Ideas and Ideals

Since the time of Galileo and Newton, physics has been engineered as a mathematical discipline, seeking its axioms, laws of nature, by means of specially organized experiments. The motivation of specifi cally this mode of cognizing nature was explored in the fi rst paper of this series, in which Christian Platonism and the Pythagorean crede of the founding fathers of modernity’s physics were discussed. The present article aims to lay out the cognitive strategy of physics as revealed by refl ecting upon its seminal discoveries. One central inquiry concerning physics is how exactly it has mined its axioms. Merely pointing to experimentation is insuffi cient. Experiments are conceived and executed as verifi cation of an already-formulated hypothesis, without which it would be indeterminate what should be observed and what there is to do with those observations. A hypothesis for a law is not derived from an experiment; on the contrary, it defi nes the experiment in order to be rigorously scrutinized by it.

The objective of this article is to demonstrate on facts that the strategy for hypothesizing physical laws has invariably emanated from the same wellspring as the originating metaphysical credo. This Pythagorean strategy is founded on the belief in mathematical elegance, high precision, and the universality of the sought-after axioms of matter. The quest for hypotheses went along the pathways of universal mathematical symmetries, equivalencies, invariances, correspondences, and analogies–complex enough to account for a plethora of relevant phenomena, yet simple enough to facilitate scientifi c discovery.

We are not the fi rst to propound this Pythagorean understanding of physics. This concept, as well as the term ‘Pythagorean strategy,’ was a quarter-century ago formulated and developed by the American-Israeli philosopher Mark Steiner (1942–2020) in his monograph, “The Applicability of Mathematics as a Philosophical Problem.” The present article serves as a free contemplation in the footsteps of that brilliant and still largely unparalleled tome.

The work continues the rethinking by the authors of the phenomena of changes in education, science and the structure of power in the 21st century within the framework of the philosophy of culture. The concepts of “carnival” according to M.M. Bakhtin, “the soul of culture” according to O. Spengler, Dionysianism (and neo-paganism) by F. Nietzsche are used for this work. The central problem of this study is the legitimation of the political regime of liberal democracy in the context of a narcissistic culture. The latter, due to its internal characteristics, does not allow the existence of any internal authority, the approval of which would provide a moral sanction to the rule of certain political actors.  History provides several options for the ontology of the legitimation process. The fi rst of them are associated with the priesthood that existed in the conditions of the domination of pagan culture, the Abrahamic religions that replaced it developed their own sacred mechanisms for granting sanctions to power. The most important shift occurs during the Modern: mass culture is forming, the role of moral authority is shifting from priests to scientists. To achieve legitimacy, political actors must ensure the progress of society on the basis of new advances in science and technology. The legitimacy is also challenged with the help of scientifi c argumentation – the authorities are presented with claims of erroneous technical and economic decisions that have entailed negative socioeconomic and/or environmental consequences. An extreme but signifi cant case is the challenge of scientifi c foundations of politics, as was the case in the case of Soviet Marxism.

Expanded reproduction of science and education in the 20th century erodes the former exclusivity of the scientifi c elite and at the same time eliminates the scientist mechanism of political legitimation. The situation is reversed: now, in order to continue pursuing science and education, the former authorities must prove their usefulness to the authorities and society. But the same thing happens with the authorities themselves: offi cials and deputies turn into “servants of people” and explain their necessity to society with the help of representatives of the humanities. They do not rule anymore but produce public goods in exchange for taxes. Bakhtin’s carnival is triumphing.

The regime of liberal democracy that ensured the protection of rights of minorities is close to narcissistic culture, in the center of which is the need for freedom and self-realization of the individual. At the same time, however, any authority – political or scientifi c – has a conditional legitimacy here. The proportion of partisans is growing – actors who recognize the legality of the existing social order but deny its internal justice. Fragility and instability are inherent in liberal democracy. The longevity of such a political regime is ensured by the rise of neo-paganism. Unlike previous pagan cults there is no separate social group of sacrifi ces. Thus, the problem of legitimation is removed: what is already there automatically becomes legitimate. With the help of the liberal discourse, each individual political personality is instilled that it has all the full rights, and the state is left with only responsibilities for the service of this personality: this is the uncontested meaning of Fukuyama’s ‘last man’.

