Basic postulates of science. Axioms and postulates in the exact sciences. Saratov State Technical University

In science (natural science), as in religion, there are such unconditional provisions - "dogmas" - which are not proved (and cannot be proved), but are accepted as initial ones, since they are necessary for building the entire system of knowledge. Such provisions are called in it postulates or axioms. Natural science is based, at least, on the following two main provisions: recognition, firstly, of the reality of the existence of the world and, secondly, the laws of its structure and cognizability by man.

Let's consider these postulates.

1) Surprisingly, but the statement about the objective, i.e. independent of human consciousness, the existence of the world is rather a direct evidence than a scientifically proven truth, more a matter of faith than knowledge. The well-known philosopher Bertrand Russell († 1970) wittily remarks on this subject: I don't think I'm sleeping and dreaming right now, but I can't prove it". Einstein († 1955) in turn explicitly states: “ Belief in the existence of an external world independent of the perceiving subject is the basis of all natural science.". These statements of famous scientists illustrate well the understanding of the reality of the external world by science: it is the object of its faith, a dogma (to put it in theological language), but not knowledge.

2). The second postulate of science - the belief in rationality, the laws of the structure of the world and its cognizability - is the main driving force of all scientific research. But it also turns out to be the same subject of faith (dogma) for science, like the first one. Authoritative scientists say this unambiguously. So, Academician L.S. Berg († 1950) wrote: " The main postulate with which the natural scientist approaches the understanding of nature is that there is a sense in nature in general, that it is possible to comprehend and understand it, that between the laws of thinking and cognition, on the one hand, and the structure of nature, on the other, there is a certain predetermined harmony . Without this tacit assumption, no natural science is possible. Perhaps this postulate is wrong (just as Euclid's postulate about parallel lines), but it is practically necessary". Einstein said the same: Without faith that it is possible to embrace reality with our theoretical constructs, without faith in inner harmony our world could not have any science. This belief is and will always remain the main motive of any scientific creativity.". The father of cybernetics N. Wiener († 1964) wrote: “ Without the belief that nature is subject to laws, there can be no science. It is impossible to prove that nature is subject to laws, for we all know that the world from the next moment can become like a game of croquet from the book "Alice in Wonderland"". The well-known contemporary American physicist C. Townes († 1992) writes: “ The scientist must be imbued in advance with the conviction that there is order in the universe and that the human mind is capable of understanding this order. The world is disordered or incomprehensible, it would be pointless even to try to understand».

But even if these postulates are true (and one can hardly doubt this), then the most important question remains, without the solution of which the very formulation of the problem of "science and religion" loses all meaning - this is the question of the reliability of scientific knowledge itself. But first, a brief note about his methods.

The world around us is largely a man-made world. information technologies, technology and scientific achievements. It determines the level of civilization of mankind, the diversity and depth of exploitation of earth's resources. The 21st century is the era of science, its grandiose progress forward and influence on the development of civilization.

The concept of "science" has several meanings, on the one hand, science - a dynamic system of reliable, most significant knowledge about the objective laws of development of nature, society and thinking. Knowledge is a product of science and, at the same time, its material, which is again drawn to scientific activity to gain new knowledge. At the same time, knowledge about the world around can be ordinary, everyday and scientific. Scientific knowledge differs from ordinary knowledge in consistency, systematicity, and also in that it creates new concepts, laws and theories. Scientific knowledge not only reveals and explains new phenomena in nature, society or economic practice, but also makes it possible to improve human activity, to foresee its results and consequences.

Science is not only a system of scientific knowledge that explains the world, but also a means of measuring and transforming it. It affects the knowledge of nature by man not through emotional perception but through a systematized logical interaction of intellect, nature and society.

On the other hand, science is specifically organized activity of people. As an industry human activity, science is a complex social institution that has been formed in the process of division of labor, the gradual separation of mental labor from physical and transformation cognitive activity into a specific type of occupation of individuals, groups and institutions. The first materialized products of scientific activity were ancient manuscripts and books; later, correspondence between researchers began, which led to the appearance in the second half of the 17th century scientific journals. But the final formation of science as a field of activity occurred when special scientific institutions began to be created, some of which were financed by the state.

