- X is sufficient for Y if and only if, if X then Y.
- C is sufficient for AvB (Principle of Disjunctive Causation)
- If C is sufficient for AvB, then C is sufficient for A.
- Therefore, C is sufficient for A.
Premise 3 is supposedly the problem, but I think it shouldn’t be. If C is sufficient for explaining a disjunctive state of affairs, then presumably it can explain any state of affairs on which the disjunction is true. Sure, something may be left out (that darn resilient contrastive problem again), but I’m still putting off dealing with that for now, and simply aiming to clarify how the Principle of Disjunctive Causation is supposed to play an explanatory role. If it works, then it very clearly does get one out of van Inwagen’s problem, since we can imagine that C is a necessary truth, and that A is a contingent truth, and yet C is clearly sufficient for explaining A (if the above argument is sound), ergo a necessary fact can sufficiently explain a contingent fact (just in case it is possible for a necessary fact C to cause a disjunctive state of affairs).
[Edit: This post obviously has a glaring difficulty, which is that premise 3 is clearly false given how sufficiency was defined in premise 1. I dealt with this in the comments so I thought I’d just leave the post as is, as a record of my mistake. However, I’ve been asked to change the post, and I think it might be worth doing in order to avoid future objections on the blog and off. So, let me be clear, this argument fails. I think maybe it could be reformulated if the first premise read as follows: “X is a sufficient explanation of Y if and only if, both, if ~X then ~Y, and, X is the cause of Y.” I say that X is the cause of Y in addition to (~X⊃~Y) because neither conjunction nor even entailments properly track causal relations.]