Imre Lakatos. Methodology of research programs. Contemporary Western Philosophy - lakatos imre Research Program Methodology
Introduction
3. Formalism in science
Conclusion
Introduction
LAKATOS, Lakatos Imre (November 9, 1922, Budapest - February 2, 1974, London) - Hungarian philosopher and methodologist of science, one of the most prominent representatives of "critical rationalism".
In 1956, he was forced to emigrate from Hungary to Austria, and then to England, where he met Popper and studied his concept well. He expounded his own views within the framework of critical rationalism.
Lakatos filled with new content the principle of falsification and ionism as the methodological basis of the theory of scientific rationality. According to this principle, the rationality of scientific activity is confirmed by the willingness of a scientist to recognize any scientific hypothesis as refuted when it encounters experience that contradicts it (not only to recognize, but also to strive for possible refutation of his own hypotheses).
Lakatos wrote small, but very capacious works. You can get acquainted with his views in the books "Proofs and Refutations" (Moscow, 1967) and "Falsification and Methodology of Scientific Research" published in Russian. research programs"(M., 1995).
In his early works (of which the most famous is Proofs and Refutations), Lakatos proposed a variant of the logic of conjectures and refutations, applying it as a rational reconstruction of the development of knowledge in mathematics of the 17th-19th centuries. Already during this period, he clearly stated that "the dogmas of logical positivism are disastrous for the history and philosophy of mathematics."
The line of analysis of the processes of change and development of knowledge is then continued by the philosopher in a series of his articles and monographs, which set out a universal concept of the development of science, based on the idea of competing research programs.
1. Falsificationism as a methodological basis for the theory of scientific rationality
Falsificationism combined the postulates of empiricism and rationality: rationality is based on the universalization of empiricism, and empiricism is adequately embodied in the criterion of rationality. Lakatos extended this connection to the realm of developing mathematics. In terms of its rational structure, the path of scientific research in mathematics is the same as in empirical natural science: the discovered "counterexamples" force the researcher to modify the hypotheses put forward, improve the evidence, use the heuristic potential of the accepted assumptions, or put forward new ones. However, in both mathematics and empirical science, the rationality of criticism does not mean a requirement for the immediate rejection of refuted hypotheses.
In the vast majority of cases, the rational behavior of the researcher contains a number of intellectual strategies, the general meaning of which is to move forward without stopping because of individual failures, if the movement promises new successes and these promises come true. This is evidenced by the history of science, which thus comes into conflict with dogmatic 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 distinguishes three stages in the development of Popper's views: Popper - dogmatic falsificationism, Popper - naive falsificationism, Popper - 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. Lakatos saw well the shortcomings of Popper's methodology. The strict methodological requirement that a theory must be abandoned if it turned out to be falsified sharply diverged from the real activities of scientists who continued to work with such a theory, tried to improve it, and even often achieved success. Popper's concept could not explain such facts from the history of science. Many scientific theories, faced with facts that disprove them, remain in the scientific community for a long time, they are used and applied. Moreover, if new theories appear in science that have successfully coped with the anomalies of their predecessors, then competing theories continue to coexist. But, of course, Lakatos was not a simple apprentice of a great master and teacher. He calls Popper's original version of methodology "naive falsificationism". Many followers of Popper tried to connect his concept with the history of science, to confirm it with historical facts. The desire to give a rational reconstruction of the history of science leads Lakatos to an independent version of critical rationalism. 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. Methodology of research programs by Imre Lakatos
In order to bring the methodological concept closer to real historical practice, Lakatos introduces a new concept of "research program" or "research program" into the methodology of science. If Popper and the logical positivists use in their reasoning the concept of "theory" or "set of theories" as the initial and main cell of analysis, then Lakatos uses the "research program" as the unit of methodological analysis. In the understanding of Lakatos, this is a set of theories accepted sequentially one after another in time and coexisting together. All these theories belong to the same program, because they have a common beginning: they have fundamental ideas and principles that unite them. Lakatos also assumes that in the history of science there are several parallel research programs related to the same subject of research, solving approximately similar problems and being