This paper invokes the axiomatic approach to explore the notion of growing awareness in the context of decision making under uncertainty. It introduces a new approach to modeling the expanding universe of a decision maker in the wake of becoming aware of new consequences, new acts, and new links between acts and consequences. The expanding universe, or state space, is accompanied by extension of the set of acts. The preference relations over the expanded sets of acts are linked by unchanging preferences over the satisfaction of basic needs. The main results are representation theorems and corresponding rules for updating beliefs over expanding state spaces that have the flavor of reverse Bayesianism.