The phenomenon of cultural specificity of the types of cognition — the everyday and scientific ones — is discussed in the present work in the frame of systemic approach. The discussion highlights the features of the Russian science. The analogies between the stages of an individual act of cognition, on the one hand, and cognition process at the level of world science, on the other hand, are considered. It is assumed that the interaction between different “local” sciences takes form of the mutual CO-operation aimed at achieving of global result — the development of world science.