in relation to each other in a competitive struggle. Such programs can coexist for quite a long time, the victory of one of them comes gradually, and the significance of this victory can be assessed, including with the help of the defeated program, in comparison with those problems that cannot be solved by the latter. The research program is structurally composed of three main elements: the core of the program, positive and negative heuristics. The core of the research program is a rigid, unchanging part of the research program, consisting of a set of fundamental theoretical principles, specific scientific and metaphysical assumptions about the ontological nature of the area under study and the general strategy for studying it. During the entire lifetime of the program, its core does not change. Positive heuristics, being the second essential part of the research program, “identifies problems for research, highlights the protective belt of auxiliary hypotheses, anticipates anomalies and victoriously turns them into confirming examples - all this in accordance with a predetermined plan. The scientist sees anomalies, but, since his research the program can withstand their onslaught, he can freely ignore them. Not anomalies, but the positive heuristics of his program - that's what his choice of problems dictates in the first place. The fulfillment of such requirements entails a significant change in theories. Scientists are forced to take measures to explain counterexamples, when it is no longer possible to ignore them in a competitive environment with other research programs, and to improve their theories. Positive heuristics is turning into the main driving force of science. Let us note that for Popper, changing falsified theories is tantamount to a rejection of falsification and was, in fact, a regressive phenomenon, a loophole for dogmatism. Negative heuristics are a set of techniques and rules that are designed to protect the core of the program from empirical rebuttals. This position also differs significantly from Popper's methodology, which forbade formulating and consciously putting forward techniques that prevent the falsification of theories. Popper defended this methodological requirement under outwardly attractive slogans: "Down with dogmatism from science!" and "Criticism is the driving force of scientific progress!" . But the thing is that these beautiful slogans turned out to be empty words and good wishes in the face of historical facts. Lakatos, formulating the principles of negative heuristics, tries to bring the methodological conception into line with the real history of science. As for the auxiliary hypotheses, which are formulated based on the general strategy of positive and negative heuristics, they are a changing part of the research program and are intended to protect both the core of the program and theories. Moreover, each of the theories of the research program has its own protective belt of auxiliary hypotheses. The research program practically exists and is implemented as a series of theories that arise sequentially in time and have the ability to exist in parallel for some time. If some of them lose support from heuristics and even their own protective belts, then the program as a whole can be saved at the expense of the core and the remaining unfalsified theories. In the history of science, several research programs coexist and compete with each other. How to determine which of them with greater reliability and evidence can achieve success? And what program will determine the progressive development of science? The main problem in this regard is the problem of determining the criteria for the success of a research program. Lakatos believes that this criterion is the heuristic value of the research program. Theoretical predictions of new facts must outstrip their empirical confirmation. critical rationalism lakatos falsificationism "A research program," wrote Lakatos, "is said to be progressing when its theoretical growth anticipates its empirical growth, i.e., when it can predict new facts with some success ("progressive problem shift"); a program regresses if its theoretical growth lags behind its empirical growth, i.e. when it gives only belated explanations of either random facts or facts anticipated and discovered by a competing program ("regressive problem shift"). If a research program progressively explains more than a competing one, then it "crowds out" it, and that competing program can be eliminated (or, if you prefer, "delayed"). So, the more successful research program is the one that produces more new predictions that are confirmed by experience. Such a program is more progressive. Experience acts as a measure in the evaluation of competing programs. If the experience refutes the theory, then the entire research program, while retaining the core and positive heuristics, remains viable. The refutation of a theory is not a basis for its rejection, much less for the rejection of the entire program. From Lakatos's point of view, there is no such thing as a decisive experiment, which is usually incorrectly associated with the collapse of a theory, in science. "So, for example, in one place Popper claims that the Michelson-Morley experiment decisively subverted the classical theory of the ether; in another place he exaggerates the role of this experiment in the emergence of Einstein's theory of relativity. One must really put on all the simplifying glasses of a naive falsificationist in order to see together with Popper, that Lavoisier's classical experiments disproved (or "sought to disprove") the phlogiston theory, that the Bohr-Kramers-Slater theory was blown to smithereens by a whiff of Compton's research, or that the parity principle was "abandoned" by a "counterexample". Denying the possibility of a decisive experiment, Lakatos tries to restore historical justice by proving that in addition to "stubborn" facts (moreover, still incorrectly interpreted), living people act in science, who very often act contrary to these facts. Lakatos's rational reconstruction of the history of science is much closer to real scientific activity than the methodology of logical positivism and Popper's abstract falsificationism. 3. Formalism in science