Science as an activity of people includes the following processes:

1) knowledge formation what happens as a result of specially organized scientific research;

2) knowledge transfer, what arises as a result of communications between scientists and other persons engaged in research work. Communication can be both formal (scientific monographs, descriptions of inventions, materials of scientific meetings, forums, conferences, symposiums, scientific reports, dissertations) and informal (correspondence, conversations, exchange of preprints, reprints of articles, as well as currently electronic journals, e-mail, electronic conferences);

3) reproduction of knowledge which consists in the training of scientific personnel, the formation of scientific schools.

The object of science is the nature and forms of the movement of matter, human society in its development, man and his activities.

The subjects of science there are people who have a certain amount of knowledge and are ready for scientific activity.

The essence of science is revealed in its functions. cognitive function science reflects the great desire of the human mind for knowledge and justifies the very existence of man on earth. The cognitive function of science is a manifestation of the most essential knowledge about the laws of development of nature, society and thinking and their relationship. Critical function science is to assess the identified patterns, properties, trends in order to strengthen positive sides phenomena, processes and elimination of negative ones. Practical functions are also connected with these functions, which consists in improving the surrounding world, especially the system of material production and social relations.

As you know, in the economic development of any state, three types of technologies are combined - pre-industrial, industrial and post-industrial. In pre-industrial and industrial technologies, the leading role belongs to material resources, labor and ways of their combination in the technological process. In post-industrial or mechatronic technologies, knowledge and information occupy a prominent place. It is the industries that use mechatronic technologies that are developing 5-10 times faster. Therefore, science and "high" technologies become the main sources economic development individual states, a huge productive force of society.

Concepts that have a connotation of special scientific value are called deadlines. It can be a word or phrase that has specific scientific content (eg discounting, interest rate, fiscal policy).

Concepts that acquire a broad content and are used in different meanings with several shades turn into categories (for example, the categories of the market, demand, money, finance, trade enterprises).

The basis for the formation of science as a system of knowledge are principles - certain key, starting points, the first degree of systematization of knowledge. Unlike laws, principles do not objectively exist in nature, but are determined by scientists. So, general principle All studies are based on the principle of dialectics - to consider all phenomena and processes in interconnection and in Russia both in space and in time. In the economic sciences, the most widely used are the principles of complexity, control, and others. A variety of principles are postulates - statements that are accepted as true within a certain scientific theory, although they cannot be proved by means of this theory and therefore play the role of axioms in it. Axiom, in turn, is a position that is accepted without logical evidence through its direct persuasiveness, visibility, and certainty. For example, one of the postulates in economic sciences is the postulate of limited resources.

Scientific laws are a statement (using principles, concepts and categories) that reflect the necessary, essential, stable and recurring objective phenomena and relationships in nature, society and thinking. Laws are objective in nature, they exist independently of the will and consciousness of people. The knowledge of laws is the task of science, which becomes the basis for the transformation of nature and society by people. There are three main groups of laws: specific or partial (for example, the law of supply and demand, the law of value), general, i.e. characteristic of large groups of phenomena (for example, the law of conservation of energy, the law natural selection, the law of cyclic development) and universal or universal (for example, the laws of dialectics).

Scientific theory is the highest degree of generalization and systematization of knowledge. A theory is understood as a system of basic ideas, provisions, laws in a particular field of knowledge, which gives a holistic view of the patterns and classification.

logical approach complements the two above and is based on the allocation of various aspects of a particular object of science, taking into account the general and the particular, the abstract and the concrete.

It should be noted that even a combination of these approaches does not make it possible to make a perfect and invariable classification of sciences, because the connections between the objects of nature and society and scientific knowledge are very multifaceted and interdependent. In addition, with the rapid development of science, new knowledge is born that complement and combine various branches of science.

In the most general form, all branches of scientific knowledge are combined into three groups:

• knowledge about nature (mathematics, physics, chemistry, biology, geography, etc.);
• knowledge about society (economic sciences, historical, legal, etc.);
• knowledge about thinking (philosophy, logic, psychology, etc.). If a we are talking it is about science, this classification can be modified and all sciences can be divided into the following enlarged groups:
• natural sciences (mathematics, physics, chemistry, biology, etc.);
• technical sciences - a system of knowledge about the purposeful transformation of natural forces and processes into technical objects;
• medical sciences;
• social sciences (economics, sociology, political science, legal sciences, demography, etc.);
• humanities (state history, art history, churches, theology, linguistics and literary criticism, philosophy, logic, psychology, etc.).

