An equivocation in the simple argument for downward causation

I argue that Kroedel's 'Simple Argument' for downward causation fails and that this failure has consequences for any attempt to establish the reality of downward causation by appealing to counterfactual theories thereof. A central premise in Kroedel's argument equivocates. On one reading, it is true but renders the argument invalid; on another, it renders the argument valid but is likely false. I dedicate most of my efforts to establishing the second of these two claims. I show that the purported physical effects of mental properties do not counterfactually depend upon the total realizers of these properties. If counterfactual dependence is necessary for causation, it follows that mental properties are not causes. If counterfactual dependence is merely sufficient for causation, it follows that no appeal to counterfactuals will by itself succeed in showing that mental properties are causes.