Lakatos contrasts the latter (as the essence of logical positivism) with a program for analyzing the development of meaningful mathematics, based on the unity of the logic of proofs and refutations. This analysis is nothing but a logical reconstruction of the real historical process of scientific knowledge. 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. He argues that this is what seems to have happened in our century in the field of the philosophy of mathematics as a result of its rapid development. 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 - "abbreviated expressions that are" theoretically optional, but typographically convenient ". Such an abstraction was invented by Hilbert in order to obtain a powerful technique for studying the problems of the methodology of 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 turns out to be possible to construct formal systems "which in some sense include them", then they can then be admitted. Under the current 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 pushes back from Turquette, who argues with Kopi that Gödel's propositions make no 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 guesses 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 a sense close to the "heuristics" of Paul and Bernays and to Popper's "logic of discovery" or "situational logic". Removing the term "methodology of mathematics" to be used as a synonym for "metamathematics" has a formalistic flavor. This shows that there is no real place in the formalist philosophy of mathematics 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: It is possible to discover the solution of problems that a Turing machine (it is a finite list of rules or a finite description of a procedure in our intuitive understanding of the algorithm) with the right 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. 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. Thus, the purpose of this book by I. Lakatos is a challenge to mathematical formalism. Conclusion
Lakatos is one of the most prominent representatives of "critical rationalism". Lakatos filled with new content the principle of falsificationism as a methodological basis for the theory of scientific rationality. According to this principle, the rationality of scientific activity is confirmed by the willingness of a scientist to recognize any scientific hypothesis as refuted when it encounters experience that contradicts it (not only to recognize, but also to strive for possible refutation of his own hypotheses). Lakatos made an attempt to combine a historical approach to science with the preservation of a rationalist attitude. This was expressed in the methodological concept of "refined falsificationism" developed by him, which is more often called the methodology of research programs. The rational development of science is presented in this concept as a rivalry of "conceptual systems", the elements of which can be not only individual concepts and judgments, but also complex complexes of dynamically developing theories, research projects and their relationships. Lakatos was looking for the possibility of moving towards the history of science on the basis of rationalism. Lakatos' methodology is essential tool rational analysis of science, one of the most significant achievements of the methodology of science in the 20th century. I. Lakatos pays attention to the problem of scientific formalism and traces it on the basis of the philosophy of mathematics, as the closest direction in the philosophy of science. According to Lakatos, "formalism" provides a fortress for logical positivist philosophy, this gloomy alternative to machine rationalism and irrational blind guessing is unsuitable for living mathematics. List of used literature
1.Lakatos I. Proofs and rebuttals. - M., 1967. - 152 p. 2.Lakatos I. History of science and its rational reconstructions. - M., 1978. - 235s. .Lakatos I. Methodology of scientific research programs // Questions of Philosophy. - 1995. - No. 4. .Lakatos I. Falsification and methodology of research programs. M., 1995. .Gubin V.D. etc. Philosophy. - M., 1997. - 432s. .Radugin A.A. Philosophy. Lecture course. - M., 1995. - 304 p. .Rakitov A.I. Philosophical problems of science. - M.; 1977. - 270s. .Reale D. Western philosophy from the origins to the present day. Part 4 / Giovanni Reale, Dario Antiseri. - L., 1997. .Sokolov A.N. The subject of philosophy and the rationale for science. - S. P.; 1993. - 160s. .Philosophy: textbook / ed. A.F. Zotova, V.V. Mironova, A.V. Razin. - 6th ed., revised. and additional - M.: Academic Project, 2009. - 688 p. .Philosophy and methodology of science. Part 1. - M.; 1994. - 304p. .Philosophy and methodology of science. Part 2. - M.; 1994. - 200s.
November 9, 1922, Budapest - February 2, 1974, London) - Hungarian philosopher and methodologist of science, one of the most prominent representatives of "critical rationalism". In 1956 he emigrated from Hungary to Austria, then to England. He taught at Cambridge, from 1960 - at the London School of Economics, where he became close to K. Popper. Lakatos filled with new content the principle of falsificationism as a methodological basis for the theory of scientific rationality. According to this principle, the rationality of scientific activity is confirmed by the willingness of a scientist to recognize any scientific hypothesis as refuted when it encounters experience that contradicts it (not only to recognize, but also to strive for possible refutation of his own hypotheses). Falsificationism combined the postulates of empiricism and rationality: rationality is based on the universalization of empiricism, and empiricism is adequately embodied in the criterion of rationality. Lakatos extended this connection to the realm of developing mathematics. In terms of its rational structure, the path of scientific research in mathematics is the same as in empirical natural science: the discovered “counterexamples” force the researcher to modify the hypotheses put forward, improve the evidence, use the heuristic potential of the accepted assumptions or put forward new ones. However, in both mathematics and empirical science, the rationality of criticism does not mean a requirement for the immediate rejection of refuted hypotheses. In the vast majority of cases, the rational behavior of the researcher contains a number of intellectual strategies, the general meaning of which is to move forward without stopping because of individual failures, if the movement promises new successes and these promises come true. This is evidenced by the history of science, which thus comes into conflict with dogmatic falsificationism. Lakatos made an attempt to combine a historical approach to science with the preservation of a rationalist attitude. This was expressed in the methodological concept of "refined falsificationism" developed by him, which is more often called the methodology of research programs. The rational development of science is presented in this concept as a rivalry of "conceptual systems", the elements of which can be not only individual concepts and judgments, but also complex complexes of dynamically developing theories, research projects and their interconnections. Such systems are organized around some fundamental ideas that form the "hard core" of the research program (as a rule, these ideas are put forward by the intellectual leaders of science and assimilated dogmatically by the scientific community). The methodological meaning of the "solid core" is revealed in the concept of " negative heuristic”, i.e. restrictions on refutation procedures: if a theory encounters refuting facts, then the statements included in the composition of the “hard core” are not discarded; instead, scientists clarify, develop existing or put forward new "auxiliary hypotheses" that form a "protective belt" around the "solid core". The task of the "protective belt" is to keep intact the creative potential of the research program, or its "positive heuristics" as long as possible. The function of the latter is to ensure the continuous growth of scientific knowledge, the deepening of its empirical content (the explanation of an ever wider range of phenomena, the correction of shortcomings and errors of "refuting experiments"). The requirement to increase the empirical content is, according to Lakatos, the main condition and criterion of scientific rationality: the researcher who chooses the optimal strategy for increasing empirical knowledge acts rationally, any other action is irrational or irrational. The methodology of research programs formulates the rules, the implementation of which optimizes this strategy. Such, for example, is the rule that determines the “progressiveness” of a particular research program: a “progressive shift in problems” is ensured by an increase in the empirical content of a new theory in comparison with its competitors, i.e., by an increase in the ability to predict new, previously unknown facts in combined with empirical confirmation of these new facts. When this rule ceases to apply and the research program begins to “mark time”, dealing with Ch. about. "self-justification", i.e., eliminates anomalies with the help of ad hoc hypotheses, but does not give a steady increase in empirical content, one can say that the program has entered the stage of "degeneration" and should soon be replaced by another, more productive program. Such rules together form the theory of scientific rationality, which explores the growth of science as a succession of scientific theories, united by a common research program. Lakatos criticized attempts to “sociologize” epistemology, in which the connection between science and cultural history was interpreted as the dependence of the scientific-cognitive process, the content of scientific theories and methods, the processes of emergence and development of conceptual systems on “extra-scientific” (psychological, socio-psychological, sociological) factors. He defended the idea of "rational reconstruction" of the history of science, without giving special significance the thesis of the "incommensurability of scientific theories" replacing one another in the course of scientific evolution, which was put forward as an argument against this idea by some philosophers (T. Kuhn, P. Feyerabend, etc.).