Each of these sciences has its own "springs" of knowledge, which branch out all the time. The process of branching, the birth of new "branches" on the "tree of science" is called the diversification of sciences. Diversification of Sciences- this is the emergence of new sciences at the junction of previously known ones or as a result of separation from them. As a result of this continuous process, such sub-branches of sciences as physics were formed in due time. solids, demand statistics, commodity science, finance of international insurance operations, ergonomics, etc.

Branching sciences contributes to their interweaving, interpenetration, integration. Integration is the unification of sciences into a new science. The integration resulted in such well-known sciences as biochemistry, mathematical statistics, engineering genetics, etc.

In general, in Ukraine it is customary to distinguish the following main branches of science: physical and mathematical, chemical, biological, geological and mineralogical, technical, agricultural, historical, economic, philosophical, philological, geographical, legal, pedagogical, medical, pharmaceutical, veterinary, art history, architecture, psychological, sociological, political, others.

According to the nature of their orientation and attitude to social practice, sciences are divided into fundamental and applied.

Basic sciences aimed at understanding the foundations and objective laws of the development of nature, society and thinking in general. their main goal is the search for truth, which can then be applied in various kinds of research, both in the fundamental sciences themselves and in applied sciences. The fundamental sciences include mathematics, certain sections of physics, chemistry, philosophy, economic theory, linguistics and others.

Applied Science, developing on the basis of fundamental ones, they develop ways and methods of applying and implementing the results in practice fundamental research. The indicator of the effectiveness of research in the field of applied sciences is not so much the acquisition of true knowledge, but the direct practical significance. The applied sciences include all technical sciences, most of the medical, economic sciences, etc. At present, almost every enlarged branch of science combines fundamental and applied sciences.

Against Vaihinger's Fictionalism and Mach's Sensational Monism. At the same time, it is not disputed here that optical and other errors of perception are possible; that there are hallucinations, delusions and insanity; that our sensations, perceptions, ideas, knowledge are partially conditioned by the subject through our language and the structures of our cognitive apparatus. It should be noted that there is no evidence for the subjectivity of all statements, and that the assumption of the existence of an external world is a hypothesis.

2. Postulate of structure: the real world is structured.

The order that is created, for example, in the Newtonian theory of gravity, has a character different from the order similar to the alphabetical order. Even if the axioms of the theory are created by people, the success of such principles implies, as Einstein noted, high level order of the objective world. Symmetries, invariances, topological and metric structures, interactions, natural laws, things, individuals, systems are considered as structures. The structures themselves are real and objective. We, with our sensory organs and cognitive functions, also belong to the real world and have a certain structure.

3. The postulate of continuity: there is a continuous connection between all areas of reality.

There is no impassable abyss between dead matter and living organisms, between plants and animals, between animals and man, between matter and spirit. Moreover, if we mean action quanta, elementary particles, mutational leaps, revolutions and fulgurations (in this context, it probably means: “irreversible destruction” - Note by I.L. Vikentiev), then perhaps a more appropriate name would be quasi-continuity. The history of science shows how fruitful the postulate of continuity was. Newton's theory of gravity showed that the "sublunar" and "supralunar" laws are the same. Through the synthesis of urea Wehler in 1831 he proved the possibility of obtaining organic substances from inorganic ones. Schleiden and Schwann established in 1838 that all organisms are made up of cells. Research recent years showed that the genetic code is also universal.

4. The postulate of someone else's consciousness: just like I, other individuals have sensory impressions and consciousness.

This postulate is in line with the assumptions of most biologists, physiologists and psychologists. Its denial leads to solipsism.

5. Postulate of interaction: our sensory organs are affected by the real world.

According to this postulate, the outer surface of our body exchanges energy with the environment. Some of the changes in sensitive cells are processed as signals and forwarded. Some of these excitations undergo special processing in nervous system and in the brain. They become perceived, interpreted as information about outside world and are realized. Perception already consists in the unconscious interpretation of sensory data and in the reconstruction of a hypothetically assumed external world.

