Abstract

In this Chapter, a notion of causal probability is developed that fits with phenomenological science as well as with variational induction. In the proposed account, causation is used to distinguish between meaningful and accidental relationships, where meaningful probabilities are those that can be reliably used for prediction and possibly manipulation. In the spirit of variational induction, different types of circumstances or conditions are distinguished, in particular collective conditions, which remain constant in different trials of a given probabilistic phenomenon, and range conditions, which can vary and which determine the outcome in a specific trial of the probabilistic phenomenon. Causal probability is then based on the fundamental notion of causal symmetries. Essentially, a causal symmetry requires that the causal structure responsible for the probability distribution of outcome events is invariant under a relabeling of the outcome events. Causal symmetries determine the relative probabilities of the relabeled outcome events according to a rule that is termed the principle of causal symmetry, which is an objective counterpart to the principle of insufficient reason. Furthermore, the random nature of subsequent outcomes is guaranteed by the independence of trials, which is explicated in causal terms. A probability interpretation relying on causal symmetries can be seen as a generalization of objective interpretations in the tradition of the method of arbitrary functions. Frequencies and symmetries are the two fundamental types of evidence for probabilistic relationships. While frequency interpretations of objective probability are well known, the proposed account attempts to base objective probability solely on symmetries.