In this study I examine some uses of connectives, and in particular co-ordinate conjunction, from a critical discourse perspective; these uses, in my view, cannot find a satisfactory explanation within current frameworks. It is suggested that we need to identify a conceptual level at which connectives function as hypo-textual signals, activating systematic law-like conditional statements (IF-THEN), which form default specifications of consistent structured knowledge frames. I argue that an account of connectives at the conceptual level of their function that does not take into consideration such tightly structured background schemata, representing both general knowledge and ideologies, cannot afford any generality. As a result, ‘deviant’ or ‘subversive’ uses of these connectives can neither be identified as such nor find an adequately general explication within existing accounts, whereas in the proposed framework such uses find a ready explanation of sufficient generality. This framework lies at the intersection of disciplines: Linguistic pragmatics (empirical pragmatics, critical discourse analysis), on the one hand, and cognitive science, on the other. Consequently, this proposal, too, can be regarded as a plea for crossing boundaries and joining forces.