6. Postulate of brain function: thinking and consciousness are functions of the brain, a natural organ.

Findings from brain research, such as electroencephalography (recording brain waves), pharmacology, and experimental psychology, such as sleep research, support the hypothesis that all conscious phenomena are related to physiological processes. This hypothesis is sometimes called the psychological axiom.

7. Postulate of objectivity: scientific statements must be objective.

Objectivity means in this case relation to reality. Scientific statements refer (except in psychology) not to states of consciousness of the observer, but to a hypothetically postulated reality. This interpretation is based on the 1st postulate - the postulate of reality.

The criteria for the objectivity of statements are as follows:

(A) Intersubjective intelligibility: scientific statements must be communicated to others, and therefore must be formulated in common language. For science is not a private enterprise.

(B) Independence from reference system: independence from the identity of the observer, his location, his state of mind, his "perspective".

(B) Intersubjective verifiability: for each statement, it should be possible to verify its correctness through appropriate procedures.

(D) Independence of method: The correctness of a statement should not depend on the method used to test it.

(E) Non-conventionality: the correctness of a statement should not be based on an arbitrary act or convention.

It should be emphasized that the various criteria mentioned above are necessary, but only in their conjunction can they be sufficient.

8. The postulate of virtuosity: working hypotheses should contribute to the study, and not hinder it.

This is a methodological postulate. It is the principle of our research strategy. It says nothing about the world or our knowledge, and does not lead constructively to new assumptions. but helps to choose between equivalent but contradictory hypotheses. Heuristically meaningful is the hypothesis that considers the object as present and observable, the property as measurable, the fact as explainable. For example, it would be non-heuristic to postulate a fundamental boundary between non-living and living systems, because one would have to deny very successful research in this area.

9. Postulate of explainability: the facts of experimental reality can be analyzed, described and explained by means of "natural laws".

This postulate follows from the heuristic postulate. To consider a process or a fact as fundamentally inexplicable is not only not heuristic, but in many cases means an irresponsible denial of knowledge. The explainability postulate is refusal from any form of irrationalism, teleology or vitalism. Such theories, for example, claim that evolution is allegedly inexplicable, and give this inexplicability various names: Demiurgical intelligence (Bennett): vital impulse (Bergson), cell consciousness (Buis); entelechy (Drish); orthogenesis (Eimer); life force(Müller), purposefulness (de Noy); aristogenesis (Osborne); vital fantasy (Palagius, Boytendik), self-image of the organism (Portman), Omega point, evolutionary gravity, onslaught of consciousness (Teilhard de Chardin). But the impulse of life explains evolution no better than the impulse of a locomotive explains the operation of a steam engine (J. Huxley).

10. The postulate of economy of thought: unnecessary hypotheses should be avoided.

This postulate is a methodological rule that can only serve to select hypotheses. Ockham also considered his principle of economy: entia non sunt multiplicanda praeter necessitatem ("Occam's razor") as a methodological rule for research. max he interpreted the principle of economy of thought as the essence of the laws of nature and as the goal of science in general. Against this claim Max Born objected that " the best way to make thinking economical is to stop it altogether.

As any mathematician well knows, such a principle only makes sense when subject to restrictive conditions. We must be united in the fact that our task is not only to bring order to the vast field of accumulated experience, but also to its incessant expansion through research; to this it should be added that without external achievements, clarity in thinking would also be lost.

Quoted in: Grishunin S.I., Philosophy of Science: Basic Concepts and Problems, M., "Urss", 2009, p. 210-215.

Workshop on general psychology Kondakov I.M.

SECTION 1. RESEARCH METHODS IN PSYCHOLOGY

TOPIC 1. MODERN METHODOLOGY OF SCIENTIFIC KNOWLEDGE

Methodology of scientific knowledge: the postulate of an active subject.

Basic concepts modern theory knowledge.

All science is based on facts. She collects facts, compares them and draws conclusions - establishes laws the area of ​​work that he is studying. The methods for obtaining these facts are called methods scientific research. The main methods of scientific research in psychology are observation, document analysis, survey, conversation, experiment (see Fig. 1) and testing. The justification of certain methods is given by the methodology of science.

