The monograph offered to readers is ideological. Drawing on an extensive bibliography, it examines the nature of randomness and probability from the perspective of aleaticism, the general science of the random. A deep historical interpretation of the key terms of the theory is given, the normal distribution and limit laws are critically assessed, but most importantly, the phenomenon of randomness without probability and theory without limit theorems is explained, the mathematical apparatus of which is empirically determined by the laws (distributions) of Pareto, Zipf, Mandelbrot, stable hyperbolic H-distributions Kudrina. The monograph is intended for scientific and practical workers of all specialties using mathematical statistics. Conceptually, the monograph is especially important for legislative and executive authorities, businessmen and managers at all levels, humanities professionals and technologists who make (cenological) decisions to improve the efficiency of large systems in conditions of uncertainty and incomplete information and are faced with the inability to focus on the average (mathematical expectation) of -for a large error (infinite variance).