity
• 3) Consistency in observation methods
• 4) Possibility of control either by repeated observation or by experiment.

The results of observation are experimental data, and possibly - taking into account the primary (automatic) processing of primary information - diagrams, graphs, diagrams. Structural components of observation: the observer himself, the object of study, the conditions of observation, the means of observation (installations, devices, measuring instruments, as well as special terminology in addition to natural language).

Scientific observation consists of the following procedures:

• 1) Determination of the purpose of observation (for what? for what purpose?)
• 2) Choice of object, process, situation (what to observe?)
• 3) Choosing the method and frequency of observations (how to observe?)
• 4) The choice of methods for registering the observed object, phenomenon (how to record the information received?)
• 5) Processing and interpretation of the received information (what is the result?)

The activity of the researcher in the act of observation is connected with the theoretical conditionality of the content of the results of observation. Observation involves not only sensual, but also rational ability in the form of theoretical attitudes and scientific standards. As the saying goes, "a scientist looks with his eyes, but sees with his head."

The activity of observation is also manifested in the selection and design of means of observation.

There are two main types of observation: qualitative and quantitative. Qualitative observation has been known to people and used by them since ancient times - long before the advent of science in its current sense. The use of quantitative observations coincides with the very formation of science in modern times. Quantitative observations are, naturally, connected with advances in the development of the theory of measurements and measurement techniques. The transition to measurements and the appearance of quantitative observations also meant the preparation for the mathematization of science.

In observation, the subject of cognition receives extremely valuable information about the object, which is usually impossible to obtain in any other way. Observation data are highly informative, providing unique information about an object that is unique to this object at this point in time and under given conditions. The results of observation form the basis of facts, and facts, as you know, are the air of science.

Characteristics of scientific observation: 1. Purposefulness. Observation should initially be focused on fixing the qualities, characteristics that are aimed at research. 2. Plannedness - a plan, a certain order in which the observation is carried out. 3. Concretization of scientific observation. 4. In scientific observation there is no influence on the object. 5. Verification of observation in different conditions.

Observation:

• 1. Armed (using technical means) and unarmed.
• 2. Field and laboratory.
• 3. Direct and indirect.
• 4. Direct and indirect (the study is based on a set of other people's data).
• 2. Measurement is a cognitive process, which consists in comparing a given value with some of its value, taken as a comparison standard.

Measurement is the definition of the ratio of one (measured) quantity to another, taken as a standard.

Unlike comparison, measurement is a more powerful and versatile cognitive tool. With direct measurement, the result is obtained directly from the measurement process itself (for example, in sports competitions, measuring the length of a jump with a tape measure, measuring the length of carpets in a store, etc.). With indirect measurement, the desired value is determined mathematically based on the knowledge of other quantities obtained by direct measurement. For example, knowing the size and weight of building bricks, it is possible to measure the specific pressure (with appropriate calculations) that a brick must withstand when building multi-storey buildings. The value of measurements is evident even from the fact that they provide accurate, quantitatively defined information about the surrounding reality. As a result of measurements, such facts can be established, such empirical discoveries can be made that lead to a radical break in the ideas that have been established in science. This applies primarily to unique, outstanding measurements, which are very important milestones in the history of science. The most important indicator of the quality of measurement, its scientific value is accuracy. Practice shows that the main ways to improve the accuracy of measurements should be considered:

• - improvement of the quality of measuring instruments operating on the basis of certain established principles;
• - creation of devices operating on the basis of the latest scientific discoveries.

