Searle's philosophical construction of social reality has three basic "building blocks": collective intentionality, constitutive rules, and the imposition of functions. This article will focus on the first of these, collective intentionality, which is taken to be the central span on the bridge from physics to society. Searle analyzes this notion in terms of his own internalist theory of intentionality. In his view, we could have all the collective intentionality we have even if we were a brain in a vat, i.e., even if we were radically mistaken about the outside world. It will be argued that such an internalist view of collective intentionality cannot capture normative aspects of social phenomena. Social reality requires a radical relational approach.