Transitions toward a Semantics for Real Possibility

The aim of this thesis consists in developing a semantics for the notion of real possibility. Real possibilities are alternative possibilities for the future in an indeterministic world. In our investigations, we depart from the theory of branching time. The task of providing a semantics for the notion of real possibility is then twofold: there is a logical and a metaphysical challenge. From a logical point of view, the challenge consists in setting up a formal branching time semantics that makes use of parameters of truth that are suited for modeling the temporal dynamics of real possibilities. The metaphysical challenge, on the other hand, consists in providing a systematic explanation of branching time models that properly accommodates the worldly aspect of real possibilities.
In chapter 1, we introduce the notion of real possibility and the theory of branching time and point out the adequacy of the branching time framework for the formal representation of real possibilities. We discuss the peculiarities of real possibilities and locate the notion of real possibility in the vast landscape of possibilities. We then provide the definition of a branching time structure and go over the two most popular semantic approaches based on the framework of branching time, viz. Peirceanism and Ockhamism. Finally, we motivate our choice of the branching time framework over the popular possible worlds framework by highlighting crucial differences between the two frameworks.
In chapter 2, we present a novel propositional semantics based on the framework of branching time, viz. the so-called transition semantics. The basic idea is to replace the moment-history pairs employed as parameters of truth in the Ockhamist semantics by pairs consisting of a moment and a set of transitions, where every transition selects one of the immediate future possibilities open at a moment. The transition semantics exploits the structural resources a branching time structure has to offer and provides a fine-grained picture of the interrelation of modality and time. We show that both Peirceanism and Ockhamism can be viewed as limiting cases of the transition approach that build on restricted resources only.
In chapter 3, we make a significant step toward a future completeness result for the transition framework. We first show that sets of transitions correspond one-to-one to certain substructures of branching time structures. On the basis of that result, we then provide a general characterization of a class of genuine Kripke structures that is shown to preserve validity.
In chapter 4, we present a dynamic, modal explanation of branching time models for real possibility in terms of potentialities. The core idea is this: by manifesting their potentialities, objects become causally efficacious and jointly give direction to the possible future courses of events. We provide a rigorous formal characterization of potentialities, whose manifestations are construed as transitions toward the future, and show how a branching time model for real possibility together with its underlying structure can be lifted in a dynamic fashion from a single momentary circumstance on the basis of the potentialities of objects.