You can select a specific dimension structure that includes the following elements:

• 1) a cognizing subject that carries out measurement with certain cognitive goals;
• 2) measuring instruments, among which there can be both devices and tools designed by man, and objects and processes given by nature;
• 3) the object of measurement, that is, the measured quantity or property to which the comparison procedure is applicable;
• 4) method or method of measurement, which is a combination of practical action, operations performed using measuring instruments and also includes certain logical and computational procedures;
• 5) the measurement result, which is a named number, expressed using the appropriate names or signs.
• 3. Comparison

This is one of the most common and versatile research methods. The well-known aphorism "everything is known in comparison" is the best proof of this. Comparison is the ratio between two integers a and b, meaning that the difference (a - b) of these numbers is divided by a given integer t, called module C. In the study, comparison is the establishment of similarities and differences between objects and phenomena of reality. As a result of comparison, the general that is inherent in two or more objects is established, and the identification of the general, which is repeated in phenomena, as you know, is a step on the way to the knowledge of the law. In order for a comparison to be fruitful, it must satisfy two basic requirements. 1. Only such phenomena should be compared between which a certain objective commonality can exist. You can not compare obviously incomparable things - it does not give anything. At best, only superficial and therefore fruitless analogies are possible here. 2. Comparison should be carried out on the most important features Comparison on non-essential features can easily lead to confusion. So, formally comparing the work of enterprises producing the same type of product, one can find a lot in common in their activities. If at the same time a comparison is omitted in such important parameters as the level of production, the cost of production, the various conditions in which the compared enterprises operate, then it is easy to come to a methodological error leading to one-sided conclusions. If, however, these parameters are taken into account, it becomes clear what is the reason and where the real sources of the methodological error lie. Such a comparison will already give a true idea of ​​the phenomena under consideration, corresponding to the real state of affairs. Various objects of interest to the researcher can be compared directly or indirectly - by comparing them with some third object. In the first case, qualitative results are usually obtained (more - less; lighter - darker; higher - lower, etc.). However, even with such a comparison, it is possible to obtain the simplest quantitative characteristics that express quantitative differences between objects in numerical form (more than 2 times, more than 3 times, etc.). When objects are compared with some third object that acts as a standard, quantitative characteristics acquire a special value, since they describe objects without regard to each other, provide deeper and more detailed knowledge about them.

With comparison, information about an object can be obtained in two different ways. First, it very often acts as a direct result of comparison. For example, the establishment of any relationship between objects, the discovery of differences or similarities between them is information obtained directly by comparison. This information can be called primary. Secondly, very often obtaining primary information does not act as the main goal of comparison, this goal is to obtain secondary or derivative information that is the result of processing primary data. The most common and most important way of such processing is inference by analogy. In order to increase the probability of obtaining true knowledge about an object, one must keep in mind the following: inference by analogy gives the more true value, the more similar features we find in the compared objects; the truth of the conclusion by analogy is directly dependent on the significance of similar features of objects, even a large number of similar, but not essential features, can lead to a false conclusion; the deeper the relationship of the features found in the object, the higher the probability of a false conclusion; the general similarity of two objects is not a basis for inference by analogy, if the one about which the conclusion is made has a feature that is incompatible with the transferred feature. In other words, in order to obtain a true conclusion, it is necessary to take into account not only the nature of the similarity, but also the nature of the difference between objects.

The comparison procedure includes, on the one hand, the manner in which the comparison operation can be carried out, and, on the other hand, the corresponding operating situation. Any of our statements about the identity or difference of any objects has a definite and exact meaning only when we can indicate the appropriate comparison procedure within the framework of a particular cognitive position. Comparison not only increases the cognitive value of observation, but also performs a semantic function, that is, it helps to reveal the meaning of our statements.

4. Modeling is a method of cognition of the surrounding world, consisting in the creation and study of models.

Different sciences explore objects and processes from different angles of view and build different types of models. In physics, the processes of interaction and change of objects are studied, in chemistry - their chemical composition, in biology - the structure and behavior of living organisms, etc.

A model is a new object that reflects the essential features of the object, phenomenon or process being studied. This method is based on the principle of similarity. Its essence lies in the fact that not the object itself is directly investigated, but its analogue, its substitute, its model, and then the results obtained during the study of the model are transferred to the object itself according to special rules.

Modeling is used in cases where the object itself is either difficult to access, or its direct study is economically unprofitable, etc. There are a number of types of modeling:

1. Object modeling, in which the model reproduces geometric, physical, dynamic or functional characteristics object. For example, bridge model, dam model, wing model

aircraft, etc.

