The Transitivity and Asymmetry of Actual Causation

The counterfactual tradition to defining actual causation has come a long way since Lewis started it off. However there are still important open problems that need to be solved. One of them is the (in)transitivity of causation. Endorsing transitivity was a major source of trouble for the approach taken by Lewis, which is why currently most approaches reject it. But transitivity has never lost its appeal, and there is a large literature devoted to understanding why this is so. Starting from a survey of this work, we will develop a formal analysis of transitivity and the problems it poses for causation. This analysis provides us with a sufficient condition for causation to be transitive, a sufficient condition for dependence to be necessary for causation, and several characterisations of the transitivity of dependence. Finally, we show how this analysis leads naturally to several conditions a definition of causation should satisfy, and use those to suggest a new definition of causation.