The article analyzes the phenomena of a «personal knowledge » in the concept of M. Polanyi, investigating classic problem of object-subject interrelation in the cognition from the point of view of the latter one. It shows that a subject in the cognitive activity is not to be determined by objective regularities, but rather by a personality, as the result of cognitive activity depends on its qualities and abilities. The author fixes the most important levels of subjective organization of cognition: humanity, society, scientific society, personality. He concludes that evolution of model vision of the role and functions in the development of science of these levels of subjective organization of cognition does not have limits, because it supposes the introduction of new subjective characteristics, recognition of the unknown and conceptually inexpressible earlier interconnections and regularities.