Great apes cognitively represent and reason (make inferences) about the world. Humans, in addition, represent the world propositionally and conceptually (perspectivally), and they reason about it recursively and reflectively. The Shared Intentionality Hypothesis posits that these uniquely human forms of cognitive representation and reasoning emerged evolutionarily as cognitive adaptations for dealing with a distinctive form of social life, specifically, one in which individuals had to coordinate their intentional states with others in cooperative, and ultimately cultural, activities. Within these cooperative activities, early humans created shared realities (joint attention, common ground), which then enabled them to direct the attention and imagination of one another in relevant ways in acts of cooperative, and ultimately conventional, communication. Learning to cooperate and communicate within a cultural group during ontogeny creates uniquely human propositional-conceptual-reflective cognition.