The subject of the research is a specific class of regularities, systematically discovered in the construction of formal models of complex systems—regularities that manifest consistently but cannot be derived from the axioms of the formal system used and do not reduce to them. In this work, such dependencies are defined as substantial laws, having an ontological genesis, operating in the described world, and revealing themselves in the operation of the formal system independently of the choice of its axioms. The ontological incompleteness of formal systems is considered a fundamental limitation of any axiomatic description, caused by the mismatch of the axioms, representing encapsulated knowledge from previous levels of cognition, with the primary properties of the described world. The action of substantial laws can be traced in the realm of numbers—the fifth postulate of Euclid, Gdel's theorems, Feigenbaum constants, and Levin's experiment—and is then applied to the task of constructing a reliable civilizational model with a hierarchy of laws: the law of excessive reaction of supersystems (LERS), the law of preservation of activating subsystem (LPAS), and the law of need satisfaction (LNS). The methodological foundation of the research consists of the systemic approach, general theory of systems, principles of post-nonclassical epistemology, hypothetico-deductive method, and the falsifiability principle by K. Popper, the theory of emergence, as well as philosophical and methodological concepts of the foundations of mathematics and the philosophy of science. The scientific novelty is defined by the introduction and development of the concept of the substantial law as an independent type of regularity, not reducible to either an axiom, a theorem, or an empirical generalization, and the justification of its ontological genesis. For the first time, a unified explanation of heterogeneous phenomena—the independence of the fifth postulate of Euclid, Gdel's incompleteness, the universality of Feigenbaum constants, and regularities in minimal computational models—has been proposed as manifestations of incompleteness of axioms concerning the primary properties of worlds. In relation to the civilizational model, a hierarchy of LERS LPAS LNS has been formulated. The main conclusion: the reliability of a complex system model is measured not only by the completeness of the axioms—principally unattainable—but also by the degree of account of substantial laws, as well as adherence to validation and interpretation procedures.
Andrey A. Gribkov (Mon,) studied this question.