Consequence arguments like Peter van Inwagen's basically conclude that if determinism is true, then if p is any truth, Np is also a truth. Here, roughly (different formulations will differ here), Np says that p is true and that there is nothing anyone could do to make p false.
Supposedly this conclusion is a problem for the compatibilist. But why? Why can't the compatibilist just say: "I freely and responsibly did A, even though N(I did A)"?
I suspect that the consequence argument has a further step that is routinely left out, and this involves an application of the inference rule:
- gamma: If Np, then no one is responsible for p.
The argument above does use a somewhat problematic step: going from "I am responsible for voting for A" to "I am responsible for its being the case that I vote for A". But the point is sufficient to show that gamma is problematic.
My suspicion is that gamma is correct in the case of finite agents and direct agent-responsibility of the sort involved in criminal law, but not in the case of the kind of outcome-responsibility that is involved in tort law. For the kind of outcome-responsibility that is involved in tort law is tied to but-for conditionals: but for my doing something, the harm wouldn't have happened. It is correct to say in the Frankfurt case that I don't have that sort of responsibility. Had I not chosen to vote for A, I would still have voted (or at least pseudovoted) for A. But I do have agent-responsibility for voting for A. If the elections were the American ones, I should be liable in criminal law for voting for A (I am Canadian, so for me to vote in U.S. elections would be an instance of fraud), but not in civil law (even if my vote causes some harm to someone), in the Frankfurt case.