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. New consequences or new acts represent genuine expansions of the decision maker's universe, while the discovery of new links between acts and consequences renders nonnull events that were considered null before the discovery. The expanding universe, or state space, is accompanied by extension of the set of acts. The preference relations over the expanding sets of acts are linked by a new axiom, dubbed act independence, which is motivated by the idea that decision makers have unchanging preferences over the satisfaction of basic needs. The main results are representation theorems and corresponding rules for updating beliefs over expanding state spaces and null events that have the flavor of "reverse Bayesianism".