The article examines the debate between, on the one hand, the proponents of the position that European reason and logic are universal and therefore the dialogue between West and East will always be unequal and, on the other hand, the advocates of a pluralistic approach, who defend the equality of parties in the dialogue as well as the independence of cultures and ways of thinking in different regions of the world. The author expands the agenda of the debate, appealing to the authors of the book Dialogue of Cultures in a Globalizing World. In addition, the author clarifies the concept of globalization, used by many participants in the discussion, and also formulates his own understanding of philosophy. The author considers philosophy, firstly, as a way of deconstructing reality that has ceased to respond to the challenges of time, secondly, as a process of the creation of schemes defining new reality and objects and, thirdly, as personal and professional methods for solving these problems. The article also discusses the condition of the comprehension of procedural phenomena. Thus, there is a methodological approach that makes possible, according to Kant, to grasp the essence of complex systemic phenomena. Therefore, the author examines a case in which C.G. Jung talks about one of his own child experiences. The author argues that the conditions of the comprehension of processuality are, on the one hand, the formation of a special integrity that is personality and, on the other hand, its actions, which make it possible to assemble the discrete states identified by the researcher into a single process. The personality is considered as the subject who, starting from ancient culture, aims for independent behavior, partially overcomes social and cultural dependence, begins to build his own world and himself in this world.