Methodology of Science- the doctrine of the principles and methods of scientific knowledge (see [Shvyrev V.S. scientific knowledge like an activity. M., 1984; Yudin B.G. Methodological analysis as a direction in the study of science. M., 1986]). It prescribes certain standards for scientific research. The main ones among these standards are:

Building a model of a particular subject area that explains certain, previously recorded facts;

Nomination based on it hypotheses s research; verification of this hypothesis, i.e. an attempt to confirm it (or falsification, i.e. an attempt to refute);

Building forecast and the possibility of obtaining new facts.

Scientific knowledge acts as an activity. Activities aimed at a specific subject, both subject-transformative and cognitive, are implemented subject(from lat. subjectum - subject), which is either an individual or social group. Subject confronts an object y. An object(from Latin objectum - object) - something that exists outside the cognizing and acting subject, regardless of his sensations, feelings and desires and can become the subject of his directed activity as an object of cognition or activity.

There are certain features inherent in the subject of knowledge [Maturana U. Biology of knowledge // Language and intelligence. M., Progress, 1984], such as:

Belonging of the subject of knowledge to living systems;

Orientation of the subject of cognition to a holistic an object, which has both a specific historical and a specific structural context;

The inclusion of the subject of knowledge in the circle of other subjects of knowledge;

Possibility as an object and knowledge to have oneself, etc.

(See: Reader. Maturana U. Biology of knowledge // Language and intelligence. M., Progress, 1984.)

AT psychological research an object- a process or phenomenon that is associated with a certain problem situation, for the solution of which a scientific and psychological research is being launched. Based on a theoretical analysis of this problem situation carried out at the preliminary stage is formulated hypotheses and research, which indicates those psychological mechanisms that presumably cause the emergence of a problem and, accordingly, are the subject of research.

On this basis, a demarcation line is drawn between the objective and the subjective, introspection onistic psychology. Objective psychology(from Greek psyche - soul) - row psychological schools, focused on the use of objective methods of analysis and based on conventional rules for fixing mental phenomena.

In different areas of objective psychology, the subject of research is:

Behavior (in behaviorism),

Reactions (in reactology),

Reflexes (in reflexology), etc.

Objective psychology is characterized by its method. This is an objective method, acting as a methodological setting based on the analysis of mental content, maximally oriented towards another subject (and not oneself, as in introspection onism) and involving the use of verifiable hypotheses, i.e. hypotheses that can be tested under standardized conditions.

The advancement of scientific hypotheses is carried out on the basis of a particular scientific paradigm. Paradigm(from the Greek paradeigma - sample) - a conceptual model formed in one or another scientific field prescribing certain rules for posing problems and determining ways to solve them. On the basis of the paradigm, the a priori possibility of confirming certain hypotheses is evaluated and the methodological support of experimental studies is formed.

Basically, a paradigm is an example from history used as evidence or for comparison. The modern content of the concept of paradigm was set by T.S. Kuhn [Kun T.S. Structure scientific revolutions. M., 1977].

During certain periods of time in scientific community dominated by certain paradigms.

In a narrower sense, a paradigm is the principle of constructing pilot study, not necessarily correlated with the generally accepted axioms scientific knowledge in a particular scientific area. It is in this sense that the concept of a paradigm is most commonly used in psychology, since up to the present time psychology does not meet the criteria of operationalization, in particular, mathematization, which are set by natural sciences(mathematics, logic, physics, etc.).

Nevertheless, it can be said that at present the most influential paradigm in Russian psychology is the activity paradigm, which predetermines the research emphasis on the process of interaction between the subject and an object a.

Within the framework of the research paradigm, certain units of mental analysis are being developed. Actually, unit of mental analysis(from the Greek. analysis - decomposition, dismemberment) - this is a methodological setting focused on highlighting in mental life such formations that cannot be divided into smaller ones without losing the quality of the mental, on the one hand, and species variations of which give a satisfactory description and forecast the course of all psychological processes, on the other.

In the history of psychology, the units of analysis have been:

Association,

Behavior,

gestalt,

Need,

Activity,

Communication,

Interaction, etc.

In real research activities after the adoption of one or another paradigm and the allocation of the main unit of analysis of the mental, the stage of putting forward specific hypotheses. Hypothesis(from the Greek. hypothesis - assumption) - an element of the cognitive process, represented by an assumption about the individual properties of the surrounding world, arising as a factor in the orientation of activity and due to the individual's subjective picture of the world.

In the event that the solution to the problem is not known to the individual, very general hypotheses are formed at the beginning, by checking which the direction of further search is established.

