Ideas and Ideals

The author of the article considers the problem of actual infi nity to be the meta-basis of the genesis of New European science. The author shows the advantages of this approach to identify the internal logic of the genesis of science of the XVII century, as well as to clarify the prospects of modern science, experiencing a crisis of its foundations. The author shows that Nikolai Kuzansky’s ontological project reveals the conditions necessary for the mathematization of nature for the transformation of the fi nite into the actually infi nite, which overcomes the hopelessness of Zeno’s similar attempts. Zeno showed that there is no transition from the fi nite to the actually infi nite. To transform the fi nite into the actually infi nite, the latter must already be given. This kind of presence is revealed by Kuzansky in the apophatic idea of the divine minimum coinciding with the maximum. But at the same time, Kuzansky speaks only about the imaginary, and not the real possibility of transforming nature on the basis of actual infi nity. And in order to turn ‘scientifi c ignorance’ into ‘scientifi c knowledge’, it was necessary to present, outside the theological context, the possibility of transforming nature on the basis of actual infi nity, discovered by Kuzansky. This task was set by the founders of the New European science. The author of the article analyzes and compares the attempts of Galileo and Descartes to ‘tame’ the actual infi nity. The author shows that the difference in their positions on the question of the achievability of reliable knowledge, which laid important milestones in the history of the genesis of New European science (the transition from the scholastic tradition to probabilistic epistemology), is due to the awareness of the complexity of the problem of actual infi nity. As a result, the author shows that neither the theoretical speculations of the founders of science, nor the attraction of modern additional resources unknown to antiquity or the Middle Ages (experiment, pinhole camera) were unable to change anything in the ratio of the fi nite and the infi nite.

In this, the penultimate article of our Pythagorean cycle, we turn to the metaphysical or natural-philosophical heritage of those great men who are referred to as founders or pioneers of physics. The choice of specifi c fi gures in this kind of research is surely arguable to some extent. Our choice is limited by the length of the paper, the availability of relevant texts, and yes, a certain subjectivity of our evaluations.

After a brief Introduction, we give an overview of the tension between the paradigm of physical reductionism and the intuition of free will. We show how the author of the fi rst universal physical theory, Isaac Newton, resolved this contradiction, and how he held the belief in the authenticity of free will while sacrifi cing not only mechanistic reductionism but also belief in the omniscience of God. These philosophical problems are then discussed in the light of the modifi cations to physical conceptions of the universe that twentieth-century physics has made.

Turning to James Clerk Maxwell, the author of the equations of electrodynamics, we note his philosophical primacy in pointing out the important feature of physical laws that ensures their discoverability: the correlation of their mathematical complexity with the diffi culty of observing the corresponding layer of reality.

Speaking of Albert Einstein’s philosophical views, we note in them a combination of a deep understanding of the mystical basis of physics with the naivety of moral philosophy. Like Einstein, Max Planck was a deistic idealist who did not believe in a “personal God,” but, aware of the enormous moral signifi cance of Christianity, only shortly before his death he publicly declared this unbelief as a long-held conviction.

Refl ections on Niels Bohr lead us to conclude that he was an apophatic mystic, combining the complementary qualities of a passionate desire for theoretical clarity and an anticipation of its impossibility.

Erwin Schrödinger, to whose views we next draw attention, expressed them in terms of Vedanta idealism. It seems to us that the same views can be expressed within a European context, albeit unorthodox.

Turning to Werner Heisenberg, who in his youth read Plato in the original, we show not only his Platonism, but also his understanding that the connection with God is the moral foundation, the loss of which is ruinous. The drama of being, according to the author of the uncertainty relation, has to do with the fact that the divine will is essentially embodied through human freedom, through the indeterminacy of conscious choice.

In the section on Wolfgang Pauli, we note his amazement at the profound harmony of the mental and the material spheres, which reveals itself with particular power in the mathematical discoverability of the material world. Hence began his search for a possible reason for this agreement, the search accompanied by many years of conversations with Carl Gustav Jung.

The concluding section of the article is devoted to Paul Dirac, who, unique among the great physicists, went from Marxist atheism to preaching about Godmathematics, and then to regular prayers in church.

There are two points of view on the systemic approach and its use: according to the fi rst, this approach is conceived as universal, suitable for any disciplines and practices, according to the second, it includes a specifi c objectivity, should grasp the features of a certain fi eld of knowledge. In order to choose one of them, the author analyzes on the basis of two cases (“The Critique of Pure Reason” by I. Kant and the works of G.P. Shchedrovitsky) the formation and features of the systemic approach, showing that it is the design of an object of study in a special epistemic situation. Its feature is, on the one hand, the presence of several objects that describe the proposed object, on the other hand, the belief in the existence of an ontology and laws in accordance with which this object can be designed. The systemic approach in this version (as the confi guration of various objects and the design of an object based on this process) is compared with humanitarian and socio-humanitarian research and development (A.S. Pushkin’s personality research and the successful Donor project), which make it possible to do without systemic ideas and thinking. They are replaced by methodology and research in the subject. The author draws attention to the fact that the ideas of identifying and searching for the integrity, nature and boundaries of the phenomenon under consideration, taking into account connections and infl uences, the correlation of synthesis and analysis, and a number of others that are today referred to as a systemic approach, were developed meaningfully (in other non-systemic concepts and languages) throughout the entire history of the development of philosophy, methodology and science. As a result, it turns out that it is necessary to distinguish between the methodology of a systemic approach and other methodologies that allow systemic problems and tasks to be solved, so to speak, non-systemically.

