Fundamental scientific discoveries in philosophy. Features of fundamental scientific discoveries. Fundamental scientific discoveries

Scientific revolutions usually affect the philosophical and methodological foundations of science, often changing the very style of thinking. Therefore, in their significance they can go far beyond the specific area where they occurred. Therefore, we can talk about private scientific and general scientific revolutions.

The emergence of quantum mechanics is a prime example general scientific revolution, since its significance goes far beyond the limits of physics. Quantum-mechanical representations at the level of analogies or metaphors have penetrated into humanitarian thinking. These representations influence our intuition, common sense, influence world perception.

The Darwinian revolution in its significance went far beyond biology. It radically changed our ideas about the place of man in Nature. It had a strong methodological impact, turning the thinking of scientists towards evolutionism.

New methods of research can lead to far-reaching consequences: to changing problems, to changing the standards of scientific work, to the emergence of new areas of knowledge. In this case, their introduction means a scientific revolution.

Thus, the appearance of the microscope in biology meant a scientific revolution. The entire history of biology can be divided into two stages, separated by the appearance and introduction of the microscope. Entire fundamental sections of biology - microbiology, cytology, histology - owe their development to the introduction of the microscope.

The advent of the radio telescope meant a revolution in astronomy. Academician Ginzburg writes about it this way: “Astronomy after the Second World War entered a period of especially brilliant development, the period of the “second astronomical revolution” (the first such revolution is associated with the name of Galileo, who began to use telescopes) ... The content of the second astronomical revolution can be seen in the process of transforming astronomy from optical to all-wave".

Sometimes a new area of the unknown, a world of new objects and phenomena, opens up before the researcher. This can cause revolutionary changes in the course of scientific knowledge, as happened, for example, with the discovery of such new worlds as the world of microorganisms and viruses, the world of atoms and molecules, the world of electromagnetic phenomena, the world of elementary particles, the discovery of the phenomenon of gravity, other galaxies, the world of crystals , radioactivity phenomena, etc.

Thus, the basis of the scientific revolution may be the discovery of some previously unknown areas or aspects of reality.

F. Bacon believed that he had developed a method of scientific discoveries, which was based on a gradual movement from particulars to generalizations. He was sure that he had developed a method for discovering new scientific knowledge that everyone could master. This method of discovery is based on an inductive generalization of experimental data. Bacon constructed a rather sophisticated scheme of the inductive method, which takes into account not only the presence of the property under study, but also its various degrees, as well as the absence of this property in situations where its manifestation was expected.

Descartes believed that the method of obtaining new knowledge is based on intuition and deduction. "These two paths," he wrote, "are the surest paths to knowledge, and the mind should no longer allow them - all others (for example, analogy) must be rejected as suspicious and leading to error."

In the modern methodology of science, it is realized that inductive generalizations cannot make the leap from empiricism to theory. Einstein wrote about it this way: “It is now known that science cannot grow on the basis of experience alone, and that in the construction of science we are forced to resort to freely created concepts, the suitability of which can be tested a posteriori empirically. These circumstances eluded previous generations. to whom it seemed that a theory could be constructed purely inductively, without resorting to free, creative creation of concepts. recent times The restructuring of the entire system of theoretical physics as a whole has led to the fact that the recognition of the speculative nature of science has become the common property.

In characterizing the transition from empirical data to theory, it is important to emphasize that pure experience, i.e. one that is not defined theoretical ideas, does not exist at all.

On this occasion, K. Popper wrote as follows: “The notion that science develops from observation to theory is still widespread. However, the belief that we can start scientific research without having something similar to a theory is absurd.” Twenty-five years ago I tried to instill this thought in a group of physics students in Vienna, beginning my lecture with these words: "Take a pencil and paper, observe carefully and describe your observations!" They asked, of course, what exactly they should observe. that the simple instruction "Watch!" is absurd. Observation is always selective. One must choose an object, a certain task, have some interest, point of view, problem...".

The role of theory in the development of scientific knowledge is clearly manifested in the fact that fundamental theoretical results can be obtained without direct reference to empirical data.

A classic example of constructing a fundamental theory without direct reference to empirical data is Einstein's creation general theory relativity. The special theory of relativity was also created as a result of consideration of a purely theoretical problem (Michelson's experiment had no significant significance for Einstein).

New phenomena can be discovered in science both by empirical and by theoretical research. A classic example of the discovery of a new phenomenon at the level of theory is the discovery of the positron by P. Dirac, the principles of Lobachevsky geometry and the foundations of quantum mechanics, the theory of relativity, Big Bang cosmology, etc.

Attempts to construct various kinds of logics of discovery ceased in the last century as completely untenable. It became obvious that there is no logic of discovery, no algorithm of discoveries in principle. At the same time, there is certainly a logic scientific research. As Professor Lord Acton of Cambridge University put it, "There is nothing more necessary for a man of science than its history and the logic of scientific research ... - ways to detect errors, use hypotheses and imagination, methods of verification."

Many major discoveries in science are made on a well-defined theoretical basis. An example is the discovery of the planet Neptune by Le Verrier and Adams on the basis of celestial mechanics by studying perturbations in the motion of the planet Uranus.

Fundamental scientific discoveries differ from others in that they are not concerned with deduction from existing principles, but with the development of new underlying principles. In the history of science, fundamental scientific discoveries are distinguished, associated with the creation of such fundamental scientific theories and concepts as the geometry of Euclid, heliocentric system Copernicus, Newton's classical mechanics, Lobachevsky's geometry, Mendel's genetics, Darwin's theory of evolution, Einstein's theory of relativity, quantum mechanics. These discoveries have changed the perception of reality in general, i.e. were worldview.

As mentioned above, there are many facts in the history of science when a fundamental scientific discovery was made independently by several scientists almost at the same time. For example, non-Euclidean geometry was built almost simultaneously by Lobachevsky, Gauss and Bogliani; Darwin published his ideas about evolution almost at the same time as Wallace; The special theory of relativity was developed simultaneously by Einstein and Poincaré.

From the fact that fundamental discoveries are made almost simultaneously by different scientists, it follows that they are historically determined. Fundamental discoveries always arise as a result of solving fundamental problems, i.e. problems that have a deep, ideological, and not private character. So, Copernicus saw that two fundamental worldview principles of his time - the principle of movement celestial bodies in circles and the principle of the simplicity of nature are not realized in astronomy; the solution of this fundamental problem led him to the greatest discovery - the heliocentric model of the world.

Non-Euclidean geometry was constructed when the problem of the fifth postulate of Euclid ceased to be a particular problem of geometry and turned into a fundamental problem of mathematics, its foundations.

Intensive development of science in the XIX - XX centuries. led to the key problems of natural science, which must be resolved in the coming years, because for this a sufficient arsenal of theoretical knowledge and experimental techniques has been accumulated. First of all, we are talking about the causes and mechanisms of the origin of life on Earth. If existing theories can explain the appearance of the simplest organic matter and amino acids as a result of the existence of a specific chemical composition surface and exposure to solar radiation, the appearance of molecules that form a double helix and carry a hereditary code remains inexplicable due to the negligible probability of spontaneous synthesis of such molecules, even taking into account the significant time period in which this process could be realized. A similar question arises when studying, for example, the mechanism of vision of highly organized living beings. It can be assumed that the chain for converting light into an electrical signal and the chain for transmitting a nerve impulse are formed independently in the evolutionary process, although it is difficult to assume their independent formation, since some function of the body cannot be formed if it is not directly necessary. But it is even more difficult to understand how these two chains "found" each other. Questions of cosmology, the origin of the world, its boundaries, multiplicity, beginning and end also require their solution, including for understanding the place and role of humanity in the world.

In accordance with the classical ideas about science, it should not contain "any admixture of delusions." Now truth is not considered as a necessary attribute of all cognitive results that claim to be scientific. It is the central regulator of scientific and cognitive activity.

Classical ideas about science are characterized by a constant search for the "beginnings of knowledge", a "reliable foundation" on which the entire system could be based. scientific knowledge.

However, in the modern methodology of science, the idea of the hypothetical nature of scientific knowledge is developing, when experience is no longer the foundation of knowledge, but mainly performs a critical function.

To replace the fundamentalist validity as the leading value in the classical ideas about scientific knowledge, such a value as efficiency in solving problems is increasingly being put forward.

Various areas of scientific knowledge acted as standards throughout the development of science. "Beginnings" Euclid for a long time were an attractive standard in literally all areas of knowledge: in philosophy, physics, astronomy, medicine, etc. However, now the limits of the significance of mathematics as a standard of scientific character are well understood, which, for example, are formulated as follows: “In a strict sense, proofs are possible only in mathematics, and not because mathematicians are smarter than others, but because they themselves create the universe for their experiments, all the rest are forced to experiment with a universe not created by them.

The triumph of mechanics in the XVII - early XIX centuries led to the fact that it began to be regarded as an ideal, a model of science. Eddington said that when a physicist sought to explain something, "his ear struggled to catch the noise of the machine. A man who could construct gravity from cogwheels would be a hero of the Victorian age."

Since the New Age, physics has been asserted as a reference science. If at first mechanics acted as a standard, then - the whole complex of physical knowledge. The orientation towards the physical ideal in chemistry was clearly expressed, for example, by P. Berthelot, and in biology by M. Schleiden. G. Helmholtz argued that the "ultimate goal" of all natural science is to "dissolve into mechanics." Attempts to construct "social mechanics", "social physics", etc. were numerous.

The physical ideal of scientific knowledge has certainly proved its heuristic, however, today it is clear that the implementation of this ideal often hinders the development of other sciences: mathematics, biologists, social sciences and etc.

In addition to socio-cultural conditioning, any scientific knowledge, including the humanities, must be characterized by internal, objective conditioning. Therefore, the humanitarian ideal cannot be realized even in its subject area, and even more so in natural science. The humanitarian ideal of being scientific is sometimes regarded as a transitional step towards some new ideas about science that go beyond the limits of classical ideas.

In general, the classical ideas about science are characterized by the desire to single out a "standard of scientific character", to which all other areas of knowledge should "catch up".

If, in accordance with the classical ideas about science, its conclusions should be determined only by the reality itself, then the modern methodology of science is characterized by the adoption and development of the thesis about the socio-cultural conditionality of scientific knowledge.

Social (socio-economic, cultural-historical, ideological, socio-psychological) factors in the development of science do not have a direct impact on scientific knowledge, which develops according to its own internal logic.

In the methodology of science, such functions of science as description, explanation, foresight, understanding are distinguished. However, such an understanding of the functions of science was formed as a result of the confrontation of different points of view on this issue.

Kant considered foresight to be the main function of science. He wrote: “True positive thinking consists primarily in the ability to know in order to foresee, to study what is, and from there to conclude what should happen according to general position about the immutability of natural laws. " Another point of view was developed by the famous philosopher and physicist E. Mach. He noted: "Does the description give everything that a scientific researcher can require? I think so! ". Mach reduced explanation and foresight to description. Theory, from his point of view, is like a compressed empirical, that is, a general description of an array of experimental data, and there is no essential difference between theory and simple observation in any way. in relation to origin, nor in relation to the final result. As a result, he concluded that the atomic-molecular theory is nothing more than a "mythology of nature. " He held a similar position in the first period of his scientific activity and the famous chemist W. Ostwald. It is interesting to note that the scientific activity of both scientists proceeded in late XIX- the beginning of the XX century. On this occasion, A. Einstein wrote: "The prejudice of these scientists against the atomic theory can undoubtedly be attributed to their positivist philosophical attitude. This is interesting example how philosophical prejudices prevent the correct interpretation of facts, even by scientists with bold thinking and subtle intuition. The prejudice that has survived to this day lies in the belief that the facts themselves, without a free theoretical construction, can and should lead to scientific knowledge. "The philosopher of the New Age V. Dilthey, known for his works on the essence of the humanities and natural sciences, believed that the cognitive basic function of the natural sciences is the explanation of nature and natural phenomena. However, in fact, the sciences of nature also perform the function of understanding. The explanation is connected with understanding, since the explanation demonstrates to us the meaningfulness of the existence of the object, and therefore allows us to understand it.

Ethical norms not only regulate the application of scientific results, but are also contained in the scientific activity itself.

The Norwegian philosopher G. Skirbekk notes: "Being an activity aimed at searching for truth, science is governed by the following norms: "seek the truth", "avoid nonsense", "speak clearly", "try to test your hypotheses as thoroughly as possible" - this is what the wording looks like these internal norms of science. In this sense, ethics is contained in science itself, and the relationship between science and ethics is not limited to the question of good or bad application of scientific results.

The presence of certain values and norms that are reproduced from generation to generation of scientists and are mandatory for a person of science, i.e. certain scientific ethics, is very important for the self-organization of the scientific community (at the same time, the normative-value structure of science is not rigid). Separate violations of the ethical norms of science in general are more likely to be fraught with great trouble for the violator himself than for science as a whole. However, if such violations become widespread, science itself is already under threat. Ethical norms that, of course, must be followed include: recognition of the priority of the scientist who discovered this or that phenomenon or regularity, publication of reliable experimental results, familiarization of the general scientific community with the details of the experiment, using scientific publications and conferences, full citation of previous works performed on the same problem, indication of the weaknesses of the study, openness of the conditions and details of the experiment for those who wish to get acquainted with them.

The ethical assessment of science should now be differentiated, relating not to science as a whole, but to individual areas and areas of scientific knowledge. Such moral and ethical judgments play a very constructive role.

Modern science includes human and social interactions that people enter into about scientific knowledge. The "pure" study of a knowable object by science is a methodological abstraction, thanks to which one can obtain a simplified picture of science. In fact, the objective logic of the development of science is realized not outside the scientist, but in his activity. Recently, the social responsibility of a scientist is an integral component of scientific activity. This responsibility turns out to be one of the factors that determine the trends in the development of science, individual disciplines and research areas.

In the 1970s, scientists for the first time declared a moratorium on dangerous research. In connection with the results and prospects of biomedical and genetic research, a group of molecular biologists and geneticists headed by P. Berg (USA) voluntarily announced a moratorium on such experiments in the field of genetic engineering, which may pose a danger to the genetic constitution of living organisms. Then for the first time, scientists on their own initiative decided to suspend research that promised them great success. The social responsibility of scientists has become an organic component of scientific activity, significantly influencing the problems and directions of research.

The progress of science expands the range of problem situations for which the entire moral experience accumulated by mankind is insufficient. A large number of such situations arise in medicine. For example, in connection with the success of experiments on the transplantation of the heart and other organs, the question of determining the moment of death of the donor has become acute. The same question arises when, in an irreversibly comatose patient, technical means breathing and heartbeat are maintained. It cannot be assumed that ethical problems are the property of only some areas of science. Valuable and ethical foundations have always been necessary for scientific activity. AT modern science they become a very noticeable and integral part of the activity, which is a consequence of the development of science as a social institution and the growth of its role in the life of society.

Among the diverse types of scientific discoveries, a special place is occupied by fundamental discoveries that change our ideas about reality in general, i.e. worldview in nature.

1. TWO KINDS OF DISCOVERIES

A. Einstein once wrote that a theoretical physicist “as a foundation needs some general assumptions, the so-called principles, from which he can derive consequences. His work is thus divided into two stages. First, he needs to find these principles, and secondly. develop the implications of these principles. To perform the second task, he is thoroughly armed since school. Therefore, if for some area and, accordingly, the set of relationships, the first problem is solved, then the consequences will not be long in coming. The first of these tasks is of a completely different kind, i.e. establishing principles that can serve as a basis for deduction. There is no method here that can be learned and systematically applied to achieve the goal.

We will deal mainly with the discussion of problems associated with the solution of problems of the first kind, but first we will clarify our ideas about how problems of the second kind are solved.

Let's imagine the following problem. There is a circle through the center of which two mutually perpendicular diameters are drawn. Through point A, located on one of the diameters at a distance of 2/3 from the center of circle O, we draw a line parallel to the other diameter, and from the point B of the intersection of this line with the circle, we drop the perpendicular to the second diameter, designating their intersection point through C. We need express the length of the segment AC in terms of a function of the radius.

How are we going to solve this school problem?

To do this, we turn to certain principles of geometry and restore a chain of theorems. In doing so, we try to use all the data we have. Note that since the diameters drawn are mutually non-pendicular, the triangle OAC is right-angled. The value of OA \u003d 2 / Zr. We will now try to find the length of the second leg, in order to then apply the Pythagorean theorem and determine the length of the hypotenuse AC. You can try to use some other methods. But suddenly, after carefully looking at the figure, we find that OABS is a rectangle whose diagonals are known to be equal, i.e. AC=OB. 0B is equal to the radius of the circle, therefore, without any calculations, it is clear that AC = r.

Here it is - a beautiful and psychologically interesting solution to the problem.

In this example, the following is important.

First, tasks of this kind usually belong to a well-defined subject area. Solving them, we clearly imagine where, in fact, we need to look for a solution. In this case, we do not think about whether the foundations of Euclidean geometry are correct, whether it is necessary to invent some other geometry, some special principles, in order to solve the problem. We immediately interpret it as referring to the field of Euclidean geometry.

Secondly, these tasks are not necessarily standard, algorithmic. In principle, their solution requires a deep understanding of the specifics of the objects under consideration, developed professional intuition. Here, therefore, some professional training is needed. In the process of solving problems of this kind, we open a new path. We notice “suddenly” that the object under study can be considered as a rectangle and it is not at all necessary to single out a right triangle as an elementary object in order to form the correct way to solve the problem.

Of course, the above task is very simple. It is needed only in order to generally outline the type of problems of the second kind. But among such problems there are immeasurably more complex ones, the solution of which has great importance for the development of science.

Consider, for example, the discovery new planet Le Verrier and Adamsom. Of course, this discovery is a great event in science, especially considering how it was done:

First, the trajectories of the planets were calculated;

Then it was found that they did not coincide with the observed ones; - then it was suggested that the existence of a new planet;

Then they pointed the telescope at the corresponding point in space and ... discovered a planet there.

But why can this great discovery be attributed only to discoveries of the second kind?

The thing is that it was made on a clear foundation of already developed celestial mechanics.

Although problems of the second kind can, of course, be subdivided into subclasses of varying complexity, Einstein was right to separate them from fundamental problems.

For the latter require the discovery of new fundamental principles which cannot be obtained by any deduction from existing principles.

Of course, there are intermediate instances between problems of the first and second kind, but we will not consider them here, but will go straight to problems of the first kind.

In general, there are not so many such problems before mankind, but their solution each time meant a huge progress in the development of science and culture as a whole. They are associated with the creation of such fundamental scientific theories and concepts as Euclid's geometry, Copernicus' heliocentric theory, Newton's classical mechanics, Lobachevsky's geometry, Mendel's genetics, Darwin's theory of evolution, Einstein's theory of relativity, quantum mechanics, and structural linguistics.

All of them are characterized by the fact that the intellectual base on which they were created, in contrast to the field of discoveries of the second kind, was never strictly limited.

If we talk about the psychological context of the discoveries of different "s ^ ^, then it is probably the same. - In the most superficial form, it can be described as direct vision, a discovery in the full sense of the word. A person, as Descartes believed, "suddenly" sees, that the problem should be considered in this way, and not otherwise.

Further, it should be noted that the discovery is never one-act, but has, so to speak, a "shuttle" character. At first there is a sense of the idea; then it is clarified by deriving certain consequences from it, which, as a rule, clarify the idea; then new consequences are deduced from the new modification, and so on.

But in the epistemological plan, the discoveries of the first and second kinds differ in the most radical way.

2. HISTORICAL CONDITIONING OF FUNDAMENTAL DISCOVERIES

Let us try to imagine the solution of problems of the first kind.

The advancement of new fundamental principles has always been associated with the activity of geniuses, with insight, with some secret characteristics of the human psyche.

An excellent confirmation of this perception of this kind of discovery is the struggle of scientists for priority. There have been so many acute situations in the history of relations between scientists associated with their confidence that no one else could get the results they had achieved.

For example, the famous utopian socialist C. Fourier claimed to have revealed the nature of man, discovered how society should be arranged so that it does not have any social conflicts. He was convinced that if he had been born before his time, he would have helped people solve all their problems without wars and ideological confrontations. In this sense, he connected his discovery with his individual abilities.

How do fundamental discoveries come about? To what extent is their implementation connected with the birth of a genius, the manifestation of his unique talent?

Turning to the history of science, we see that such discoveries are indeed carried out by extraordinary people. At the same time, attention is drawn to the fact that many of them were made independently by several scientists almost at the same time.

N. Ilobachevsky, F. Gauss, J. Bolyai, not to mention the mathematicians who developed the foundations of such geometry with less success, i.e. a whole group of scientists almost simultaneously came to the same fundamental results. For two thousand years, people have been struggling with this problem of the fifth postulate of Euclid's geometry, and "suddenly", for literally 10 years, a dozen people solve it at once.

C. Darwin first published his ideas about the evolution of species in a report read in 1858 at a meeting of the Linnean Society in London. At the same meeting, Woyales also spoke with a presentation of the results of research, which essentially coincided with Darwin's.

The special theory of relativity wears, how known, the name of A. Einstein, who outlined its principles in 1905. But in the same 1905, similar results were published by A. Poincaré.

The rediscovery of Mendelian genetics in 1900 by Cermak, Correns, and de Vries, simultaneously and independently of each other, is quite surprising.

Such situations can be found in the history of science a huge number.

And as soon as the situation is such that fundamental discoveries are made almost simultaneously by different scientists, then, consequently, there is their historical conditionality.

What is it in this case?

Trying to answer this question, we formulate the following general proposition.

Fundamental discoveries always arise as a result of solving fundamental problems.

First of all, let's pay attention to the fact that when we talk about fundamental problems, we mean such issues that concern our general ideas about reality, its cognition, about the value system that guides our behavior. Fundamental open problems are often treated as solutions to particular problems and are not associated with any fundamental problems.

For example, when asked how the Copernican theory was created, they answer that studies showed a discrepancy between observations and those predictions that were made on the basis of the Ptolemaic geocentric system, and therefore a conflict arose between new data and the old theory.

To the question of how non-Euclidean geometry was created, the following answer is given: as a result of solving the problem of proving the fifth postulate of Euclid's geometry, which could not be proved in any way.

3. HELIOCENTRIC COPERNICK SYSTEM

Let's look from these positions at the features of the process of fundamental discoveries, starting our analysis with a study of the history of the creation of the heliocentric system of the world.

The presentation of the Copernican system of the universe as arising from the discrepancy between astronomical observations and the geocentric model of the world of Ptolemy does not correspond to historical facts.

First, the Copernican system did not at all describe the observed data better than the Ptolemaic system. By the way, that is why it was rejected by the philosopher F. Bacon and the astronomer T. Brahe.

Second, even assuming that the Ptolemaic model had some discrepancies with observations, one cannot deny its ability to cope with these discrepancies. After all, the behavior of the planets was represented in this model with the help of a carefully developed system of epicycles, which could describe an arbitrarily complex mechanical movement. In other words, there was simply no problem of coordinating the motion of the planets according to the Ptolemaic system with empirical data.

But how, then, could the Copernican system arise and even more so assert itself?

To understand the answer to this question, you need to be aware of the soup. worldview innovations that she carried with her.

In the time of Copernicus, the theologized Aristotelian idea of the world dominated. Its essence was as follows.

The world was created by God specifically for man. For man, the Earth was created as a place of his dwelling, placed in the center of the universe. The firmament moves around the Earth, on which all the stars, planets, as well as spheres associated with the movement of the Sun and Moon are located. . The entire heavenly world is meant to serve earthly life of people.

In accordance with this installation, the whole world is divided into

sublunar (earthly) and supralunar (heavenly).

The sublunar world is a mortal world in which everyone lives

individual mortal. – Heavenly peace is peace for humanity in general, eternal peace. II which have their own laws, different from those of the earth. - In the earthly world, the laws of Aristotelian physics are valid,

according to which all movements are carried out as a result of

direct influence of some forces. - In the celestial world, all movements are carried out in circular orbits (a system of epicycles) without the influence of any forces.

Copernicus radically changed this generally accepted picture of the world.

He not only swapped the Earth and the Sun in the astronomical scheme, but

changed the place of man in the world, placing it on one of the planets, confusing the earthly and heavenly worlds.

The destructive nature of the ideas of Copernicus was clear to everyone. The Protestant leader MLuther, who had nothing to do with astronomy, spoke in 1539 about the teachings of Copernicus as follows: “A fool wants to turn the whole art of astronomy upside down. But, as Scripture indicates, Joshua commanded the Sun to stop, not the Earth.”

Could any insignificant reason have caused such new radical ideas?

What does a person do when he gets a bang on his finger? He, of course, is trying to pull out a splinter, to treat his finger. But if gangrene has begun, then he will not spare a whole arm.

The problems of an accurate description of the observed trajectories of the planets, as already mentioned, could not be the basis for such bold and decisive actions.

Also, it should be borne in mind that the astronomy of that time contained considerable opportunities for quite significant innovations. So, Tycho Brahe, solving astronomical problems associated with improving the calculations of the trajectories of the planets, proposed, in full accordance with the traditional worldview, a new system in which the Sun revolved around the Earth, and all the other planets revolved around the Sun.

Why did Copernicus need to put forward his ideas? Apparently, he was solving some fundamental problem of his own.

What was the problem?

Both Ptolemy, and Aristotle, and Copernicus proceeded from the fact that in the heavenly world all movements occur in circles.

At the same time, even in antiquity, a profound idea was expressed that nature is, in principle, simple. This idea has become over time one of the fundamental principles of cognition of reality.

At the same time, observational astronomy had discovered by that time the following. Although the Ptolemaic model of the world had the ability to accurately describe any trajectory, for this it was necessary to constantly change the number of epicycles (today - one number, tomorrow - another). But in this case, it turned out that the planets did not move along the epicycles at all. It turns out that the epicycles do not reflect real movements planets, but are simply a mathematical device for describing this movement.

In addition, according to Ptolemy's system, it turned out that to describe the trajectory of one planet, a huge number of epicycles must be introduced. Complicated astronomy did not perform its practical functions well. In particular, it was very difficult to calculate the dates of religious holidays. This difficulty was so clearly realized at that time that even the Pope himself found it necessary to make reforms in astronomy.

Copernicus saw that two fundamental worldview principles of his time - the principle of the movement of celestial bodies in a circle and

the principle of the simplicity of nature is clearly not realized in astronomy.

The solution of this fundamental problem led c1 to the great discovery.

4. GEOMETRY OF LOBACHEVSKY

Let us turn to the analysis of another discovery - the discovery of non-Euclidean geometry. Let us try to show that here, too, we dealt with a fundamental problem. Considering this example, we will find out a number of other important points in the interpretation of fundamental discoveries.

The creation of non-Euclidean geometry is usually presented as a solution to the well-known problem of the fifth postulate of Euclid's geometry.

This problem was as follows.

The basis of all geometry, as it followed from the system of Euclid, was represented by the following five postulates:

1) through two points it is possible to draw a straight line, and moreover, only one;

2) any segment can be extended in any direction to infinity:

3) from any point as from the center, you can draw a circle of any radius;

4) all right angles are equal:

5) two straight lines intersected by a third will intersect on the side where the sum of the interior one-sided angles is less than 2d.

Already in the time of Euclid, it became clear that the fifth postulate is too complicated compared to other initial Provisions of his geometry. Other positions seemed obvious. It is because of their obviousness that they were considered as postulates, i.e. as something that is accepted without evidence. At the same time, Thales proved the equality of angles at the base isosceles triangle, i.e. a position much simpler than the fifth postulate. From this it is clear why this postulate has always been regarded with suspicion and attempts have been made to present it as a theorem. And Euclid himself constructed geometry in such a way that first those provisions were proved that were not based on the fifth postulate, and then this postulate was used to develop the content of geometry.

It is interesting that literally all major mathematicians up to N.I. Lobachevsky, F. Gauss and J. Bolyai, who eventually solved the problem, sought to prove the fifth postulate of Euclid's geometry as a theorem, while maintaining the conviction of its truth. Their decision consists of the following points:

The fifth postulate of Euclid's geometry is indeed a postulate, not a theorem;

It is possible to construct a new geometry by accepting all the Euclidean postulates, except for the fifth, which is replaced by its negation, i.e., for example, by the statement that through a point lying outside a line, one can draw an infinite number of lines parallel to the given one:

As a result of such a replacement, non-Euclidean geometry was constructed.

Let us now pose the following questions.

Why, for two millennia, no one even thought about the possibility of constructing non-Euclidean geometry?

To answer these questions, let's turn to the history of spiders.

Before Lobachsky, Gauss, Bolyan, geometry was viewed as the ideal of scientific knowledge.

Literally all thinkers of the past worshiped this ideal, believing that geometric knowledge in Euclid's exposition is perfect. It seemed to be a model of the organization and proof of knowledge.

For Kant, for example, the idea of the uniqueness of geometry was an organic part of his philosophical system. He believed that Euclidean perception of reality is a priori. It is a property of our consciousness, and therefore we cannot perceive reality differently.

The question of the uniqueness of geometry was not just a mathematical question.

It was ideological in nature, was included in the culture.

It was by geometry that they judged the possibilities of mathematics, the features of all objects, the style of thinking of mathematicians, and even the possibilities of a person to have accurate, demonstrative knowledge in general.

Where, then, did the idea of the possibility of different geometries come from?

Why were N.I. Lobachevsky and other scientists able to come to a solution to the problem of the fifth postulate?

Let us pay attention to the circumstance that the time of the creation of the central geometries was a crisis from the point of view of solving the problem of Euclid's fifth postulate. Although mathematicians have been dealing with this problem for two thousand years, they have not had any stressful situations about the fact that it has not been solved for so long. They apparently thought this:

- Euclid's geometry is a magnificently built building; - it is true that there is some ambiguity in it associated with the fifth postulate, but in the end it will be eliminated.

However, tens, hundreds, thousands of years passed, and the ambiguity was not eliminated, but this did not particularly worry anyone. Apparently, the logic here could be as follows: there is only one truth, but there are as many false paths as you like. Until you find the right solution to the problem, will surely be found. The statement contained in the fifth postulate will be proved and will become one of the theorems of geometry.

But what happened at the beginning of the 19th century?

The attitude to the problem of proving the fifth postulate changes significantly. We see a number of direct statements about the very unfavorable situation in mathematics due to the fact that it is not possible to prove such an ill-fated postulate.

The most interesting and striking evidence of this is a letter from F. Bolyai to his son J. Bolyai, who became one of the founders of non-Euclidean geometry. “I beg you,” my father wrote, “just don’t make any attempts to overcome the theory of parallel lines; you will spend all your time on it, and you will not prove the propositions of this all together. Do not try to overcome the theory of parallel lines in the way you tell me, or in any other way. I have studied all the nougat to the end; I haven't come across a single idea that I haven't developed. I passed through all the hopeless darkness of that night, and I buried every light, every joy of life in it. For God's sake, I beg you, leave this matter, fear it no less than sensual passions, because it can deprive you of all your time, health, peace, all the happiness of your life. This hopeless darkness can sink thousands of Newtonian towers. It will never clear up on earth, and the unfortunate human race will never possess anything perfect even in geometry.

Why does such a reaction appear only at the beginning of the 19th century?

First of all, because at that time the problem of the fifth postulate ceased to be private, which may not be solved. In the eyes of F. Bolyai, it appeared as a whole fan of fundamental questions.

How should mathematics be constructed in general? – Can it be built on really strong

grounds?

Is it valid knowledge? Is it logically solid knowledge at all?

Such a formulation of the question was due not only to the history of the development of research related to the proof of the fifth postulate. It was determined by the development of mathematics in general, including its use in various fields of culture.

Up until the 17th century. mathematics was in its infancy. The most developed was geometry, the beginnings of algebra and trigonometry were known. But then from the 17th century mathematics began to develop rapidly, and by the beginning of the XIX century. it represented a rather complex and developed system of knowledge.

First of all, under the influence of the needs of mechanics, differential and integral calculus were created.

Significant development has received algebra. The concept of a function organically entered mathematics (a large number of different functions were actively used in many branches of physics).

The theory of probability has developed into a fairly coherent system. - The theory of series was formed.

Thus, mathematical knowledge has grown not only quantitatively, but also qualitatively. At the same time, a large number of concepts appeared that mathematicians could not interpret.

For example, algebra carried with it a certain idea of number. Positive, negative and imaginary quantities were equally its objects. But what negative or imaginary numbers are, no one knew this until the beginning of the 19th century. - There was no clear answer to a more general question: what is a number in general?

What are infinitesimal quantities? – How can one justify the operations of differentiation, integration, summation of series? - What is a probability?

At the beginning of the XIX century. no one could answer these questions.

In short, in mathematics by the beginning of the 19th century. the overall situation is difficult.

On the one hand, this field of science has been intensively developed

and found valuable applications, on the other hand, it rested on very obscure foundations.

In such a situation, the problem of the fifth postulate of Euclid's geometry was perceived differently.

The difficulties of interpreting new concepts could be understood as follows: what is unclear today will become clear tomorrow, when the corresponding field of research has received sufficient development, when enough intellectual efforts have been concentrated to solve the problem. The problem of the fifth postulate, however, has existed for two millennia. And she still doesn't have a solution.

Maybe; perhaps this problem sets a standard for interpreting state of the art mathematics and understanding what mathematics is in general?

Maybe then mathematics is not exact knowledge at all?

In the light of such questions, the problem of the fifth postulate ceased to be a particular problem of geometry.

It has become a fundamental problem in mathematics.
This analysis gives us yet another confirmation of the idea that fundamental discoveries are solutions to fundamental problems.

He also shows that fundamental problems become within the framework of culture, i.e., in other words, fundamentality is historically conditioned.

But within the framework of culture, not only fundamental problems are formed, as a rule, many components of their solution are also prepared in them. From this it becomes clear why such problems are solved precisely in this moment and not at any other time.

Consider again in connection with this the process of creating non-Euclidean geometry. Let us pay attention to the following interesting fragments of the history of research in this area.

The proofs of the fifth postulate of Euclid were carried out for two millennia, but at the same time they were considered a problem of the second kind, i.e. the postulate was represented as a theorem of Euclidean geometry. It was a task with a clearly fixed foundation for its solution.

However, in the second half of the XVIII century. There are studies in which the idea of the unsolvability of this problem is expressed. In 1762, Kugel, publishing a review of research on this problem, came to the conclusion that Euclid was, apparently, right in considering the fifth postulate to be just a postulate.

Regardless of how Kugel felt about his conclusion, his conclusion was very serious, as it provoked the following question: if the fifth postulate of Euclid's geometry is really a postulate, and not a theorem, then what is a postulate? After all, a postulate was considered an obvious position, and therefore not requiring proof. But such a question was no longer a question of the second kind. He already presented a meta-question, i.e. brought thought to the philosophical and methodological level.

So, the problem of the fifth postulate of Euclid's geometry began to give rise to a very special kind of thinking.

The translation of this problem into Mstaurovs gave it an ideological sound.

It has ceased to be a problem of the second kind.

Another historical moment. Very interesting are the studies carried out in the second half of the 18th century. Lambert and Saccheri. Kant knew about these investigations, and he accidentally spoke about the hypothetical status of geometric positions. If things-in-themselves are characterized geometrically, then why not them posed the question of Kant, not to obey any other geometry, different from Euclidean? The course of Kant's reasoning was inspired by the ideas of the abstract possibility of non-Euclidean geometries, which were expressed by Lambert and Saccheri.

Saccheri, trying to prove the fifth postulate of Euclid's geometry as a theorem, i.e. looking at it as an ordinary problem, he used a method of proof called "proof by contradiction."

Saccheri's line of reasoning was probably the following. If we take instead of the fifth postulate a statement that is opposite to it, combine it with all other statements of Euclidean geometry and, deriving consequences from such a system of initial positions, we arrive at a contradiction, then we will thereby prove the truth of the fifth postulate.

The scheme of this reasoning is very simple. It can be either A or not-D, and if all the other postulates are true and we allow not-A, but get a lie, then it is A that is true.

Using this standard method of proof, Saccheri began to develop a system of consequences from his assumptions, trying to discover their inconsistency. Thus, he deduced about 40 theorems of non-Euclidean geometry, but did not find any contradictions.

How did he assess the current situation? Considering the fifth postulate of Euclid's geometry to be a theorem (i.e., a problem of the second kind), he simply concluded that in his case the method of "proof by contradiction" does not work. So, looking at this problem as the problem of the second n^»i. he, having new geometry in his hands, could not correctly interpret the situation.

Two conclusions follow from this:

First, in a certain sense, the new geometry appeared in culture already before non-Euclidean geometry was discovered.

Secondly, it is precisely the correct assessment of the problem of the fifth postulate, i.e. its interpretation as a problem of the first, and not of the second kind, allowed N.I. Lobachevsky, F. Gauss and J. Bolyai to come to a solution to the problem and create a non-Euclidean geometry. It was necessary to understand the very possibility of creating such geometries. Saccheri allowed it only as a logical one, taking a constructive step in solving the problem of the Euclidean postulate in the traditional style. But he didn't take her seriously at all. As well as after him Kant, who believed that non-Euclidean geometries are impossible, although logically admissible.

Thus, history not only prepares the problem, but also largely determines the direction and possibility of its solution.

Consider the Copernican revolution from this perspective.

As is well known, it was not Copernicus who discovered the heliocentric system. It was created by Aristarchus in antiquity. Maybe Copernicus didn't know about it? Yes, nothing like that! He knew and referred to Aristarchus.

But then why are they talking about Copernicanism?

The fact is that Copernicus transferred the already known model to a completely new cultural environment, realizing that it could be used to solve a number of problems. This was precisely the essence of his revolution, and not at all in the creation of a heliocentric system.

5. DISCOVERY OF MENDEL

Let us now consider the question of the cultural preparation of discoveries, using the example of Mendel's discovery.

In this discovery, there are not only the so-called Mendel's laws, which represent the empirical patterns that are usually talked about, but also a system of very important theoretical provisions, which, in fact, determines the significance of Mendel's discovery.

Moreover, the empirical regularities, the establishment of which is attributed to Mendel, were not established by him at all. They were known even before him and were studied by Sazhre, Knight, Nodsn. Msidsl, sibsshsppi, “ilki clarified them.

It is also significant that his discovery had methodological significance. For biology, it provided not only a new theoretical model, but also a system of new methodological principles, with the help of which it was possible to study the very complex phenomena of life.

Mendel suggested the presence of some elementary carriers of heredity, which can be freely combined during cell fusion during fertilization. It is this combination of the rudiments of heredity, which is carried out at the cellular level, that gives different types hereditary structures.

Such a theoretical model includes a number of very important ideas.

Firstly, this is the selection of elementary carriers at the cell level.

Justifying such a selection, Mendel obviously relied on the theory of the cellular structure of living matter. She was very important to him. Mendel became acquainted with its main provisions in the course of Unger's lectures at the University of Vienna. Unger was one of the innovators in the use of physicochemical methods in the study of the living. At the same time, he believed that these studies should reach the level of the cell. - Secondly, Mendel believed that the laws governing the carriers of heredity are as certain as the laws that govern physical phenomena.

Obviously, here Mendel proceeded from a general worldview that was deeply rooted in the culture of that time, i.e. installations about the laws of nature, which extended to the phenomena of heredity.

Thirdly, Mendel implemented in his studies the general ideal of physical knowledge of the world, according to which one should identify an elementary object, find the laws governing its behavior, and then, based on this knowledge, construct more complex processes, describing and explaining their features.

Fourth, Mendel suggested that laws; governing its elementary carriers are probabilistic laws. For 1865, in which he published his discovery, this was a very new idea. After all, it was at that time that probabilistic representations began to be introduced into physics. A little earlier - in the 1930s - the character-by-line description of the phenomena of reality entered the culture thanks to the works of Quetelet on social statistics. Mendel borrowed the ideas of probabilistic description from social statistics.

In addition, Mendel assumed that his theory would explain heredity only if it was confirmed by experience. This was very important, especially since in the science of that time the phenomena of life, like many other phenomena, were explained in a speculative way.

But how could the comparison be made?

this theory with experience in biology?

For Mendel, a new problem arose here. The comparison was to be carried out on the basis of statistical processing of elementary data. It was the inability to process statistical material, according to Mendel, that did not allow, for example, Naudin to establish the correct quantitative relationships in the splitting of features.

Finally, it should be noted that the Mendelian experimental approach in biology was planned for a very long time. Mendel himself conducted experiments for about ten years, realizing a pre-planned research program.

The success of his experiments was due primarily to the choice of material. Mendelian laws of heredity are very simple, but actually appear on a small number of biological objects. One of these objects is peas, for which, moreover, it was necessary to choose clean lines. Mendel worked on this selection for two years. He clearly imagined, following the physical ideal, that the object he chooses should be simple, completely controllable in all its changes. Only then can precise laws be established. Of course, Mendel did not imagine for sure all the details that he would receive in the future.

But there is no doubt that all his studies were clearly planned and based on a system of theoretical views on the patterns of inheritance.

In principle, he could not take even one step along this path if he did not have sufficient theoretical ideas developed in advance.

Thus, Mendel's openness includes not just the discovery of a set of empirical patterns that were not so much discovered by him as clarified.

The main thing is that Mendel was the first to build a theoretical model of the phenomena of heredity, which was based on the selection of its elementary carriers, subject to probabilistic laws.

The very system of ideas of a methodological nature, connected with the assessment of the role of statistics, probability, and the plan for the implementation of empirical research, deserves special attention.

Mendel's discovery was not accidental.

It, kah and other fundamental discoveries, is due to the peculiarities of the culture of his time, both European and national.

But why was this outstanding discovery made precisely by Mendel the monk, and why precisely in Moravia, essentially the periphery of the Austrian Empire?

Let's try to answer these questions.

Mendel was a monk of the Augustinian monastery in Brio, which concentrated within its walls a multitude of thoughtful and educated people. Thus, the abbot of the monastery F.C.Napp is considered an outstanding figure of Moravian culture. He actively contributed to the development of education in his region, was interested in natural science and dealt, in particular, with selection problems.

Among the monks of this monastery was T. Bratranek, who later became the rector of Krakow University. Bratranek was attracted by the natural philosophical ideas of Goethe, and he wrote works in which he put the evolutionary ideas of Darwin and the great German poet.

Another monk of this monastery, M. Klatzel, was passionately fond of Hegel's teaching on development. He was interested in the patterns of formation of plant hybrids, and conducted experiments with peas. It was from him that Mendel inherited the site for his experiments. For his liberal views, Klatzel was expelled from the monastery and went to America.

P. Krzhizhkovsky, a reformer of church music, who later became a teacher of the famous Czech composer L. Janacek, also lived in the monastery.

Mendel from childhood showed great ability in the study of spiders. The desire to receive), a good image: Yuianis and get rid of heavy material worries led him in 1843 to the monastery. Here, while studying theology, he at the same time showed an interest in agriculture, horticulture, and viticulture. In an effort to obtain systematic knowledge in this area, he listened to lectures on these subjects at the Philosophical School in Brno. As a very young man, Mendel taught Latin, Greek, and German languages, as well as a course of mathematics and geometry in the gymnasium of the city of Znojmo. From 1851 to 1853 Mendel studied natural Sciences at the University of Vienna, and from 1854, for 14 years, he taught physics and natural history at the school.

In his letters, he often called himself a physicist, showing great affection for this science. Until the end of his life, he retained “it to various physical phenomena. But in particular he was occupied with the problems of meteorology. When he was “taken as a helper of a mopasgy-rya, he no longer had time to conduct his biological experiments, and besides, his eyesight deteriorated. But he was engaged in meteorological research until his death, and at the same time he was especially fond of their statistical processing.

Already these facts from the life of Mendel give us an idea of why Mendel the monk was able to make a scientific discovery. But why did this discovery take place in Moravia, and not, say, in England or France, which at that time were the undoubted leaders in the development of science?

During Mendel's lifetime, Moravia was part of the Austrian Empire. Her indigenous people was subjected to severe oppression, and the Habsburg monarchs were not interested in the development of Moravian culture. But Moravia was an extremely favorable country for the development of agriculture. Therefore, in the 70s of the XVIII century. The Habsburg ruler Maria Theresa, carrying out economic reforms, ordered the organization of agricultural societies in Moravia. In order to collect more products from the land, everyone who manages the economy was even ordered to take exams in the basics of agricultural sciences.

As a result, agricultural schools began to be created in Moravia, and the development of agricultural sciences began. In Moravia, a very significant concentration of agricultural societies has developed. There were probably more of them than in Ashlia. It was in Moravia that “the first people started talking about selective science, which was introduced into practice. Already in the 20s of the XIX century. in Moravia, local breeders actively use the hybridization method to develop new breeds of animals and especially new varieties of plants. The problems of breeding science became colossally acute just at the turn of the 18th and 19th centuries, since the rapid growth of industry and the urban population required the intensification of agricultural production.

In this situation, the discovery of the laws of heredity was of great practical importance. This problem was also acute in theoretical biology. 19th century scientists knew quite a lot about the morphology and physiology of the living. Thanks to the theory natural selection Charles Darwin managed to understand the essence of the process of evolution of life on Earth. However, the laws of heredity remained unknown.

In other words, a clearly expressed problem situation of a fundamental nature has been created.

The remarkable and even surprising results obtained by Mendel were also rooted in the culture of that time.

In the 1st sense, the idea of the probabilistic nature of the laws of heredity is especially indicative. It was borrowed by Mendel from social statistics, which, thanks primarily to the work of A. Quetelet, attracted general attention at that time. The practice of statistical processing of empirical material, both in social statistics and in physics, which was expanding at that time, undoubtedly contributed to its spread to the field of life phenomena.

At the same time, the desire to isolate the elementary units of inheritance and, on the basis of their interaction, to explain the features of the process of inheritance as a whole represented a clear adherence to the physical methodology of cognition.

This ideal was clearly formulated already at the beginning of the 19th century. And he actively penetrated into all sciences. Incidentally, following him, in biology has become more widely used physical and chemical methods. Herbert's research in psychology was directly guided by this ideal. O. Comte was guided by it, substantiating the need to create sociology. Mendel followed the same path in studying the phenomena of heredity.

The idea to construct a scientific theory of inheritance at the cell level could only have arisen in the middle of the 19th century.

Finally, if we talk about such details as the choice of the object of study itself - peas, then the properties of splitting, dominance of this object were discovered and late XVIII- early 19th century There are a number of works that describe these properties, which attracted the attention of Mendel.

In short, here, as in other examples, we see that fundamental discoveries are the solution to a fundamental problem.

They are always historically prepared.

Prepared is not only the problem itself, but also the components of its solution.

But this should not create the illusion that geniuses are not needed at all for such discoveries. Awareness of the fundamental problem, finding real ways to solve it require a huge intellect, broad education, purposefulness, which allow the scientist to feel the breath of the times better than others.

Among the diverse types of scientific discoveries, a special place is occupied by fundamental discoveries that change our ideas about reality in general, i.e. worldview in nature.

1. Two kinds of discoveries

We will deal mainly with the discussion of problems associated with the solution of problems of the first kind, but first we will clarify our ideas about how problems of the second kind are solved.

How are we going to solve this school problem?

Here it is - a beautiful and psychologically interesting solution to the problem.

In this example, the following is important.

Of course, the above task is very simple. It is needed only in order to generally outline the type of problems of the second kind. But among such problems there are immeasurably more complex ones, the solution of which is of great importance for the development of science.

Consider, for example, the discovery of a new planet by Le Verrier and Adamsom. Of course, this discovery is a great event in science, especially considering how it was done: