Abstract: For some time now, psychological inquiry on reference has assumed that reference is achieved through causal links between words and entities (i.e., direct reference). In this view, meaning is not relevant for reference or co-reference. We argue that this view may be germane to concrete objects, but not to diffuse objects (that lack clear spatio-temporal limits, thus preventing the use of direct reference in interactions). Here, we propose that meaning is the relevant dimension when referring to diffuse entities, and introduce Conceptual Agreement Theory (CAT). CAT is a mathematized theory of meaning that specifies the conditions under which two individuals (or one individual at two points in time) will infer they share a diffuse referent. We present the theory, and use stereotype stability and public opinion as case studies to illustrate the theory's use and scope. (C) 2011 Elsevier Ltd. All rights reserved.