  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.
