This article is devoted to understanding the problems of interaction between the discourses of traditionalist and modernist societies, and the possibility of achieving a dialogical consensus in intercivilizational communication. A polydiscursive consensus in the dialogue of cultures creates a new cross-cultural communication event, based on the duality of inclusive and exclusive types of rationality. The principle of equivocative discursiveness is laid on the basis of universal civilizational ethics and intercivilizational interaction. From an analysis of the types of social communication of Yu, Habermas and M. Weber, a typology of discourses participating in the dialogue of cultures of traditionalist and modernist society from the aspect of the concept of post-secularism is proposed. The principles of universal civilizational ethics underlie the dialogical project of a multipolar world of civilizations as a safe strategy for the development of mankind.