The article highlights main problem points of the discussion on the article by Zhuravlev, Mironenko, Yurevich “Psychological science in the global world: challenges and prospects”, the comments received on the article are discussed. The meanings of the concepts of “global” and “universal” psychology are clarified. Different approaches in contemporary international science to the question of whether global psychology can and should become universal in the future are considered. In contemporary discourse “universalists” dominate. Acknowledging heuristic power and significance of the results of the universalist approach, the authors question its lack of alternativeness and point out its limitations. Another focus of the discussion related to the question of the possibility of discovering the “universal” laws of the psychic, was the problem of the criteria of truth in relation to psychological knowledge - traditional, but revealing new aspects as a new type of collective subject of psychological knowledge develops in a multicultural world. Can a psychology, which is not claiming to discover the universal laws of the psychic be considered scientific? It is shown that psychological schools, which deny the possibility of universal psychology are well present in the discourse of the international psychological science, they entered it in 1980-1990 and their impact is growing, which shows by indicators of the number of publications and citation. It is argued that the unity of the tendencies of integration and differentiation in the formation of global psychological science, its development according to the network principle, is due to the diversity of modern humanity, thus, differentiated epistemology is a direct consequence of differentiation at the level of ontology, the very subject of study.