Compatibilists like Hume accept the Principle of Alternate Possibilities (PAP): if x freely does A, then x could have refrained from doing A. However, they give a counterfactual spin to the "could have": x could have done A if and only if were x to have willed to do A, x would have done A.
- This Humean analysis of "could have" is correct.
- Lewis's account of counterfactuals is correct.
- Determinism holds.
- On some non-initial occasion I could have done otherwise (in the Humean sense).
The argument is simple. Suppose on that occasion I did A. Let p be the proposition that on that occasion I did not do A. On Lewis's account of counterfactuals, I evaluate counterfactuals of the form "were p to hold, q would hold" by looking at worlds close to w0 but where p holds, and in a deterministic case, these worlds match the actual world up to near the time of that occasion, and but depart therefrom in a way that goes against the laws of the actual world, i.e., in a way that is w0-miraculous. Hence, "were p to hold, a w0-miracle would occur" holds, and by the Humean analysis of "could have", it follows that I could have acted in such a way that a w0-miracle would have occurred.