Theoretical concepts can serve as grounds for putting forward hypotheses. At the same time, the process of putting forward hypotheses can also be outside the original theoretical constructions, i.e. intuitive, without reflection of logical grounds.

Basic postulates of the modern theory of knowledge.

Traditionally, within the framework of psychological problems, there are two most common topics:

The study of motivational processes (motivation-need field of activity; in terminology D.B. Elkonin (see Fig. 2) );

Research of cognitive processes (operational and technical sphere).

Within the framework of the first topic, motives, emotions, temperament, character, personality are considered, the second - sensations and perception, attention, memory, thinking. In terms of everyday consciousness, in the first case, we are talking about what the body needs, in the second, how this “necessary” is achieved.

But if we take the point of view of the modern theory of knowledge, then this dichotomy, at first glance quite clear and understandable, inevitably changes.

Turning to early theory m of knowledge, namely to the classical theory of knowledge, it can be seen that two areas have been defined here:

Subject area, i.e. knowing person,

Region an object and those. known reality.

The subject was treated as completely “impartial”, and the object as completely objectively existing.

But as knowledge (including psychological) accumulated, it became more and more clear that the subject is not so impartial, and objective reality itself is structured by a reflection of the needs of this cognizing subject.

Therefore, it was formulated anthropic principle in epistemology ". This principle is illustrated by the following analogy.

Bohr's quantum postulates, which explained the processes occurring in atoms that were not understood by physicists before, became the foundation on which quantum physics subsequently grew. The basis of the quantum theory developed by Niels Bohr includes three postulates formulated by him as a result of experiments or observations of the behavior of atoms of various substances, a quantization rule derived from the study of the hydrogen atom, and several formulas that mathematically explain Bohr's postulates.

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Postulates included in Bohr's quantum theory

First rule

The first rule is that the energy En in systems formed from atoms can exist only if these atoms are in specialized or, in other words, quantum states. In other cases, the atom does not give up its energy to its environment.

This rule, deduced by the scientist, absolutely contradicts the knowledge accumulated by classical mechanics. According to the axioms of classical mechanics, any atoms or electrons that are currently moving have energy, and this energy can be of any kind.

In addition, the main conclusion from the first postulate of one of the fathers of quantum physics fundamentally contradicts the knowledge in the field of electromagnetism obtained by Maxwell in the nineteenth century, since it allows the possibility of the movement of molecular particles without radiation into the surrounding space of electromagnetic impulses.

The second rule of the theory

It says that the light that an atom emits is the result of its transition from a state during which it had a higher energy Ek to a state in which it already has a lower energy En. The formula that calculates the amount of energy that a photon radiates into the surrounding space is the difference Ek - En.

Second Bohr theory rule provides that the reverse process is possible, i.e., the atom can return to a state where it stores a larger supply of energy than it had before, if before that it absorbs a certain amount of light energy.

Bohr's third postulate

Its essence is that an electron in an atom or an atom in a molecule moves from one orbit to another and during this either emits, or absorb energy. This energy is released from them in so-called quanta or portions, which science can measure and calculate.

The third rule, discovered by Bohr, was studied by other famous physicists and confirmed as a result of an experiment conducted by scientists Frank and Hertz.

The third postulate played a significant role in the development of optics, since it proved that atoms emit only those spectra of light that they can also absorb.

Hydrogen atom and quantization rule

In order to develop atom model the simplest of the currently known elements, hydrogen, Bohr postulated a quantization rule or, in other words, a pattern according to which the energy levels of an electron are determined depending on its stationary values ​​occupied by it in orbit.

From this it follows that depending on the orbit in which an electron in an atom or an atom in a molecule is located, the coefficient of the energy they possess is determined.

Using the quantization rule, based on the laws of mechanics derived by Newton, Niels Bohr was able to calculate the value of the minimum possible radius of the orbit of an electron in an atom, as well as the energy values ​​\u200b\u200bthat atoms and electrons have when they are in stationary states.

The meaning of postulates and their impact on the scientific world

Despite the fact that some of the assumptions and opinions expressed by Bohr later turned out to be incorrect and erroneous, for which he was mercilessly criticized by colleagues in the scientific workshop, including Albert Einstein himself, nevertheless, his postulates played an important role in physics: