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Imre Lakatos Philosophy. Philosophy of Science I. Lakatos. Methodology of scientific research programs

Lakatos (1922-1974) is the third surname of this scientist. During World War II, he was forced to change his Jewish surname Lipschitz to the Hungarian Molnar, and later took the surname Lakatos. In 1947, a Hungarian scientist was arrested on charges of revisionism and sentenced to three years in the camps. In 1956 he emigrated to Austria, and then to Great Britain, where from 1960 he worked at the Department of Philosophy at the London School of Economics. There Imre Lakatos met K. Popper, whose ideas he successfully developed and modernized in his philosophical and methodological works.
According to the philosopher himself, his theory of research programs is a modernized version of K. Popper's falsificationism (I. Lakatos calls his methodology of research programs "refined falsificationism"). Just like Popper, Lakatos considers the development of science from the point of view of the logic of science, i.e., he recognizes internal (rational in nature) factors as the main "engine", rejecting Kuhn's assertion about the decisive role of socio-psychological factors.
I. Lakatos considers as a functional unit of scientific knowledge not a theory, but a number of interrelated theories continuing each other. This sequence is called the research program. I. Lakatos bases his understanding of scientific criteria on the concept of theoretical progress. A scientific program may not be a separate theory, but a research program - provided that it has the ability to predict new facts. The ability of a program to predict new facts I. Lakatos calls it heuristic power. The program achieves theoretical progress if, as a result of its application, it becomes possible to expand the empirical content, that is, to predict new facts. If the application of the program leads to the actual discovery of the predicted facts, then there is also empirical progress. Otherwise, if with an increase in the number of theories there is no increase in the facts explained, we are dealing with a regressive shift in the research program.
The development of a research program is governed by two main groups of methodological rules: some of them describe methods to be avoided (negative heuristic), others indicate the most desirable research paths (positive heuristic).
The main rule of the negative heuristic establishes a list of basic hypotheses ("hard core") that cannot be questioned within the framework of this program. The hard core of the program is, in fact, the prism through which scientific facts are viewed.
The hard kernel can be abandoned only if the program can no longer predict previously unknown facts, i.e. if it becomes theoretically regressive; the hard core dies only together with the program itself.
A positive heuristic consists of secondary arguments and assumptions that are needed in order to refine and modify the program. These arguments form the "protective belt" of the program, since they adapt it to a specific empirical reality - this is how those facts are explained.
you (anomalies), which can refute the statements included in the "core", that they turn from anomalies into another confirmation of the program.
Positive heuristics consists in building models (as defined by I. Lakatos, “a model is a set of boundary conditions (perhaps, together with some “observational” theories), which are known to be replaced in the course of further development of the program.” Theories and the techniques included in the "protective belt" are not once and for all established and can be accepted and rejected depending on how well they perform their adaptive function.
I. Lakatos gives the following example: if an astronomer who works within the framework of Newtonian theoretical mechanics has calculated the trajectory of some newly discovered planet, and if observations of it show that the planet does not move along this trajectory at all, the astronomer will not conclude that his observations refute Newton's theory - this is forbidden by the rules of negative heuristics, Newton's theory is part of the hard core and cannot disappear from the system without destroying it. Most likely, our hero will try to explain the behavior of the planet by some unaccounted for factors, for example, the presence of another planet, whose gravity affects the movement of the first. This is a manifestation of the positive heuristic.
The same example can be used to explain the concept of theoretical progress. It will take place if scientists really discover a hypothetical second planet - it turns out that the research program was able to predict the discovery of a new fact. If the planet is not detected, the next adaptive hypotheses will come into play. They can assert, for example, that the planet is hidden by a cloud of cosmic dust, that it cannot be seen with a modern telescope, etc. If these hypotheses turn out to be untenable in the end, then we are dealing with a regressive shift in the research program.
The elimination of the research program, according to I. Lakatos, occurs not because of the appearance of facts that contradict this theory (as K. Popper believed), but because of its inability to explain and turn into its confirmation (in other words, the theory exhausts its heuristic force). Such a program can easily be superseded by another one that can explain the anomalies that its predecessor was powerless to face. In addition, the new program must explain the unrefuted content of the previous one. The repression of scientific theory, according to Lakatos, does not occur immediately after the discovery of a fatal anomaly - there is no question of any falsification until a better program appears.
L. R. Khamzina Regular revised article

Imre Lakatos
hung. Imre Lakatos
Imre Lakatos Imre Lakatos
Date of Birth:
Place of Birth:	Debrecen
Date of death:
Place of death:

Imre Lakatos(in Hungarian Lakatosh- hung. Imre Lakatos, real name and surname Avrum Liposhits; November 9, 1922, Debrecen - February 2, 1974, London) - English philosopher of science of Hungarian origin.

Biography

Sharing Popper's belief in a universal criterion of scientific rationality, in contrast to his contemporaries T. S. Kuhn and M. Polanyi, Lakatos developed Popper's proposed methodological research program with more emphasis on rationally reconstructed history using concrete examples. According to Lakatos, “The philosophy of science without the history of science is empty; the history of science without philosophy is blind.”

Philosophy of Science

The main achievement of Lakatos in the philosophy of science is the postulation of research programs as a key to understanding the progress of theoretical science. Unlike Popper, who believed that the criterion of falsifiability applied to individual theories, Lakatos considered research programs that included a series of theories and contained both falsifiable and non-falsifiable elements, more suitable for assessing the durability of scientific theories and the rationality of their rejection.

Lakatos described science as a competitive struggle of "research programs" consisting of "hard core" a priori accepted in the system of fundamental assumptions that cannot be refuted within the program, and "safety belt" auxiliary hypotheses ad hoc, modified and adapted to the counterexamples of the program. The evolution of a specific program occurs due to the modification and refinement of the "safety belt", while the destruction of the "hard core" theoretically means the cancellation of the program and its replacement with another, competing one.

The main criterion for the scientific nature of the program Lakatos calls the increase in factual knowledge due to its predictive power. While the program gives an increase in knowledge, the work of a scientist within its framework "rational". When the program loses its predictive power and begins to work only on the "belt" of auxiliary hypotheses, Lakatos prescribes to abandon its further development. However, it is pointed out that in some cases the research program experiences its own internal crisis and again gives scientific results; thus, the "loyalty" of the scientist to the chosen program, even in times of crisis, is recognized by Lakatos "rational".

Method of rational reconstructions

The method of rational reconstructions of the history of science is applied by Lakatos in the book Evidence and refutation to the history of the proofs of the Descartes-Euler-Cauchy theorem on the relationship between the number of vertices, edges and faces of an arbitrary polyhedron. At the same time, in the footnotes, Lakatos gives a broader picture of the history of mathematics, especially the history of calculus and mathematics foundation programs in the 19th and early 20th centuries. Lakatos discusses the history of mathematics as a chain in which

“the verification of an ordinary proof is often a very delicate undertaking, and it takes as much intuition and happiness to attack a 'mistake' as it does to stumble upon a proof; discovering "errors" in informal proofs can sometimes take decades, if not centuries. Informal quasi-empirical mathematics does not develop as a monotonous increase in the number of undeniably proven theorems, but only through the continuous improvement of conjectures through reflection and criticism, through the logic of proofs and refutations.

The book itself is not written in the form of a historical study, but in the form of a school dialogue. Using the dialogic method, Lakatos artificially constructs a problem situation in which the concept of the "Eulerian polyhedron" is formed. Rational reconstruction by Lakatos does not reproduce all the details of real history, but is created specifically for the purpose of rationally explaining the development of scientific knowledge.

The attitude of philosophers and scientists to the ideas of Lakatos was ambiguous. Despite the objections of some of them, Lakatos' research programs have become part of the modern philosophy of science.

Major works of Lakatos

"Proofs and rebuttals: the logic of mathematical discoveries" (1976) "Philosophical articles" (vol. 1 - "Methodology of research programs", vol. 2 - "Mathematics, science and epistemology", 1978).

Links to essays

Lakatos I. Proofs and rebuttals. How theorems are proved. Per. I. N. Veselovsky. Moscow: Nauka, 1967.
Lakatos I. Falsification and Methodology of Research Programs. M.: Medium, 1995.
Lakatos I. History of science and its rational reconstructions // App. to the book: Kuhn T. The structure of scientific revolutions. M.: AST, 2001.

ca:Imre Lakatos cs:Imre Lakatosfa:ایمره لااتوش fi:Imre Lakatoshr:Imre Lakatos hu:Lakatos Imrenl:Imre Lakatos no:Imre Lakatos pl:Imre Lakatos pt:Imre Lakatos ro:Imre Lakatos sk:I :Imre Lakatos Notification: The preliminary basis for this article was a similar article in http://ru.wikipedia.org , under the terms of CC-BY-SA, http://creativecommons.org/licenses/by-sa/3.0 , which was subsequently changed, corrected and edited.

Notification: The preliminary basis for this article was the article

lakatos (lakatos) imre

(1922 -1974) Hung.-Brit. philosopher and historian of science. Genus. in Hungary, during the Second World War he participated in the anti-fascist resistance. During the Nazi period, he changed his real name (Lipschitz) to Molnar (Melnik), and during the communist rule to the more proletarian Lakatosh (Joiner). He worked on his dissertation on the philosophy of mathematics at Moscow University. In the late 1940s he was accused of revisionism and spent more than three years in prison. In 1956 he emigrated to Austria, then to England. From 1960 he taught at the London School of Economics, became a student and follower of Popper and made an important and striking contribution to the philosophy and methodology of critical rationalism through his work. In his early works L. offered an original version of the logic of conjecture and refutation, applying it as a rational reconstruction of the growth of knowledge in mathematics XVII-XIX centuries. Partially reviewing their original methodological guidelines, L. later developed a universal concept for the development of science, based on the idea of competing research programs. Methodology L. considers the growth of "mature" theoretical science as a change of research programs, representing a continuously connected sequence of theories. Each theory of the program (with the exception of the original one) arises as a result of adding auxiliary hypotheses to the previous theory. The continuity of the program is subject to special regulatory rules. Some of these rules prescribe which paths to follow in the course of further research ("positive heuristic"), others tell which paths to avoid here ("negative heuristic"). An important structural element of research programs is a "hard core" that combines conditionally unrefuted fundamental assumptions specific to a given program. The "negative heuristic" forbids in the process of checking research programs to direct the modus tollens rule of classical logic to this "hard core" when faced with anomalies and counterexamples. Instead, she proposes to invent auxiliary hypotheses that form a "safety belt" around the "hard core" of the research program. This protective belt can be modified or even completely replaced when confronted with facts that contradict the program. For its part, "positive heuristics" includes ideas and recipes on how to modify or develop a theory that does not withstand empirical testing, how to modify or refine the "safety belt", what new models need to be developed to expand the scope of the program.

According to L., in the development of research programs can be divided into two main stages progressive and degenerate. At the progressive stage, "positive heuristics" can stimulate the development of auxiliary hypotheses that expand the empirical and theoretical content of the program. However, later on, having reached the "saturation point", the development of the research program slows down sharply. The number of ad hoc hypotheses and incompatible facts is increasing, internal conceptual contradictions, paradoxes, etc. appear in it. Nevertheless, the presence of such symptoms cannot yet serve as an objective basis for refusing the research program. Such a basis, according to L., appears only from the moment of the emergence of a rival research program that is able to explain the empirical success of its predecessor, as well as theoretically predict previously unknown facts that receive empirical confirmation.

L. attached particular importance to the creation of models for the development of scientific and theoretical knowledge of historical and scientific research. His famous aphorism is: "The philosophy of science without the history of science is empty; the history of science without the philosophy of science is blind." The methodological analysis carried out in order to identify the scientific nature of a particular research program, falls, in his opinion, into the following stages: the promotion of rational reconstruction; comparison of this rational reconstruction with historical and scientific data on a particular period in the development of the corresponding science; criticism of rational reconstruction for its lack of historicity and of real history for its lack of rationality. The concept of L. is one of the best achievements of modern philosophy and methodology of science. According to his philosophical attitudes, he was a consistent supporter of rationalism, which was reflected in his intense controversy in the 60-70s with Kuhn, Feyerabend and a number of other philosophers of science.

I. P. Merkulov

Evidence and refutation. M, 1967; History of science and its rational reconstructions // Structure and development of science. M., 1978; Falsification and methodology of research programs. M, 1995; The Changing Logic of Scientific Discovery. L., 1973.

The philosophical concept of I. Lakatos was formed under the influence of the teachings of K. Popper. Sharing the position of the latter in many respects, Lakatos believes (although he does not explicitly mention this anywhere) that Popper's doctrine needs a significant addition. It is about the following. Having proposed the principle of falsification, Popper, according to Lakatos, did not take care to develop mechanism falsification. And the absence of such a mechanism can negate the very fruitful idea of falsification.

In his work Methodology of Research Programs, Lakatos draws the reader's attention to the fact that no scientific theory arises simultaneously (the same can be attributed to any fundamental principle that unites several theories around itself). In the process of its formation, the theory goes through several stages. A theory (or set of interrelated theories) in development is what Lakatos calls a "research program." A scientific research program is a sequence characterized by "continuity, connecting ... elements into a single whole".

Since it is customary in our textbook to use the terms "empiricism" and "theory", in order not to introduce additional difficulties, we will not deviate from this tradition - and we will replace the Lakatosian term "program" in our presentation with the term "theory", bearing in mind that Lakatos is primarily interested in theory as a living, developing organism.

Suppose that any scientific theory can be written down as economically as possible. This means that it is possible to formulate such a series of interrelated statements and formulas that will clearly express the main idea of this theory. For example, Newtonian mechanics in its brief formulation consists of the law of universal gravitation and three laws of dynamics. Such a summary of the theory, in the terminology of Lakatos, is called solid core theory.

The core of the theory must be treated with the utmost care; under no circumstances make the slightest change to it. This means that no matter what new facts are discovered in that area of nature or society, the explanation of which this theory claims, the core cannot be replaced in any case. For such prohibition of changing the kernel, Lakatos introduces a special term - negative heuristics. The negative heuristic is a kind of "protective belt" around the kernel.

But if the essence of the theory cannot be changed, then how should the theory react to emerging circumstances that do not fully agree with it (internal contradictions of the theory, facts that contradict it)? The theory must have the so-called positive heuristics, i.e. it must be able to develop auxiliary hypotheses that can transform the content of the theory in such a way that the core remains unchanged, and new facts organically enter the empirical basis of this theory. For example, for the scheme of the solar system proposed by N. Copernicus, where the "core" is the idea of the rotation of the planets around the Sun, various options for the trajectories of the planets are quite acceptable. It was this circumstance that allowed I. Kepler, having made some changes in the theory of Copernicus (known to us as Kepler's laws) and without affecting its core, to give the heliocentric system a logically harmonious and scientifically substantiated form. Thus, positive heuristics are the possibilities of its modification, provided in advance in the theory, which are safe for the integrity of the solid core of the theory.

In general, the research program looks like this (Fig. 2.2):

1) the solid core of the theory - a brief formulation of its main ideas;
2) negative heuristics - a ban on changing the core of the theory;
3) positive heuristics - the possibility of such changes in the theory that will not affect its core.

Rice. 2.2. Structure of the research program

Everything that has been said so far looks somewhat paradoxical in the light of Lakatos' main intention - to develop a mechanism for falsifying a theory. While the mechanism of its infinite preservation turns out.

But the whole point is that this is not yet the actual mechanism for changing theories, but rather the clarification and systematization of the real process of formation and the mode of existence of a scientific theory. Very often, a scientist (or a team of scientists) who has created a new concept defends its main idea in every possible way, correcting, if necessary, its peripheral areas. Lakatos formulates in a rational way the peculiarities of the scientific process, implicitly believing that science develops precisely “programmatically” and nothing needs to be changed here (and it is impossible), but only these rules need to be clearly understood and observed. You also need to be aware of the fact that "voluntarily" theory does not "cancel" itself.

A theory can only be replaced by another theory, formulated independently of the first one, a competing theory.

What requirements should the competitor theory (hereinafter - T2) meet?

1. T2 must have a solid core absolutely different from the first theory (hereinafter - Tx).
2. T2 must have a negative heuristic (the negative heuristic is the same for all theories).
3. T2 must have a positive heuristic other than that of G.
4. T2 should explain all the facts that T1 unable to explain (i.e. T2 should have a more powerful empirical base than Gj).
5. T2 should predict all those facts that G1 predicts, and, in addition, predict facts (or indicate the direction of their search) that G cannot predict (i.e. T2 should have more powerful heuristic power).

If the requirements listed in these five points are met, then T2 replaces T1 and becomes the leading theory in a certain field of knowledge.

Now let's return to the question posed at the beginning of the conversation about Lakatos: how is the theory falsified? The answer will be this: the theory is falsified by facts that do not contradict it (there is no such fact that the theory could not "digest"), but another a theory that offers a different conception of reality and is confirmed by a large set of facts, and this set (as part of it) includes facts that support the falsifiable theory.

Refers to "Theory of the Universe"

Imre Lakatos. Methodology of research programs

Imre Lakatos(1922-1974), born in Hungary, prepared a dissertation on philosophical questions of mathematics at Moscow University. For dissident views in the late 40s he spent two years in prison. After the Hungarian events of 1956, he emigrated, worked at the London School of Economics and Political Science, where he became the most prominent among Popper's followers. Lakatos was called the "Knight of Rationality" because he defended the principles of critical rationalism and believed that most processes in science admit of a rational explanation. Lakatos wrote small, but very capacious works. You can get acquainted with his views in the books "Proofs and Refutations" (M., 1967) and "Falsification and Methodology of Research Programs" (M., 1995) published in Russian.

He is one of the most profound and consistent critics of Kuhn's concept of paradigm shift, and opposes the almost theological sense of the scientific paradigm expressed by Kuhn. Lakatos also developed one of the best models of the philosophy of science - methodology of research programs.

1. Three types of falsificationism

Science, according to Lakatos, is and should be a competition between competing research programs. It is this idea that characterizes the so-called refined methodological falsificationism developed by Lakatos in line with Popper's concept. Lakatos tries to soften the sharpest corners of Popper's philosophy of science. He identifies three stages in the development of Popper's views: Popper 0 - dogmatic falsificationism, Popper 1 - naive falsificationism, Popper 2 - methodological falsificationism. The last period begins in the 50s and is associated with the development of a normative concept of the growth and development of knowledge based on comprehensive criticism. The first sees science as a process marked out by solid constructions and infallible falsifications (such ideas were promoted by A. Ayer). Nevertheless, Popper showed the fallacy of such a position, because the empirical basis of science is unstable and indefinite, and therefore there can be no talk of fixed protocol sentences and refutations that are not revised in principle.

That our rebuttals can also be fallacious is confirmed by both logic and the history of science.

Methodological falsificationism corrects the error of the dogmatists, showing the fragility of the empirical base of science and the means of hypothesis control it offers (this is shown by Popper in "The Logic of Scientific Discovery"). However, Lakatos continues, methodological falsificationism is not enough. The picture of scientific knowledge presented as a series of duels between theory and facts is not entirely correct. In the struggle between the theoretical and the actual, Lakatos believes, there are at least three participants: facts and two competing theories. It becomes clear that a theory becomes obsolete not when a fact that contradicts it is announced, but when a theory that is better than the previous one declares itself. Thus, Newtonian mechanics became a fact of the past only after the advent of Einstein's theory.

In an effort to somehow mitigate the extremes of methodological falsificationism, I. Lakatos put forward the concept of research programs as a weakening mechanism of evolutionary epistemology.

2. Research programs

I. Lakatos focuses not on theories as such, but talks about research programs. The research program is a structural-dynamic unit of his model of science. To understand what a scientific search program is, think about the mechanism of Descartes or Newton, about the evolutionary theory of Darwin or about Copernicanism. A successive change of theories arising from one core occurs within the framework of a program with an irrefutable methodology that shows its value, fruitfulness and progressiveness in comparison with another program. Overcome by childhood illnesses, theory needs time for its development, formation and strengthening.

Thus, the history of science appears, according to Lakatos, as the history of competition between research programs. This approach highlights the relationship between different epistemologies and historiography of science, as well as the evolutionary moment of scientific inquiry.

“Some philosophers,” writes I. Lakatos, “are so preoccupied with solving their epistemological and logical problems that they never reach the level at which they could be interested in the real history of science. If the actual history does not meet their standards, they may with desperate boldness they will propose to start anew the whole work of science.

According to I. Lakatos, any methodological concept should function as a historiographic one. Its most profound assessment can be given through criticism of the rational reconstruction of the history of science that it offers.

This is the difference between the position of Lakatos and the theories of Kuhn and Popper. Lakatos accuses Popper of being unhistorical ("History of Science and Its Rational Reconstructions"), he sees in his principle of falsifiability a logical ambiguity that distorts history and adapts it to his theory of rationality.

On the other hand, writes Lakatos in his work "Falsification and Methodology of Scientific Research Programs"(1970), according to Kuhn's theory, the scientific revolution is irrational, one can see in it only the material of adaptation to the psychology of the crowd. In mystical conversion from one paradigm to another, according to Kuhn, there are no rational rules, and therefore Kuhn constantly falls into the sphere of social psychology of discovery. Scientific mutations are starting to look like a kind of religious conversion. Nevertheless, Lakatos himself remains within the problems and atmosphere of Popper's falsificationism. Kuhn's influence is also quite obvious (take, for example, the ideas of the "dogmatic function" of scientific research and "progress through revolutions"). Yet his arguments are more often free from prejudice.

I. Lakatos develops his own concept, quite close to Kuhn's, of the methodology of scientific knowledge, which he calls the methodology of scientific research programs. It is used by him not only to interpret the features of the development of science, but also to evaluate the various competing logics of scientific research.

According to I. Lakatos, the development of science is a competition of research programs, when one research program replaces another.

The essence of the scientific revolution lies in the fact that it is necessary to compare with empiricism not one isolated theory, but a series of successive theories linked together by common fundamental principles. He called this sequence of theories research program.

Therefore, the fundamental unit for evaluating the process of developed science is not a theory, but a research program.

This program has the following structure. It includes " hard core ", which includes fundamental provisions (non-falsifiable hypotheses) that are irrefutable for the supporters of the program. That is, this is what is common to all its theories. This metaphysics programs: the most general ideas about the reality that the theories included in the program describe; basic laws of interaction of elements of this reality; the main methodological principles associated with this program. For example, the rigid core of the Newtonian program in mechanics was the idea that reality consists of particles of matter that move in absolute space and time in accordance with the three well-known Newtonian laws and interact with each other in accordance with the law of universal gravitation. Scientists working in a certain program accept its metaphysics, considering it adequate and unproblematic. But in principle there may be other metaphysics that define alternative research programs. So, in the XVII century. Along with Newton's there was a Cartesian program in mechanics, the metaphysical principles of which differed significantly from Newton's.

Thus, the core can be used to judge the nature of the entire program.

The program includes negative heuristic , which is a set of auxiliary hypotheses that protect its core from falsification, from refuting facts. All ingenuity is directed to its articulation and development of hypotheses supporting the core (the so-called "protective belt"). This "protective belt" of the program bears the fire of critical arguments. The ring of auxiliary hypotheses is designed to restrain the attacks of control probes and to protect and consolidate the core in every possible way. That is, they are a kind of methodological rules, some of which indicate which paths should be avoided.

Positive heuristic is a strategy for selecting priority problems and tasks that scientists must solve. The presence of positive heuristics allows for a certain time to ignore criticism and anomalies and engage in constructive research. With such a strategy, scientists have the right to say that they will still get to the facts that are incomprehensible and potentially disproving the program and that their existence is not a reason to abandon the program.

Falsifications, i.e. theoretical criticism and empirical refutation, only the hypothesis of the "protective belt" is subjected. By general agreement, it is forbidden to falsify a hard core. The center of gravity in the methodology and research programs of Lakatos shifts from the refutation of many competing hypotheses to falsification, and at the same time to the verification and confirmation of competing programs. At the same time, the elimination of individual hypotheses of the protective belt leaves the hard core of the program intact and intact.

According to Lakatos, research programs are the greatest scientific achievements and can be evaluated on the basis of a progressive or regressive shift of problems. Those. the research program can develop progressively and regressively. The program progresses until the presence of a rigid core allows us to formulate more and more hypotheses of the “protective layer”. When the production of such hypotheses weakens and it turns out to be impossible to explain new, and even more so to adapt anomalous facts, the regressive stage of development sets in. Those. in the first case, its theoretical development leads to the prediction of new facts. In the second, the program only explains new facts predicted by a competing program or discovered by accident. The research program experiences the greater difficulties, the more its competitor progresses, and vice versa, if the research program explains more than the competing one, then it displaces the latter from the circulation of the community. This is due to the fact that the facts predicted by one program are always anomalies for another.

That is why the development of a different research program (for example, Newton) takes place in a "sea of anomalies" or, like Bohr, occurs on unrelated grounds. When subsequent modifications of the "protective belt" do not lead to the prediction of new facts, the program shows itself to be regressive.

I. Lakatos emphasizes the great sustainability of the research program.

"Neither the logical proof of inconsistency, nor the verdict of scientists about an experimentally discovered anomaly, can destroy the research program with one blow."

Those. Unlike Popper's hypotheses, which are struck to death by criticism or experiment, Lakatos' "programs" not only live long, but also die a long and painful death, since the protective belt is sacrificed for the sake of preserving the core.

A research program succeeds if it successfully solves problems, and it fails if it fails to solve these problems.

As part of a successful program, it is possible to develop more and more advanced theories that explain more and more facts. That is why scientists tend to work steadily positively within such programs and allow a certain dogmatism in relation to their fundamental principles. However, this cannot continue. Over time, the heuristic power of the program begins to weaken, and the question arises for scientists whether it is worth continuing to work within its framework.

Lakatos thinks scientists can rationally evaluate the possibilities of the program and decide whether to continue or refuse to participate in it (unlike Kuhn, for whom such a decision is an irrational act of faith). To do this, he proposes the following criterion for rational evaluation of the "progress" and "degeneration" of the program.

A program consisting of a sequence of theories T 1 , T 2 ... T n -1 , T n is progressing if:

T n explains all the facts that T n -1 successfully explained;

T n covers a larger empirical area than the previous theory T n -1 ;

Some of the predictions from this additional empirical content of T n are confirmed.

Those. in a progressively developing program, each successive theory must successfully predict additional facts.

If new theories fail to successfully predict new facts, then the program is "stagnant" or "degenerate." Usually such a program only interprets in hindsight the facts that were discovered by other, more successful programs.

Based on this criterion, scientists can determine whether their program is progressing or not. If it progresses, then it will be rational to adhere to it, but if it degenerates, then the rational behavior of the scientist will be an attempt to develop a new program or a transition to the position of an already existing and progressive alternative program. But at the same time, Lakatos says that “it is impossible to curtail a newly emerged research program just because it failed to overcome a stronger rival program ... Until the new program is rationally reconstructed as a progressive self-propulsion of the problem, for a certain time it needs support from a stronger and more established rival program.

Thus, the main value of the program is its ability to replenish knowledge and predict new facts. Contradictions and difficulties in explaining any phenomena - according to I. Lakatos - do not significantly affect the attitude of scientists towards it.

In the geometry of Euclid for two thousand years it was not possible to solve the problem of the fifth postulate.

For many decades, infinitesimal calculus, probability theory, and set theory have been developed on a very contradictory basis.

It is known that Newton could not explain the stability of the solar system on the basis of mechanics and argued that God corrects deviations in the motion of the planets caused by various kinds of perturbations.

Despite the fact that such an explanation did not satisfy anyone at all, except, perhaps, Newton himself, who, as you know, was a very religious person (he believed that his research in theology was no less significant than in mathematics and mechanics), the heavenly mechanics as a whole developed successfully. Laplace managed to solve this problem only at the beginning of the 19th century.

Another classic example.

Darwin could not explain the so-called "Jenkins nightmare", and yet his theory was successfully developed. It is known that the Darwinian theory is based on three factors: variability, heredity and selection. Any organism has variability, which is carried out in an undirected way. Because of this, variability can only in a small number of cases be favorable for the adaptation of a given organism to the environment. Some variability is not inherited, some is inherited. Evolutionary value has inherited variability. According to Darwin, those organisms that inherit these kinds of changes that give them a greater opportunity to adapt to the environment have a great opportunity for the future. Such organisms survive better and become the basis for a new evolutionary step.

For Darwin, the laws of inheritance—how variation is inherited—were crucial. In his concept of inheritance, he proceeded from the idea that heredity is carried out in a continuous manner.

Let's imagine that a white man came to the African continent. The signs of white, including "whiteness", will, according to Darwin, be transmitted as follows. If he marries a black woman, then their children will have half the blood of "white". Since there is only one white on the continent, his children will marry blacks. But in this case, the proportion of "whiteness" will asymptotically decrease and eventually disappear. It cannot have evolutionary significance.

Jenkins expressed such considerations. He drew attention to the fact that positive qualities that contribute to the adaptation of the organism to the environment are extremely rare. And consequently, an organism that will have these qualities will certainly meet with an organism that will not have these qualities, and in subsequent generations the positive sign will dissipate. Therefore, it cannot have evolutionary significance.

Darwin could not cope with this task in any way. It is no coincidence that this reasoning is called "Jenkins' nightmare". Darwin's theory had other difficulties as well. And although Darwin's teachings were treated differently at different stages, Darwinism never died, it always had followers. As you know, the modern evolutionary concept - the synthetic theory of evolution - is based on the ideas of Darwin, connected, however, with the Mendelian concept of discrete carriers of heredity, which eliminates the "Jenkins' nightmare".

Within the framework of the concept of I. Lakatos, the importance of theory and the research program associated with it for the activity of a scientist becomes especially obvious. Outside of it, the scientist is simply not able to work. The main source of the development of science is not the interaction of theory and empirical data, but the competition of research programs in the best description and explanation of observed phenomena and, most importantly, the prediction of new facts.

Therefore, when studying the patterns of development of science, it is necessary to pay special attention to the formation, development and interaction of research programs.

I. Lakatos shows that a sufficiently rich scientific program can always be protected from any apparent inconsistency with their empirical data.

I. Lakatos argues in this style. Let us assume that we have calculated the trajectories of the planets on the basis of celestial mechanics. With the help of a telescope, we fix them and see that they differ from the calculated ones. Would a scientist say in this case that the laws of mechanics are wrong? Of course not. He doesn't even have that thought. He will surely say that either the measurements are inaccurate or the calculations are wrong. He can finally admit the presence of another planet, which has not yet been observed, which causes the planet's trajectory to deviate from the calculated one (this was actually the case when Le Verrier and Adams discovered a new planet).

And suppose that in the place where they expected to see the planet, it would not be there. What would they say in this case? What mechanics is wrong? No, that wouldn't happen. They certainly would have come up with some other explanation for this situation.

These ideas are very important. They allow us to understand, on the one hand, how scientific concepts overcome the barriers that stand in their way, and, on the other hand, why there are always alternative research programs.

We know that even when Einstein's theory of relativity entered the context of culture, anti-Einstein's theories continued to live.

And remember how genetics developed. Lamarck's ideas of the impact of the external environment on the body were defended despite the fact that there were a lot of facts that contradicted this.

A theoretically strong enough idea always turns out to be rich enough to be defendable.

From the point of view of I. Lakatos, one can "rationally adhere to a regressing program until it is overtaken by a competing program, and even after that." There is always hope for temporary setbacks. However, representatives of regressing programs will inevitably face ever-increasing socio-psychological and economic problems.

Of course, no one forbids a scientist to develop the program that he likes. However, society will not support him.

“The editors of scientific journals,” writes I. Lakatos, “will refuse to publish their articles, which in general will either contain broad-based reformulations of their position, or the presentation of counterexamples (or even competing programs) through ad hoc linguistic tricks. Organizations that subsidize science will deny them funding...

"I do not claim," he remarks, "that such decisions will necessarily be indisputable. In such cases, one should rely on common sense."

In his works, Lakatos shows that in the history of science there are very few periods when one program (paradigm) reigns supreme, as Kuhn claimed. Usually in any scientific discipline there are several alternative research programs. That. the history of the development of science, according to Lakatos, is the history of the struggle and change of competing research programs that compete on the basis of their heuristic strength in explaining empirically their facts, anticipating the development of science and taking countermeasures against the weakening of this strength. Competition between them, mutual criticism, alternation of periods of prosperity and decline of programs give the development of science that real drama of scientific research, which is absent in Kuhn's monoparadigm "normal science".

Those. in fact, here I. Lakatos reproduces in other terms, in a more differentiated form, Kuhn's concept of the development of science based on paradigms. However, when interpreting the driving reasons for changing research programs, the specific mechanisms for the development of science, Lakatos does not share Kuhn's views. He sees in science an internal and external history. The internal history of science is based on the movement of ideas, methodology, methods of scientific research, which, according to Lakatos, constitutes the own content of science. External history is the forms of organization of science and the personal factors of scientific research. Kuhn emphasized the great importance of these "external factors", but Lakatos gives them secondary importance.

So far, science is more like a battlefield of research programs than a system of isolated islands. “Mature science consists of research programs that look not so much for new facts as for supporting theories, and this, in contrast to the crude check-and-error scheme, is its heuristic strength.” Lakatos saw the weakness of the research programs of Marxism and Freudism precisely in the underestimation of the role of auxiliary hypotheses, when the reflection of some facts was not accompanied by the anticipation of other unusual facts.

Imre Lakatos calls the research program of Marxism degenerate. “What new fact has been predicted by Marxism since, say, 1917?” He calls well-known predictions about the absolute impoverishment of the working class, about the coming revolution in the most developed industrial powers, about the absence of contradictions between the socialist countries, unscientific. The scandalous failure of such prophecies was explained by the Marxists with the dubious “theory of imperialism” ( in order to make Russia the "cradle" of the socialist revolution). There were “explanations” for Berlin in 1953, and Budapest in 1956, and Prague in 1968, and the Russian-Chinese conflict.

Not to notice: if Newton's program led to the discovery of new facts, then Marx's theory remained behind the facts, giving explanations after the events. And these, Lakatos notes, are symptoms of stagnation and degeneration. In 1979, John Worrall returned to this problem in his essay "How the Methodology of Research Programs Improves Popper's Methodology". Science, he stressed, is inherently dynamic: either it grows and remains a science, or it stops and disappears as a science. Marxism ceased to be a science as soon as it ceased to grow.

That. The concept of I. Lakatos's research programs can, as he himself demonstrates, be applied to the very methodology of science.

3. Formalism in science

I. Lakatos pays attention to the problem of scientific formalism. He deals with this problem in his book “Proofs and Refutations” and traces it on the basis of the philosophy of mathematics, as the closest direction to the philosophy of science.

The book by I. Lakatos is, as it were, a continuation of the book by G. Polya - "Mathematics and Admissible Reasoning" (London, 1954). Having analyzed the questions concerning the origin of the conjecture and its verification, Polia in his book stopped at the proof phase; I. Lakatos dedicated this book to the study of this phase.

I. Lakatos writes that it often happens in the history of thought that when a new powerful method appears, the study of problems that can be solved by this method is quickly brought to the fore, while all the others are ignored, even forgotten, and its study is neglected.

The subject of mathematics consists in such an abstraction of mathematics, when mathematical theories are replaced by formal systems, proofs - by some sequences of well-known formulas, definitions - by "abbreviated expressions, which" are theoretically optional, but typographically convenient.

This abstraction was invented by Hilbert in order to obtain a powerful technique for studying the problems of methodology and mathematics. But at the same time, I. Lakatos notes that there are problems that fall outside the framework of mathematical abstraction. Among them are all problems related to "meaningful" mathematics and its development, and all problems related to situational logic and the solution of mathematical problems. The term "situational logic" belongs to Popper. This term denotes productive logic, the logic of mathematical creativity.

The school of mathematical philosophy, which seeks to identify mathematics with its mathematical abstraction (and the philosophy of mathematics with metamathematics), I. Lakatos calls the "formalist" school. One of the clearest characteristics of the formalist position is found in Carnap. Carnap requires that:

a) philosophy was replaced by the logic of science... but

b) the logic of science is nothing but the logical syntax of the language of science...,

c) mathematics is the syntax of a mathematical language.

Those. the philosophy of mathematics should be replaced by metamathematics.

Formalism, according to I. Lakatos, separates the history of mathematics from the philosophy of mathematics; in fact, the history of mathematics does not exist. Any Formalist must agree with Russell's remark that Boole's Laws of Thought (Boole, 1854) was "the first book ever written on mathematics. Formalism denies the status of mathematics for most of what is usually understood to be included in mathematics, and nothing cannot speak of its “development.” “None of the “critical” periods of mathematical theories can be admitted into the formalistic sky, where mathematical theories dwell like seraphim, cleansed of all stains of earthly unreliability. However, the formalists usually leave a small back door open for fallen angels; if for some "mixtures of mathematics and something else" it will be possible to construct formal systems "which in some sense do not include them", then they can then be admitted.

As I. Lakatos writes, under such conditions, Newton would have to wait four centuries until Peano, Russell and Quine helped him climb into the sky, formalizing his infinitesimal calculus. Dirac turned out to be happier: Schwartz saved his soul during his lifetime. Here I. Lakatos mentions the mathematician's paradoxical difficulty: according to formalist or even deductivist standards, he is not an honest mathematician. Dieudonné speaks of "the absolute necessity for every mathematician who cares about intellectual honesty to present his reasoning in axiomatic form."

Under the modern dominance of formalism, I. Lakatos paraphrases Kant: the history of mathematics, having lost the guidance of philosophy, has become blind, while the philosophy of mathematics, turning its back on the most intriguing events in the history of mathematics, has become empty.

According to Lakatos, "formalism" provides a fortress for logical positivist philosophy. According to logical positivism, a statement only makes sense if it is "tautological" or empirical. Since meaningful mathematics is neither "tautological" nor empirical, it must be meaningless, it is pure nonsense. Here he starts from Turquette, who argues with Kopy that Gödel's propositions do not make sense. Kopi believes that these provisions are "a priori truths", but not analytic, they refute the analytic theory of a priori. Lakatos noted that none of them noticed that the special status of Gödel's propositions from this point of view is that these theorems are theorems of informal meaningful mathematics, and that in fact they both discuss the status of informal mathematics in a particular case. The theories of informal mathematics are definitely conjectures that can hardly be divided into a priori and a posteriori. That. the dogmas of logical positivism are disastrous for the history and philosophy of mathematics.

I. Lakatos in the expression methodology of science, uses the word "methodology" in the sense of e, close to the "heuristics" of Paul and Bernays and to the "logic of discovery" or "situational logic" of Popper. Removing the term "methodology and mathematics" to be used as a synonym for "metamathematics" has a formalist flavor. This shows that in the formalist philosophy of mathematics there is no real place for methodology as the logic of discovery. Formalists believe that mathematics is identical to formalized mathematics.

He argues that two sets of things can be discovered in a formalized theory:

1. you can open the solution of problems that the Turing machine (it is a finite list of rules or a finite description of the procedure in our intuitive understanding of the algorithm a) with a suitable program can solve in a finite time. But no mathematician is interested in following this boring mechanical "method" prescribed by the procedures for such a solution.

2. One can find solutions to problems like: whether or not some formula of a theory will be a theorem, in which the possibility of a final solution has not been established, where one can be guided only by the "method" of unguided intuition and luck.

According to I. Lakatos, this gloomy alternative to machine rationalism and irrational blind guessing is unsuitable for living mathematics. The researcher of informal mathematics gives creative mathematicians a rich situational logic that will be neither mechanical nor irrational, but which cannot in any way be recognized and encouraged by formalist philosophy.

But all the same, he admits that the history of mathematics and the logic of mathematical discovery, i.e. phylogenesis and ontogeny of mathematical thought cannot be developed without criticism and the final rejection of formalism.

The formalist philosophy of mathematics has very deep roots. It represents the last link in a long chain of dogmatic philosophies of mathematics. For more than two thousand years there has been a dispute between dogmatists and skeptics. Dogmatists claim that by the power of our human intellect and feelings, or just feelings, we can reach the truth and know that we have reached it. Skeptics claim that we absolutely cannot reach the truth, or that even if we can reach it, we will not be able to know that we have reached it. In this dispute, mathematics was the proud fortress of dogmatism. Most of the skeptics tried on the impregnability of this fortress of the dogmas theory of knowledge. I. Lakatos argues that it has long been necessary to challenge this.

Thus, the purpose of this book by I. Lakatos is a challenge to mathematical formalism.

4. The activity of a scientist in revolutionary

and interrevolutionary periods of science

On the question of the activity of a scientist in revolutionary and inter-revolutionary periods, Lakatos expresses such an understanding of cumulative periods when, in interpreting scientific theories, we proceed from the premise that in the course of the revolution The theory of union does not emerge in a fully completed form.

Development, improvement of the program in post-revolutionary period are a necessary condition for scientific progress.

Lakatos recalls Newton, who despised those people who, like Hooke, were stuck on the first naive model and did not have enough perseverance and ability to develop it into a research program, thinking that the first version already constitutes a "discovery".

According to the very original plan of Lakatos, the activities of the scientist in interrevolutionary periods is creative.

How the originally expressed conjecture develops, transforms, changes, improves, Lakatos revealed in his book Proofs and Refutations.

Even in the course of proof, substantiation of knowledge, received during the last more or less significant revolution, this knowledge is transformed, because, Lakatos believes, "man never proves what he intends to prove." Besides,

In Lakatos, unlike Kuhn, revolutionary scientific research activity is not in direct contrast to the activity of a scientist in inter-revolutionary periods. This is primarily due to the understanding of the scientific revolution.

Since in the course of the revolution only the initial draft of a new research program is created, the work on its final creation is distributed over the entire post-revolution period. tional period.

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