We provide a formally rigorous framework for integrating singular causation, as understood by Nuel Belnap's theory of causae causantes, and objective single case probabilities. The central notion is that of a causal probability space whose sample space consists of causal alternatives. Such a probability space is generally not isomorphic to a product space. We give a causally motivated statement of the Markov condition and an analysis of the concept of screening-off. 1. Causal dependencies and probabilities1.1Background: causation in branching space-times1.2What are (...) probabilities defined for?2. Basic transitions2.1Basics of basic transitions2.2Sets of basic transitions3. Causal probability theory3.1Some simple cases3.2General causal probabilities3.3Application: probability of suprema of a chain. (shrink)

We introduce the notion of a Minkowskian Branching Structure ("MBS" for short). Then we prove some results concerning the phenomenon of funny business in its finitary and infinitary variants.

Branching space-times (BST; Belnap, Synthese 92:385–434, 1992 ) is the most advanced formal framework for representing indeterminism. BST is however based on continuous partial orderings, while our natural way of describing indeterministic scenarios may be called discrete. This paper establishes a theorem providing a discrete data format for BST: it is proved that a discrete representation of indeterministic scenarios leading to BST models is possible in an important subclass of cases. This result enables the representation of limited indeterminism in BST (...) and hopefully paves the way for the representation of substances with capacities in that framework. (shrink)