Colloquium Mathematical Philosophy, Dirk Kindermann (Graz) gives a talk at the MCMP Colloquium (25 June, 2015) titled "Context, Conversation, and Fragmentation". Abstract: What is a conversational context?One inuential account (Lewis, Stalnaker, Roberts) says that it is a shared body of information | the information conveyed and/or presupposed by all interlocutors. Conversation, on this account, proceeds by variously influencing, and being influenced, by this body of information. In this talk, I argue that standard idealising assumptions, according to which this body of information is consistent and closed under entailment, put the account at risk of being inapplicable to ordinary speakers|rational agents with limited cognitive resources. I argue that to mitigate the problem, we should think of context as a fragmented body of information. I explain what fragmentation amounts to and develop a simple model of afragmented common ground. I close by presenting some advantages of a fragmentation strategy in explaining some otherwise puzzling conversational phenomena.