This Thesis is to show cultural pluralism without relativism. In general, cultural pluralism with relativism is claimed due to incommensurability between different cultures. But we argue that this is wrong, by showing that the incommensurability between cultures is not strong one but weak one, because. strong incommesurability cannot explain even the construction of culture itself. The differences between cultures are related with the concept of cultural identities. Cultural identies are refered by homeostatic-cluster theory of reference by Boyd, rather than constructive view. We argued that by this theory of reference the cultures are rigidly referred through the changed of cultures. We also argued that cultural identit has two components, essential component and constructive component. We also discussed the possibility of cultural communication with these weak incommensurability thesis and the proposed concept of cultural identities. The obstacle to the cultural communication is the fear of losing their cultural identities. We argue that we can our cultural identies with constructive identies of cultures. Therefore we discuss that through cultural dialogues, each culture interpret the other culture as well as one's own culture to optimize the interpretation by using Davidson's therory of interpretation. This requires change of one's own culture too. We argue that to have successful communication between cultures one has better to give initiative to the communication partner.