Lakatos was looking for the possibility of moving towards the history of science on the basis of rationalism. The methodology of "refined falsificationism" was supposed to answer the question: how are research programs formed, changed and then "cancelled", i.e. forced out by competitors, research programs? In real historical and scientific situations, the factors of formation and transformation of scientific knowledge are found both among metaphysical ideas and among religious beliefs, and among ideological or political orientations. Lakatos suggested that such factors be taken into account "on the margins" of rational reconstructions of the "internal" history of science and attributed to deviations of the "external" history from the normal, i.e. rationally reconstructed, course of events. This gave grounds to some critics to accuse Lakatos of a lack of "historical intuition" (S. Toulmin, K. Huebner, P. Feyerabend, and others). In "rational reconstructions" some of the most important processes scientific development presented as "irrational". However, according to critics, this spoke more about the narrowness of Lakatos' ideas about rationality than about some kind of "irrationalism" of real science. Nevertheless, the methodology of Lakatos is the most important tool for the rational analysis of science, one of the most significant achievements of the methodology of science in the 20th century.
Cit.: Changes in the Problem of Inductive Logic. - The Problem of Inductive Logic. L., 1968; The Changing Logic of Scientific Discovery. L.. 1973; Proofs and Refutations and Other Essays in the Philosophy of Mathematics. L.. 1974; Evidence and refutation. Moscow, 1967; History of science and its rational reconstructions. - In: Structure i] paiBimic Science. M., 1978; Infinite Regression and the Foundations of Mathematics. - In the book: Modern Philosophy of Science. Reader. M.. 1994: Falsification of programs and methodology of research programs. M.. 1995.
Great Definition
Incomplete definition ↓
Imre Lakatos(in Hungarian Lakatosh- hung. Lakatos Imre real name and surname Avrum Lipschitz; November 9, Debrecen - February 2, London) - an English philosopher of Hungarian origin, one of the representatives of postpositivism and critical rationalism.
Biography
At the same time, due to the persecution of Jews that had begun (his mother and grandmother died in Auschwitz), he was forced to change his surname to Molnar (in Hungarian - Melnik), then to Lakatosh (Prime Minister Geza Lakatosh, who opposed the destruction Hungarian Jews). There is another point of view, according to which he took the “proletarian” surname Lakatosh (Locksmith) when he got a job in the government of the Hungarian People's Republic. In the Russian-speaking tradition, it is customary to transmit his pseudonym as Lakatos.
After the war, he studied at the graduate school of Moscow University under the guidance of S. A. Yanovskaya. For a short time he was a functionary of the Department of Culture in the Ministry of Education of communist Hungary. At that time, he was strongly influenced by the ideas of his compatriots György Lukacs, György Poya (Lakatos translated his book How to Solve a Problem into Hungarian) and Sandor Karacsony (Hungarian) Russian.
Methodology of research programs
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 , modifying and adapting to program counterexamples. 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 mathematical analysis 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 historical research but in the form of a school dialogue. Using the dialogic method, Lakatos artificially constructs a problematic 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.
LAKATOS (Lakatosh) Imre (originally Liposhits, then Molnar; Imre Lakatos; 1922, Debrecen, Hungary - 1974, London), Hungarian, then English philosopher of science.
He graduated from the University of Debrecen (1944), postgraduate studies in Budapest (1945–46) and Moscow (1949). In 1947–50 worked as a secretary in the Hungarian Ministry of Education. During the years of communist terror (1950–53) he was imprisoned. Released after the death of I. Stalin and the departure from the post of Prime Minister M. Rakosi. He worked as a translator at the Research Institute of Mathematics of the Hungarian Academy of Sciences (1954–56). After the suppression of the Hungarian revolution (1956) he emigrated to England. In 1957–58 - doctoral student at the University of Cambridge (doctorate degree - 1958). In 1969–74 was a lecturer, then professor of logic at the London School of Economics.
Lakatos challenged the traditional view of mathematics as a purely deductive science, where theorems are strictly deduced from undeniable axioms and postulates. According to Lakatos, the subject of mathematics is "quasi-empirical" and not purely formal, but meaningful. Lakatos proposed an original version of the logic of conjectures and refutations formulated by K. Popper.
Sharing Popper's belief in the 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 greater 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.”
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.
The research program, according to Lakatos, contains a “hard core” - (a conditionally non-falsifiable part), a “problem solving technique” (mathematical apparatus) and a “protective belt” of additional hypotheses that must be modified or replaced with new ones when confronted with examples that contradict them. "Negative heuristic" prohibits making changes to the "hard core"; the "positive heuristic" directs the scientist to make modifications to the "protective belt". The emergence of a new research program that can explain the theoretical success of its predecessor and better predict previously unknown facts leads to a change in programs. A research program is "theoretically progressive" if each new theory in it is capable of predicting some new facts, and "empirically progressive" if some of these predictions are confirmed. According to Lakatos, neither confirmation nor refutation are purely logical relations between propositions, but depend in part on context.
