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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.

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 specific figures 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 first universal physical theory, Isaac Newton, resolved this contradiction, and how he held the belief in the authenticity of free will while sacrificing not only mechanistic reductionism but also belief in the omniscience of God. These philosophical problems are then discussed in the light of the modifications 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 difficulty 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 significance of Christianity, only shortly before his death he publicly declared this unbelief as a long-held conviction. Reflections 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.

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", finding not 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 of the universe, whether the fruits of this cognition are good or not. A number of attempts 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 of the boundary between the 'magisteria' of science and religion, inadmissibility of its 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.

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.