Millsian causation

The Directed Acyclic Graph (DAG) theory of causation is based on the assumption that randomly sampling the variables of a causal system will yield a joint probability distribution that satisfies the Markovian condition. It is shown here that this condition can be split into two parts, one of which is named the Millsian condition. It is further shown that the Millsian condition alone implies that causally unrelated sets of variables are conditionally independent given their common causes, very likely a key requirement stated by John Stuart Mill 150 years ago. In Millsian causation, unlike Markovian causation, it is possible for an indirect cause to be associated with its effect even when controlling for the intermediate direct causes. This phenomenon is explained by taking into account the existence of potential causal modulation.