On Preemption and Overdetermination in Formal Theories of Causality

One of the key challenges when looking for the causes of a complex event is to determine the causal status of factors that are neither individually necessary nor individually sufficient to produce that event. In order to reason about how such factors should be taken into account, we need a vocabulary to distinguish different cases. In philosophy, the concept of overdetermination and the concept of preemption serve an important purpose in this regard, although their exact meaning tends to remain elusive. In this paper, I provide theory-neutral definitions of these concepts using structural equations in the Halpern-Pearl tradition. While my definitions do not presuppose any particular causal theory, they take such a theory as a variable parameter. This enables us to specify formal constraints on theories of causality, in terms of a pre-theoretic understanding of what preemption and overdetermination actually mean. I demonstrate the usefulness of this by presenting and arguing for what I call the principle of presumption. Roughly speaking, this principle states that a possible cause can only be regarded as having been preempted if there is independent evidence to support such an inference. I conclude by showing that the principle of presumption is violated by the two main theories of causality formulated in the Halpern-Pearl tradition. The paper concludes by defining the class of empirical causal theories, characterised in terms of a fixed-point of counterfactual reasoning about difference-making. It is argued that theories of actual causality ought to be empirical.