A problem for counterfactual sufficiency

The consequence argument purports to show that determinism is true only if no one has free will. Judgments about whether the argument is sound depend on how one understands locutions of the form ‘p and no one can render p false’. The main interpretation on offer appeals to counterfactual sufficiency : s can render p false just in case there is something s can do such that, were s to do it, p would be false; otherwise, s cannot render p false. Here I show that, in the context of the consequence argument, this interpretation conflicts with widely endorsed principles governing the logic of counterfactuals.