The Intransitivity of Causation Revealed in Equations and Graphs

[Introduction] We live in exciting times. By 'we' I mean philosophers studying the nature of causation. The past decade or so has witnessed a flurry of philosophical activity aimed at cracking this nut, and, surprisingly, real progress has been made. Two developments are especially worthy of note. First, there has been a resurgence of interest in the counterfactual theory of causation, given its best-known formulation by David Lewis. Second, there has been increasing philosophical interest in the techniques of causal modeling developed and employed within fields such as econometrics, epidemiology, and artificial intelligence. These two developments have been largely independent and addressed to different sorts of problems. Work in the counterfactual tradition has been primarily concerned with issues involving "token" or "singular" causation, while work in the second tradition has tended to focus on issues concerning "type-level" or "general" causation