I argue that the management of uncertainty by agents in a social world is foundational to the formation of social structures and to the definition of culture. I present a deep Bayesian model for this management of uncertainty in intelligent systems, and I argue for its applicability to cultural sociology. As social systems grow more heterogeneous, management of uncertainty in any participating agent becomes computationally difficult, and I propose that combinations of a small number of layers of reasoning in a deep Bayesian model are sufficient to account for some of the salient ways by which humans manage this uncertainty. Three forces come into play when considering such a model, and each is connected to a particular form of uncertainty. A denotative layer in the model represents uncertainty in the world or environment (ambiguity and risk about outcomes), a connotative layer manages the uncertainty about relationships with other social agents, and the connection between denotative and connotative handles uncertainty about identities of the self and others, and of behaviours taken. I show how the tradeoff between these three factors maps to different social structures, and I use use the model to make predictions across a range of domains, and show its relationship to cultural sociological, social psychological, economic and sociological theorizing. I further link this model to Bayesian views of the mind, primarily the enactive inference model of human intelligence, and compare and contrast to more traditional artificial intelligence.