The Interacting Cognitive Subsystems framework, ICS (Barnard, 1985) proposes that central executive phenomena can be accounted for by two autonomous subsystems, which process different forms of meaning: propositional and schematic (implicational) meanings. The apparent supervisory role of the executive arises from limitations on the exchange of information between these and other cognitive subsystems. This general proposal is elaborated in four experiments in which a total of 1,293 participants are asked to spontaneously generate a large verbal number to varying task constraints, with the intention of specifying the representations of number and task that underlie responses. Responses change systematically according to participants' use of explicit propositional information provided by the instructions, and inferred implicational information about what the experimenter is requesting. There was a high error rate (between 6% and 24%), participants producing responses that did not fall within the large range indicated by the instructions. The studies support the distinction between propositional and implicational processing in executive function, and provide a framework for understanding normal executive representations and processes.