Ideas and Ideals

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.

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.