• 2. Analog modeling, in which the model and the original are described by a single mathematical relationship. An example is the electrical models used to study mechanical, hydrodynamic and acoustic phenomena.
• 3. Symbolic modeling, in which schemes, drawings, formulas act as models. The role of sign models has increased especially with the expansion of the use of computers in the construction of sign models.
• 4. Mental modeling is closely connected with the sign, in which models acquire a mentally visual character. An example in this case is the model of the atom, proposed at the time by Bohr.
• 5. Finally, a special type of modeling is the inclusion in the experiment not of the object itself, but of its model, due to which the latter acquires the character of a model experiment. This type of modeling indicates that there is no hard line between the methods of empirical and theoretical knowledge.

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

OBSERVATION

OBSERVATION - a method of scientific research, which consists in an active, systematic, purposeful, planned and deliberate perception of an object, during which knowledge is obtained about the external aspects, properties and relationships of the object under study. N. includes as elements: the observer (subject) N., the object N. and the means N. As the latter, various specially created devices are used in the developed forms of N., acting as a continuation and strengthening of the human senses, as well as used in as tools for influencing an object (which turns N. into an integral part experimental activities). The main methodological requirements for N. are as follows: 1) activity (not the contemplation of an object, but the search and fixation of the perspective of seeing it that interests the researcher); 2) purposefulness (attention should be fixed only on the phenomena of interest); 3) planning and premeditation (following a predetermined plan or scenario); 4) consistency (guidance according to a certain system for multiple (sufficient for the formulated goals) perception of an object in given modes). Especially at the methodological level of organization of scientific activity, the problem of monitoring the progress and results of N., as well as the related problem of N. reproducibility is discussed. Important factors in N. are psychological factors that characterize the level of activity and the state of the observer, as well as the factor of his (not) prejudice , "assignments" to obtain a certain result. It is impossible to completely abstract from these factors, which poses the problem of separating subjective strata from the results obtained by N.. There are fixing (grasping of details, sides, parts of an object) and fluctuating (holistic grasping of an object) N. In addition, they distinguish direct (the researcher deals directly with the properties of the object being studied) and indirect (not the object of interest to the researcher is perceived, but those consequences that it causes), direct (carried out by the human senses without the use of auxiliary means) and indirect (instrumental) N. Being a universal cognitive procedure, a prerequisite for cognitive activity in general, N. gives primary information about the object in the form of a set of empirical statements. Neopositivism qualified the fixation of the data of experience (N. in the broad sense of the word) as a problem of protocol sentences from which a scientific theory is derived and to which a scientific theory can be reduced in principle for its verification. Linguistically oriented positivism introduced into science the notion of linguistic fixation of objects as their primary schematization. In the modern methodology of science, N. is rarely considered as an independent and universal scientific method: even in the simplest version, N. is always associated with thought processes; in complex procedures, it acts as a necessary, but still an auxiliary method. A special topic is set by the application of the N. method in social disciplines (sociology, anthropology, social Psychology). The observer-object relationship is here rethought as an observer-observed relationship, which can also act as an active agent of the procedure (resist N., change behavior due to the presence of the N. fact, demonstrate what the observer expects, try to influence the observer). Thus, in this case, the very presence of the observer already creates problems that need to be solved. For the first time, sociology was able to test a fundamentally different scheme of N., when the observer is included in the vital processes of the group that is being studied (the so-called included (participating) N., in different options involving varying degrees of "inclusion"); anthropology has used a similar methodology to study cultures other than the one in which the observer was socialized; psychology methodically provided the method of self-observation (introspection), which significantly expanded the boundaries and possibilities of the N. method as a whole. In addition, in terms of approaches (ethnomethodology, etc.), the very possibility of a fundamental difference between N. as a scientific practice and N. as an ordinary procedure of everyday life has been called into question.

The latest philosophical dictionary. - Minsk: Book House. A. A. Gritsanov. 1999

Synonyms:

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