Scientifi c natural science, which had been established in European culture since the mid-17th century, began to transmit samples of scientifi c knowledge into the fi eld of studying social reality. Until the 19th century, the only mental form of refl ecting this reality was “primary history,” as Hegel defi ned it, i.e. tradition of historiography coming from Herodotus. This tradition received its design, oriented towards the fi eld of scientifi c rationality, from the German historian Leopold von Ranke: to show “how it really was” (wie es eigentlich gewesen). Its social function is the formation of national historical memory. But methodological refl ection at the turn of the 19th and 20th centuries revealed, as it seemed to it, two radical differences between “primary history” and other “sciences of culture” from natural science. In this regard, the categories of “values” and “understanding” were emphasized. The presence of these categories in the foundations of any science determines its specifi cation as a humanitarian science. The fi rst attempts to transfer certain aspects of the disciplinary matrices of natural science to the sphere of social science are associated with the names of Kant and Marx. Both attempts were unsuccessful. But, unlike Kant’s, the “materialist understanding of history” found its supporters and successors. Its main error is the unlawful direct transfer of the semantic content of the category “matter”, as it developed in natural science (the relationships of things), to the relationships between people endowed with consciousness. The addressee of social sciences are cultural forms, the existence of which has an objective status of existence, but relative to the individual consciousness of acting people. These are, for example, social institutions. The humanities deal with meanings, the existence of which is determined by systems of social communications.

The article is devoted to a critique of the Pythagorean argument, explicit and implicit, offered by philosophers of different epochs.

We begin with Kant’s “critique of the physicotheological argument”, findingnot a refutation of the argument, but a mixture of support and fair remarks re­moved by the further development of physics.

We next assess objections to the Pythagorean argument which may be called “downplaying” emphasizing the incompleteness of physical conceptions of the world. We note that, despite this incompleteness, the cosmic scope and incred­ible precision of knowledge of modern physics require an explanation of why this turned out to be possible. Another variant of the downplay is connected with the negative attitude to the fruits of the “Pythagorean faith”, with the pos­sibility of rejecting it according to the pragmatic criterion. We noted that, as far as we know, none of the adherents of this retrograde position have answered the question about the reason for the effectiveness of mathematics in cognition ofthe universe, whether the fruits of this cognition are good or not. A number ofattempts to explain this efficiency are associated with a sort of omnipotence at­tributed to an aspect of cognition. Karl Popper suggested that the effectiveness of the language of mathematics is not surprising, because languages are general­ly effective in describing reality. Anatoly Akhutin explained the success of math­ematical physics by the fact that mathematized methodology was originally in­corporated into physics, ‘what we put in, we get out’. Ivor Grattan-Guinness and Andrei Rodin deduced the success of physics from the general way of progress. Noting the inadequacy of such explanations, we tried to respond to them cor­rectly.

One more direction of criticism of the Pythagorean argument is connected with ethical, political and politically-correct requirements of strict observance ofthe boundary between the ‘magisteria’ of science and religion, inadmissibility ofits crossing. Our response consists in pointing out the incompatibility of such a ‘Chinese wall’ with the task of philosophical reflection of scientifi c cognition and developing a meaningful worldview.

The article then moves on to a series of remarks that may seem relevant without actually being so. Finally, the role of irrational motivations in solving metaphysical problems is considered.

Modernization of domestic education and global diversification of peda­gogical education make it relevant to analyze the role and place of the subject‘Philosophy’ in order to diagnose new goals for teaching this discipline. Basedon the methodological innovation of the semiotic approach proposed by

I.V. Melik-Gaykazyan, the correspondence between the semantics of universalcompetencies and the pragmatics of the formation of individual trajectories forthe training of future teachers is established. This correspondence captures thenavigational role of philosophy, firstly, in the development of basic academicdisciplines, and, secondly, in understanding the continuity of their curricula.The implementation of this role will not happen naturally, since the domestictradition of university philosophy has its own characteristics, which are retro­spectively indicated in the article. The retrospection emphasizes the context inwhich S.I. Gessen formulated his well-known thesis that pedagogy is an ap­plied philosophy. This thesis is of essential importance for determining therole and place of teaching philosophy for the future teacher training, and alsoremains relevant in the situation of modern diversification of the goals of ped­agogical education. The purpose of teaching philosophy is the propaedeuticsof the development of special courses devoted to modern theories and the ac­tual practice of education. At the same time, the actual practice of educationtakes place in social conditions that transform behavioral and ethical norms,therefore, the goals of teaching philosophy in the context of pedagogical edu­cation include explaining intellectual traditions and the limits of their effective­ness in order to find ways to solve situational problems generated by moderncommunication tools and systems. These situational problems are formed un­der the infl uence of multiple factors, and therefore, to solve them, it is neces­sary to understand the essence of transdisciplinarity. The simultaneous multi­plicity of communications and the variability of their formats in specifi c psy­chological and pedagogical conditions make the modern understanding of theessence of the mediatization phenomenon relevant. Modern requirements foreducation to ensure the training of unique specialists fixes the need for the for­mation of tolerance, which is a condition for the implementation of inclusiveeducation. The listed principles of modern philosophical anthropology andpost-non-classical methodology – tolerance, mediatization, transdisciplinarity,multidimensionality – coincide with those competencies which formation canbe led by the teaching of philosophy.

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’.

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 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.