We live in a world of possibilities, and there are many kinds of possibility. One popular way to conceive of possibilities is to view them as modal alternatives to actuality. Different kinds of possibility can then be distinguished in terms of their modal strength. However, not all kinds of possibility fit into this general scheme. In this paper, I will introduce the notion of real possibility into the vast landscape of possibilities and show that it requires a fundamental shift in perspective with respect to how actuality and possibility can be related: real possibilities constitute temporal alternatives for actuality rather than modal alternatives to actuality. I will discuss how this distinction bears on the formal representation of possibilities. The upshot is this: while possible worlds provide a perspicuous framework for modeling possibil- ities as modal alternatives to actuality, real possibilities—as temporal alternatives for actuality—are most adequately represented in Prior’s theory of branching time.

The transition semantics presented in Rumberg (2016) constitutes a novel approach to Prior’s theory of branching time. It has its roots in the peculiar interrelation of actuality and possibility that we find in branching time structures: the forking paths in the tree of possibilities represent temporal alternatives for a dynamic actuality to evolve rather than modal alternatives to a given actuality. In this paper, we discuss the peculiar interrelation of actuality and possibility that is at the heart of the theory of branching time and illustrate how this interrelation is reflected in the transition semantics.