The article presents the experience of building an epistemological space of communication of the concepts of the philosophy of science. Based on his experience of teaching philosophy of science at three universities, the author raises the question of the conditions for building such a space. One condition is the analysis of different approaches to constructing the concepts of science. The second is the correction of one’s own approach and understanding of science, which would take into account other approaches to the study of science and the results obtained in them. The concepts of K. Popper, T. Kuhn, S. Toulmin, I. Lakatos are chosen for correction. In addition, the author’s concept of science is presented, carried out within the framework of the cultural-historical approach and general methodology. The author distinguishes two start-ups of science - the ancient one, where the ‘genome of science’ is formed, and the new European one, in which science and its genome function as an ‘institution of modernity’ are presented. He shows that in the construction of the theory of science, an important role is played by problems arising in culture, their resolution with the help of schemes, the construction of ideal objects based on schemes and logic requirements, which allow building a theoretical discourse, solving problems within its framework, comprehending empirical material. The methodological analysis made it possible to state that the development of science is not only a law-like process, due to the change of cultures, personality traits of scientists and forms of understanding science (“conceptualization” of science), but also a singular process in which each historical step in the development of science brings unique features with it. (they can be described, but cannot be subsumed under the concepts of ‘law’ or ‘regularity’). These provisions correspond to the ideas about science by Popper, Kuhn, Toulmin and Lakatos. At the same time, the author shows that they set themselves the task of explaining scientific revolutions or the historical development of science, but they took modern natural science as the ideal of science, often referred to the situation of the formation of modern science to illustrate these processes, and replaced the historical study of science by constructing it as a constant mechanism.

This article is first in a series of publications on the problem of a special character of fundamental physical laws, which combine two opposite qualities: they are complex enough to allow fine-tuning to life,  yet simple enough to be discoverable by emerging intelligent life. In other words, the laws permit the emergence of not just living beings, but those capable of discovering these very laws. How could this be possible?

Known laws can be looked at from both logical, objective, and historical, subjective, perspectives. On the one hand – the logical – the successes achieved by physics testify to the adequacy of physical theories, to their conformity to the fabric of the Universe itself. This conformity is fundamentally different from fitting complex formulas to facts, like those implemented by the algorithms of Ptolemy, Copernicus or artificial intelligence. Fits describe only what is already embedded in them, whereas physical theories allow to predict phenomena that have never been observed, often unbeknownst  even to the authors of those theories. This predictive power  stems from the same qualities  as the ability to unambiguously falsify physical theories: the simplicity, universality, precision, and completeness of their mathematical principles. In addition to these qualities, and in addition to the fact that the fundamental physical laws possess numerous symmetries, invariants, and equivalences, they also permit that constructive richness of stable material configurations, that is chemistry, which is a necessary condition of life as we know it. Research of recent decades shows how finely tuned the physical constants are to meet this requirement: even small changes in their values would make chemistry impossible.  What is the reason for these amazing Pythagorean qualities of the Universe? Purposeful design of this rational elegance of nature, that is, the intelligent design of the Universe, appears to be the only passable answer to this question, as we intend to demonstrate in this series of publications.

On the other hand, the history of science testifies that the belief in the mathematical perfection of nature’s arrangement lies at the origin of modern physics, indicating both the possibility and, without exaggeration, the sacredness of cognition of the Universe. This belief is clearly visible in the worldview of the founders of mathematical physics, as a special, emotionally intense Pythagorean credo, a variant of Christian Platonism. The initial presumption of perfect design may not be recognized by the masses of scientists and philosophers who came later, and it may even be rejected by them verbally, but this does not cancel its status as the foundation of physics: there has been and is no other answer to the question of why the understanding of the Universe is possible and important for humanity.

The justification of the assumption of intelligent design as the cause of such specific laws of nature, on the one hand, and, on the other hand,  discerning and contemplating the meaning of the Pythagorean credo by granting it the status of a metaphysical working hypothesis, together form a dual objective-subjective logical structure, which the authors designate as the Pythagorean argument, as presented in this article.

This paper is a response to the article by V.I. Razumov “Effective Methodology and Its Place in Intellectual Culture”. According to Razumov, cognition can be viewed as a control system, within which the methodology plays the role of the structure of the management subsystem, while the available empirical material is the manageable subsystem. Philosophers and methodologists occupy a place in the control subsystem, playing a crucial role within the framework of the processes of collective cognition. However, modern trends in the development of technology have led to an unexpected loss by methodologists of their privileged positions. This article raises doubts both about the validity of Razumov’s argumentation and about the very premise of the existence of an effective methodology. It is demonstrated that the search for a ‘family’ of such technologies is possible within the framework of Cartesianism, which separates the subject and objects of cognition. Such a philosophy is enshrined in domestic scientific social practices, including the examination of the results obtained by the All-Russian Attestation Commission. Thus, the task of finding an effective methodology becomes legitimate. And such a methodology, in contrast to formal logic, is dialectical logic, which makes it possible to identify contradictions and construct conclusions necessary for the subject. Razumov is mistaken in believing that it is formal and dialectical logic that coincide; formal logic, in contrast to dialectical logic, often does not allow achieving the predetermined results desired by the subject. However, a no less effective methodology is the usual numerology, which allows the subject to find the cyclical patterns of behavior of social objects. All of these are variants of philosophical realism. Within the framework of nominalism, where the separation of subject and object is denied, the search for an “effective methodology” becomes impossible.

