The purpose of our article is to analyze the Phenomenological Scientific Approach to the characteristics of general intelligence of a personality; to consider Intelligence structure as a basic general category, to describe the problem of its origin and essence as one concept of the “eternal”, “planetary” problems; to show Measuring (or Testological) Scientific Approach to characterize the general intelligence of a person; to propose the characteristics of Associated-systems theory; to study the problem of general and social intelligence, to analyze correlation of these definitions according to the thoughts of teachers of preschool educational establishments. Methods of the research. The following theoretical methods of the research were used to solve the tasks formulated in the article: the categorical method, structural and functional methods, methods of the analysis, systematization, modeling, generalization. Also, in our research we used empirical methods, like statement study. The results of the research. We proved that in the paradigm of Cognitive Psychology the study of social cognitions and social intelligence has greatly enriched in the Psychology by the essence and the content of social intelligence, which previously had been developed in the psychometric tradition. Thanks to Cognitive Psychology, the actualization of the concepts of social representation was intensified. However, the analysis of existing models of representations of social knowledge suggests that the greatest attention in the history of Cognitive Psychology was given to abstract representations, and existing mental models (which relate to both verbal and figurative presentation formats of information) were not systematically checked. In addition, the functioning of these models, as a rule, plays a leading role in such a field of social cognition, as actualization of processes of social categorization and stereotyped thinking, in the field of perception of psychological features, the formation of the first impression, understanding of subjects of interpersonal interaction, etc. This situation, we deal with, sets the prospect of further empirical research on the development of social intelligence. Conclusions. So, Intellect (from the Latin Intellectus – feeling, perception, understanding, concept, mind) is a quality of the psyche of a personality, which is based on the ability to adapt to new situations, the ability to learn on the basis of acquired personally significant experience, understanding and application of both specific and abstract concepts to use their knowledge in order to influence and manage the environment. Intelligence is defined as the general ability of an individual to know and solve problems and tasks, which unite all cognitive processes and present human cognition: feelings, perception, memory, representation, imagination and thinking.