This study aims to solve the problems of the methodology of holistic and systemic approaches and to establish the form of relations between them. In the general theory of systems between the concepts of "system" and "whole" the relation of primacy is established, namely: the system is recognized as primary, and the concept of "whole" is applied to the formation of properties of the system: emergence and integrativity. For the whole, the regularity of the relationship between the part and whole is established and studied. Besides, it is this pattern is the basis for establishing the characteristics of the system and its elements. In this study, it is proposed to abandon this form of relationship between the system and the whole and move on to the study of the whole as an independent object. In the study of this whole, it is also proposed to abandon the establishment of the form of interaction between the part and the whole and to proceed to the study of the interaction of the parts as a whole. The study of the concept of "organized whole" based on the theory of functional systems, which is considered a natural intellectual system, provided the separation of two parts in an organized whole. Thus, the problem of synthesis of the organized whole is solved. For these two parts, the ways of realization of activity in the form of the decision of the corresponding problems are established. On this basis, the logical principle of mutual relations between the parts of the whole and the results of the realization of their activity in the form of a dialectical triple relation "general" - "special" - "singular, concrete" was determined. It is established that the form of representation of the middle member of this relationship, namely, "special" should be the appropriate sign. The proposed approach investigates the mechanism of interaction (dialectical unity) of two active parts of an organized whole, for which the result of this interaction (zero) is known. The relationship between the system and the organized whole is established in the form of "part" - "whole." The logical sequence of formation of contradictions, axioms, and rules of formation and activity of natural intellectual system which is realized in the given work, is an example of the practical application of a logical method of knowledge of laws.