The article discusses the current situation in mathematics, which is interpreted as a crisis. The problems that allow making such a conclusion are considered: the question of the scientific status of mathematics, the possibility of its substantiation, the mental or experimental nature of mathematics, the time of its formation. The author presents the results of the genesis of geometry, the generalization of which makes it possible to assert that mathematics, on the one hand, can be considered a kind of empirical science, on the other, a constructive scientific discipline, in which more complex ideal objects are created on the basis of initial ideal objects and knowledge. Two different understandings of the foundations of mathematics are considered - general scientific and David Hilbert’s, as well as what paradoxes are in science and how they are removed. The author is inclined to believe that antinomies in mathematics cannot be eliminated once and for all, their source is attributing inconsistent characteristics to objects of mathematics, which is due to the very structure of mathematics. The fact is that the construction of ideal objects of mathematics proceeds under the influence of at least four areas: the empirical area, describing which mathematicians create initial ideal objects and knowledge; areas of design based on the original more complex ideal objects; areas of geometric theorem proofs; area of ​​construction of the theory of geometry. In addition, here it is necessary to add the concept of the foundation of mathematics by D. Hilbert, and also take into account that there are different concepts of the foundation of mathematics. At the end of the article, the features of the current crisis in mathematics and the possible direction of its resolution are discussed.

The article presents a detailed response to the new book of the philosopher Oleg Bazaluk “Discursive Thinking through Education”. The problem of understanding Plato’s terms is discussed, in connection with which the author of the article expresses the idea that the correct reconstruction of the statements of ancient philosophers allows not only to choose the necessary values from the existing ones, but also to set new ones; at the same time, he believes, understanding the narratives of a foreign culture (or one’s own, but cultivating a different type of thinking) is quite possible, however, the condition for this is a change in one’s own consciousness, which, figuratively speaking, must be re-educated through the methodology and practice of historical and cultural thinking. The author reconstructs the picture of the world that Plato built and the ontological foundations taken by Bazaluk as the basis of his research and constructions. The author of the article raises the questions why the author of the book took the project of Plato as a basis, who began to doubt it even in antiquity, and also whether knowledge of the cosmos and its evolution can help in building a good society and sociality, as well as make a person happy. Special attention is paid to the issue of Bazaluk’s reconstruction of the evolution of the cosmos and the support of the discursive thinking of education on the knowledge and results obtained in this reconstruction. A number of questions and problems are discussed here: what the author of the book understands by education, what are the features of his reconstruction of the evolution of the cosmos, if it is possible to deepen his understanding of the basic reality (matter) in the direction of taking into account not only the first nature, but also the second. Evaluating the book, the author of the article proceeds from the understanding of Bazaluk’s work as a tradition and discourse that implements at least three principles: Plato himself, Russian cosmism, and the cognitive approach, which is popular nowadays. The author of the article understands his response as a benevolent discussion of the book, calling on other readers to do the same.

The article shows the causes and consequences of the deplorable state of the Russian economic science and higher economic education. They are rooted, first of all, in the persecution to which economics was subjected in Soviet times, especially during the Stalinist period. As a result, it lost the most talented scientists. There was no need for good economists in the command economy, so higher economic education had low prestige. In the post-Soviet period, due to the transition to a market economy, the need for economists to work in government institutions and commercial structures increased. However, it turned out that the current system of higher economic education is unable to satisfy it. The author shows negative consequences of a low level of economic education for solving national economic problems and managing companies. The low level of economic science did not allow economists to justify an effective transition to a market economy, taking into account the peculiarities of the Soviet economy and Russian history. In the post-Soviet period, the political leadership focused only on economists loyal to the government, without taking into account their professionalism.

The author proposes the ways of improving the quality of economic science and higher economic education. The emphasis is on a sharp reduction in the number of researchers and teaching staff (and a reduction in the number of students), with a simultaneous significant increase in the remuneration of researchers and teachers basing on objective criteria for evaluating their activities. This will allow democratizing the management of universities and scientific institutions, abolishing bureaucratic control over their activities.

The article is about Meillassoux’s ideas regarding mathematics. According to Kant, our cognitive abilities are fundamentally limited. We cannot know what is beyond our cognitive abilities. There is no guarantee that the knowledge of a thing in itself does not require the abilities, that a man simply does not have. In addition, according to Kant, mathematics requires intuition. Meillassoux argues that mathematics offers the opportunity to explore the properties of things in themselves. He argues that the laws of logic and physics are contingent, while the laws of mathematics are reliable. The article states that the laws of mathematics cannot be reliable while of the laws of logic are contingent. In addition, the laws of physics are essentially connected with those of mathematics, and we should carefully clear up the question of the extent to which they can be contingent with the same laws of mathematics. Hilbert does not accidentally introduce the idea of ​​a predetermined harmony between mathematics and physics, and Wigner points to this also. We cannot assume that mathematics provides an outlet to things in themselves, and physics is a strictly empirical science that studies only contingency. It is necessary to distinguish in physics the invariant and variable parts for a given mathematics. In addition, it is pointed out that modern mathematics does not always set itself the goal of describing the world, and even more so the thing in itself: a significant part of it is engaged in the construction of models that can describe the phenomenon under study only approximately. The issue of the ontology of Meillassoux’s mathematics is investigated and its proximity to modern Pythagoreanism is indicated. The conclusion states that modern formal mathematics overcomes Kant's limitations, but does not overcome transcendental limitations at all.