Judea Pearls insight that, when errors are assumed independent, the Pure (aka Natural) Direct Effect (PDE) is non-parametrically identified via the Mediation Formula was `path-breaking in more than one sense! In the same paper Pearl described a thought-experiment as a way to motivate the PDE. Analysis of this experiment led Robins & Richardson to a novel way of conceptualizing direct effects in terms of interventions on an expanded graph in which treatment is decomposed into multiple separable components. We further develop this novel theory here, showing that it provides a self-contained framework for discussing mediation without reference to cross-world (nested) counterfactuals or interventions on the mediator. The theory preserves the dictum `no causation without manipulation and makes questions of mediation empirically testable in future Randomized Controlled Trials. Even so, we prove the interventionist and nested counterfactual approaches remain tightly coupled under a Non-Parametric Structural Equation Model except in the presence of a `recanting witness. In fact, our analysis also leads to a simple sound and complete algorithm for determining identification in the (non-interventionist) theory of path-specific counterfactuals.
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