The paper argues that research in intercultural communication should change the way we think about language. Standard linguistic and pragmatic theories assume that communication and language use depends on there being commonalities, conventions, standards and norms between language users. These conventions of language and conventions of usage create a core common ground on which intention and cooperation-based communication is built. When, however, this core common ground is limited as usually is the case in intercultural communication interlocutors cannot take them for granted, rather they need to co-construct them, at least temporarily. So there seems to be reason to take up the question of how people go about formulating utterances and interpreting them when they can't count on or have limited access to those commonalities and conventions, and in a sense, they are expected to create, co-construct them (at least a part of them) in the communicative process. How does this intensive co-construction of core common ground, lack of conventions, and temporarily established standards affect language development and use? Will this corrupt the structurality and logic of language? How does linguistic creativity work in these circumstances? These and similar questions will be answered in the paper with a special focus on three issues: (1) shift of emphasis from the communal to the individual, (2) modified understanding of linguistic creativity, and (3) the changing role of context in language use.