Probabilities in Branching Structures

Abstract

A common, natural view about probabilities, shared by philosophers of diverse persuasions, is that probabilities are graded possibilities. On this view, which I will presuppose, there are no probabilities without underlying possibilities, and there is room for different notions of probability at least to the extent that there are different underlying notions of possibility. In this paper I want to trace out consequences of this view for the specific case of possibilities that are grounded in branching structures. Such structures afford a natural representation of real possibilities: concrete possibilities in indexically specifiable situations, like a concrete laboratory experiment or other indeterministic happenings. I will argue that branching-based probabilities lead to interesting probability structures that can shed light on, e.g., the causal Markov condition. My paper is structured as follows: I start by discussing different types of possibility and zooming in on branching-based real possibilities, giving formal details about the theory of branching time. I then work out a theory of probabilities based on branching time structures and discuss a number of peculiarities and limitations of that approach. Finally I give a brief overview of the way in which the branching time framework is extended in the theory of branching space-times, and what an appropriate probability theory for that framework looks like.