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.
The main 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).
Imre Lakatos
Lakatos - (real name Lipsitz, Lipsitz) (1922-1974), English mathematician, logician and philosopher of science. He had a significant impact on the philosophy and history of science of the twentieth century. He worked in Cambridge, and for many years was the editor-in-chief of the British Journal of the Philosophy of Science.
He made a major contribution to the development of the philosophy and methodology of critical rationalism.
Lakatos proposed an original version of the logic of conjecture and refutation, applying it as a rational reconstruction of the growth of scientific knowledge in meaningful "quasi-empirical" mathematics of the 17th-19th centuries.
According to Lakatos, the development of science is a competition of research programs, when one research program replaces another.
Essence scientific revolution lies in the fact that it is necessary to compare with empiricism not one isolated theory, but a series of successive theories, interconnected by common fundamental principles. This sequence of theories he called the research program. Therefore, the fundamental unit for evaluating the process of developed science is not a theory, but a research program.
For Lakatos, the procedure for proving the truth of the original version of the research program does not lead to faith in it, but to doubt, gives rise to the need to rebuild, improve, make clear the possibilities hidden in it. In his book, Lakatos analyzes how the growth of knowledge is carried out through a series of proofs and refutations, as a result of which the very premises of the discussion are changed and something other than what was originally supposed to be proved is proved.
In Lakatos, unlike Kuhn, revolutionary research activity is not in direct contrast to the activity of a scientist in interrevolutionary 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 scientific research program is created, the work on its final creation is distributed over the entire post-revolutionary period.
Imre Lakatos and his scientific views
Imre Lakatos (1922-1974), born in Hungary, student of György Lukács.
During the Second World War, he was a member of the anti-fascist resistance. At the same time, due to the persecution of Jews that had begun (his mother and grandmother died in Auschwitz), he was forced to change his surname to Lakatos (Prime Minister Geza Lakatos, who opposed the extermination of Hungarian Jews, had the same surname). There is another point of view, according to which he accepted the “proletarian” surname Lakatosh (Joiner) when he got a job in the government of the Hungarian People's Republic.
After the war, he studied at the graduate school of Moscow University under the guidance of S. A. Yanovskaya. For a short time he was a functionary of the Ministry of Education of communist Hungary. During this time, he was strongly influenced by the ideas of his compatriots György Lukács, György Polja and Sandor Karacsony. During the cult of personality Rakosi in 1950-1953. was illegally repressed as a "revisionist" and was imprisoned for two years. During the Hungarian Revolution on November 25, 1956, he fled to the West through Austria. From 1958 he lived permanently in the UK, from 1969 he was a professor at the London School of Economics and Political Science. He died in 1974 at the age of 51 from a cerebral hemorrhage.
Lakatos was called the "Knight of Rationality" because he advocated 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" and "Falsification and Methodology of Research Programs" 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 meaning of Kuhn's scientific paradigm. Lakatos also developed one of the best models of the philosophy of science - the methodology of research programs.
The theory of Lakatos is aimed at studying the driving factors in the development of science, it continues and at the same time challenges the neo-positivist theory of K. Popper, argues with the theory of Thomas Kuhn.
Lakatos described science as a competitive struggle between “research programs” consisting of a “hard core” of fundamental assumptions a priori accepted in the system that cannot be refuted within the program, and a “safety belt” of ad hoc auxiliary hypotheses that change and adapt to program counterexamples. 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. As long as the program gives an increase in knowledge, the work of a scientist within its framework is “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 as "rational".
Although Lakatos failed to adequately reconcile the logical-normative nature of his reconstruction with the real diversity of the growth processes of scientific knowledge, his methodology of research programs is one of the most striking achievements of modern philosophy and methodology of science. Always remaining a consistent supporter of philosophical rationalism, he defended the positions of this trend in the intense controversy of the 1960s and 1970s. with T. Kuhn, P. Feyerabend, and a number of other philosophers of science.
