Ideas and Ideals

The article discusses approaches to understanding the nature of probability in mathematics and physics with the consequences of these approaches, as well as the difficulties that arise. The ontological status of probability is discussed. It is shown that probability theory, contrary to R. Mises, should be classified as a mathematical science, using the definition formulated by A.N. Kolmogorov. The application of this definition in practice is provided within the framework of the classical approach, provided that the connection with physical reality is defined through the concept of equal opportunity. To do this, the concepts of simple and complex events are introduced, and the method of decomposing complex events into simple ones is explained. The point of view is substantiated, according to which a mathematical probability determined and related to physical reality in this way can be considered an objective probability, that is, existing independently of any tests.

Various interpretations of quantum mechanics and approaches to understanding probability are also revealed. It is shown that in physics today the existing approaches to understanding the nature of probability contradict each other. In the Bohm interpretation, probability is an analogue of the classical approach – statistical objective probability, which has a mathematical formalization, and in quantum Bayesianism, probability quantifies the degree of reliability and depends on the subject conducting the experiment. The Copenhagen interpretation of quantum mechanics tries to eliminate the difficulties associated with combining the wave and corpuscular properties of light and electron beams into a single picture by giving the ontological status of probability, which leads to the problem of understanding physical reality. The article argues for the need for a new connection between the mathematical description of probability and physical reality.

The empirical (frequency) approach of R. Mises is analyzed, which causes a lot of criticism, as it does not have a clear consistent formalization. The article argues that this approach is inconsistent with quantum mechanics. The probability given by M. Born in the Copenhagen interpretation of quantum mechanics is also considered, which formulates a new definition of probability, which does not exclude the difficulties associated with the physical interpretation of probability. Born’s approach is based on the classical approach and is reduced to a formal axiomatic definition, which assumes the interpretation of probability as a mathematical construct. The connection of probability with physical reality and the consistency of the statistical method of finding probability values remain unresolved problems, which creates a dualism of understanding probability: in mathematics – one thing, in physics – another. If in the mathematical approach, the solution of these problems is carried out through the connection of probability with physical properties, then in quantum mechanics, in the Copenhagen interpretation, problems persist, which is caused by giving the wave function an ontological status.

This article presents an analysis of the emergence and development of the concept of transgression in philosophy, particularly in relation to the formation of the subject. The author explores the main factors that contributed to the emergence of this concept. Drawing on the ideas of Georges Bataille and Michel Foucault, the author examines how transgression connects to notions of prohibition, limits, and the sacred. The article delineates the relationship between transgression and fundamental aspects of human existence, such as eroticism and death, suggesting that familiarity with these themes illuminates the discontinuities in human life. It highlights both the continuity and distinctions in the approaches of Bataille and Foucault regarding transgression: for Bataille, it is associated with a temporary lifting of prohibitions, whereas for Foucault, it signifies a definitive overcoming of limits. The author concludes that Bataille’s and Foucault’s approaches can be viewed as two different perspectives: the cultura lanthropological and the ontological. The article also discusses the ‘bestial’ aspect that Bataille describes as the ‘Other’ within the self, proposing that authenticity in existence may be achieved through acts of transgression. Additionally, the article reveals the connection between transgression and the phenomenon of ‘guilty pleasure,’ emphasizing the social significance of transgressive acts as violations of prohibitions in the presence of the Other. For the first time, the role of the unconscious in transgression is considered, with transgression being described as foundational to the development of the subject. The author proposes a novel way of conceptualizing the subject, suggesting that individuals can redefine their foundations through acts of transgression. The central role of metanoia – changes in consciousness – is elucidated as a crucial event in transgression and its enabling conditions. Furthermore, the potential application of the concept of transgression to human cognitive development theory is explored. Ultimately, the author concludes that the concept of transgression can be utilized in various ways, underscoring its complexity and heuristic potential within contemporary philosophical discourse.

Medieval thought in its philosophical, theological and poetic guise appeared to readers of Modern Times as the thought of the ‘highbrow’, which was facilitated by the scholastic method of research. The Renaissance era contrasted the ‘highbrow’ with a man rediscovering the world, who appeared as multidimensional, open to different traditions, and therefore unable to claim the completeness of knowledge. One of the main principles of thinking was the polylogicality of philosophical logic. And although this meant the coupling of various cognitive systems, taking place in the mainstream of communication (not generalization), the reliance on the Word and its expression of thought remained unchanged for everyone, which initially placed the philosopher in a religious atmosphere: the philosopher worked with something that expressed itself and was ready for its own renewal (philosophy was originally religious). This was realised by Nicholas of Cusa, who understood the original thought as having a willingness to think and the ability to think, which is why the text of the Bible seemed self-speaking. He was the herald of ‘scientifi c ignorance’. He was rather an ignoramus (a layman, a simpleton, a fool) relative to the ‘highbrow’ scholastics. But the introduction of the idea of the simpleton itself meant that the philosophical context included the whole of human life with its faith and hopes, education and upbringing of each person, which was expressed in S. Brant’s “Ship of Fools”, in the “Laudatory Word of Stupidity” by Erasmus of Rotterdam, in the “Letters of dark People” by W. Von Hutten and in the “Book about the Sage” by S. de Beauvel, an informative text, sometimes reminiscent of textbooks, which is the knowledge of a Simpleton.

