On the Consistency Rule in Causal Inference: An Axiom, Definition, Assumption, or a Theorem?

In two recent communications, Cole and Frangakis and VanderWeele conclude that the consistency rule used in causal inference is an assumption that precludes any side-effects of treatment/exposure on the outcomes of interest. They further develop auxiliary notation to make this assumption formal and explicit. I argue that the consistency rule is a theorem in the logic of counterfactuals and need not be altered. Instead, warnings of potential side-effects should be embodied in standard modeling practices that makes causal assumptions explicit and transparent.