Explaining conjunctions and conjuncts

Alice is the chair of a small Department, there being only one other faculty member, Bob. Alice asks IT to run anti-virus software on all the Department faculty computers, namely her computer and Bob’s computers. IT does so. The software deletes a virus on Alice’s computer but finds none on Bob’s.

Alice’s order that anti-virus software be run on her and Bob’s computer explains why her and Bob’s computer are now virus-free by ensuring that they are both virus-free. But Alice’s order does not explain why her computer is now virus-free. Hence once can explain a conjunction without explaining every conjunct.

Van Inwagen’s famous argument against the Principle of Sufficient Reason (PSR) as well as some versions of the Cosmological Arguments from the PSR to theism depend on the idea that if something explains the conjunction of all contingent truths, then it explains every contingent truth. This in turn seems to be based on the claim that when you explain a conjunction, you explain every conjunct—something we have just seen to be false.

I think these arguments can be fixed by noting that although Alice’s order didn’t in fact explain why her computer is now virus-free, it ensured that her computer is virus-free. And perhaps one can weaken the conjunction principle to say that if p explains a conjunction, then p explains some conjuncts and the facts reported by p ensure the other conjuncts. I suspect that will be good enough for the applications (even the one I disagree with, namely van Inwagen’s).