The round table “The Pythagorean Argument of the Intelligent Design of the Universe” was held in the online format on 12, December, 2024. The discussion was held on the cycle of articles by A.V. Burov and A.M. Tsvelik “The Pythagorean Argument of the Reasonable Design of the Universe and its Critique” published in the journal “Ideas and Ideals” in Nos. 3 and 4 of 2023 and Nos. 1–3 of 2024. The discussion was attended by such scholars as Mikhail Arkadyev, Andrei Baumeister; Alexander Bobylev; Alexei Burov (moderator); Igor Dmitriev; Igor Dymov; Konstantin Zuev; Andrey Ivanchenko; Kirill Kopeikin; Irina Rybakova; Alexey Tsvelik.

The author proposes a hypothesis of two types of mechanisms of social self-organization: its launch and maintenance of structural integrity. These are two fundamentally different mechanisms. Social self-organization requires four mandatory conditions: (1) a set of interacting elements (individuals), homogeneous in origin and creating, due to their common habitat, a behavioral population system; (2) the obligatory identification of a pacemaker in the population, which “captures” the activity rhythms of other individuals, which is a condition for the emergence of heterogeneities in behavioral activity; (3) the lifetime of a population system must be significantly longer than the lifetime of an individual element; (4) the homogeneity of individuals and the complexity of their behavior in a long-existing population create conditions for functional subordination (heterarchy, in general sense).

The behavioral mechanism of self-organization in populations with complex behavior of individuals is reciprocal altruism. Altruism presupposes a hereditarily determined ability for sacrifi cial behavior. Its natural basis is the universal phenomenon of individual recognition and preference. The author examines four sociological concepts of self-organization, in which altruism is presented as a mechanism of self-organization: Ibn Khaldun, E. Durkheim, P.A. Kropotkin and P.A. Sorokin.

The mechanism for maintaining an already formed structure is different in nature; it is aimed at continuously ensuring solidarity. This is a “Game” that is implemented in two forms – competition (game) and performance (play). Game is not a specifically human attribute of social life. The content of the “game” satisfies the basic conditions of self-organization. The “game” has three important attributes: (1) isolation of the playing space and temporary organization; (2) the immutability and binding nature of the rules that set the order of actions and form a special ethos and ritual; (3) the game determines the emergence of associations that strive to survive and spread. The associations are based on altruistic behavior. The expansion of the game leads to the creation of male “alliances”; their forms are the basis of solidarity.

One of the objections to the Pythagorean argument is the reference to the authority of modern physicists, most of whom call themselves atheists or agnostics. Even if there had not been any atheists among the founding fathers of physics, something is wrong with the argument of the intelligent design of the Universe, since so many physicists of the last half-century do not believe in God, the critique goes. To answer this sort of objections, we discuss here the views of Richard Feynman, Steven Weinberg, and Stephen Hawking, each of whom called himself an “atheist”. We attempt  to show in what sense they indeed were atheists and in what sense they were not. Roger Penrose, the eminent physicist and thinker, called himself “rather agnostic”, but he was convinced of the universe’s purpose, and explained what this conviction was based on: not blind faith but the very special character of the physical laws and the initial conditions of the Big Bang. Penrose illustrated his metaphysical views by means of graphic images, one of which we discuss in a dedicated chapter.

Our review of contemporary physicist-philosophers would be very incomplete without the “practicing but unbelieving Christian” Freeman Dyson, with his concept of “the most interesting of all possible worlds”, and so we talk about him too.

We also consider Max Tegmark’s mathematical multiverse hypothesis and show that it does not stand up to criticism in light of the cognitive self-consistency of the universe.

Is it rational to reject the hypothesis of intelligent design when all other hypotheses about the cause of the highly refi ned nature of physical laws fail? The chapter “Absurdity and Skepticism” is devoted to this question.

At the end of this essay and the whole series, we familiarize the reader with the view of the mass man in science and the nature of his “atheism” that was expressed by Jose Ortega y Gasset, supported by Erwin Schrödinger, and commented on by Steven Weinberg.

The article analyses both the book of American philosopher ChristophCox “Sonic Flux: Sound, Art and Metaphysics” and a wide range of criti­cal publications dedicated to this book. The project “Sonic Flux” belongs tosonic materialism (a branch of “New Materialism’) also known as “Deleuziansound studies”. For Cox this means a development of “immanent metaphys­ics” launched by G. Deleuze. But while continuing the project of Deleuze,Cox inherits his predicaments. Their range is as broad as the specter of Cox’ssources covering philosophy, arts, theory of perception. Debates around theproject “Sonic Flux” highlighted such problems as the way Cox understandsmaterialism and how he understands access to reality. Cox’s correlation of fi­nite and infinite; particularity and universality, and anti-historicism are highlyproblematic for critics. Since Cox claims to develop a theory of sound art weassess his ideas from this perspective. This allows us to focus on modernism,anonymity and anti-humanism, central to Cox’s project but not to its criti­cism. A less important aspect – resentiment in Cox’s style – turned out to behelpful in drawing conclusions that the whole project “Sonic Flux” is builtupon a range of assumptions. Cox himself names some of them while weindicated some others.

The main conclusion of the article is the idea that the project “Sonic Flux” cannot provide an adequate theory of sound art nor contribute to sound stud­ies because it is too embedded in the worst kind of modernism and structural­ism. Such important notions of sonic materialism as autonomy and anonymity of sounds perfectly fit the tradition of Modernism while being completely alien to the sound studies.

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.

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.