Abstract: In the literature on subject matters, it is now often assumed that logical connectives like conjunction and disjunction do not contribute to what we talk about. This is usually informally characterized as their ‘not adding’ any subject matter to the subject matter of sentences in which they’re used. However, the formal constraints that are imposed correspond to a stronger constraint: that such connectives must not alter in any way the subject matters of the sentences they connect to. In this talk I want to consider the outlook of relaxing this constraint and allowing connectives to restrict but not add any subject matter, give potential examples of instances where this might happen, and apply this idea to taking first steps to provide a quantitative notion of grasp of a subject matter with some analogies to that of degrees of belief.