We discuss the problems of developing a theory of context that applies to the phenomena of naturally occurring discourse and that might be useful in assisting with the problems that arise in generating and interpreting discourse. The theories of context that have recently emerged in AI treat context as a determinant of literal meaning. This idea does in fact fit some natural language phenomena. But we suggest (1) that the account is inadequate for important effects that occur in discourse, and moreover (2) in discourse, the mutuality of context provides important constraints on the dynamics of context. We explore these ideas in the paper, and also describe an ongoing project that seeks to develop an empirically adequate and computationally useful approach to the problem of contextual effects on inference in discourse. Readers, please note that this is a provisional draft that describes ongoing work.