Peter van Inwagen and Jonathan Bennett developed a simple and influential argument that the principle of sufficient reason (PSR) entails that there is no contingency in the world. Everything that happens, necessarily happens. The problem is deeper than it first appears. If PSR is true and God explains everything else, as many theists believe, then the cost of preserving God’s perfect rationality is the loss of His freedom, His moral perfection, and His providence and sovereignty. We are left with a single necessary world. The costs also include the loss of contingency and moral agency among created beings in the world. On the other hand, the cost of abandoning His perfect rationality is the unintelligibility of the world (which has disastrous effects on our reasoning with one another) and the unintelligibility of God’s actions in it. We cannot easily give up PSR.
The argument can look gimmicky, and I’ve heard that criticism of it. But it’s no gimmick. Suppose we talk of the explanation of states of affairs derivatively, and the explanation of propositions directly. For every true contingent proposition p, PSR requires that there is some explanation q such that q explains p if and only if ☐(q ⊃ p). But the conjunction P of all true contingent propositions is a contingent proposition, so P too has an explanation. Let G be the explanation of P. G must be a necessarily true proposition, since otherwise G would be a conjunct in P. But then G would be a contingent proposition that explained, among other things, itself. No contingent propositions explain themselves. So, P has an explanation just in case for some Q, ☐(Q ⊃ P) & ☐Q. But it follows uncontroversially from this that ☐P, and we are left with all of the unwanted implications above. I think there’s a neat way out of this problem that does not require weakening PSR, or adopting a weaker notion of explanation or defending infinite chains of contingent explanation.
Make the observation that if the conjunction P is contingent and true, then so is the conjunction P & ◊P’, where P’ is itself a conjunction of all true propositions in possible world W’. (◊P’ is just the proposition that possibly P’). Let the larger conjunction be R. Now, we know that R is contingent, but we also know that R is necessarily contingent. There is no possible world in which the conjunction of propositions in R are all true and there is some necessary Q that explains R. That is, there is no world in which there is some Q such that ☐(Q ⊃ R) & ☐Q. So, it is impossible to derive ☐R from any necessarily true proposition. It is not merely the case that R is a contingent proposition with no explanation; rather, it is the case that R is a contingent proposition that is impossible to explain. But surely PSR cannot entail that a perfectly rational being would explain contingent propositions that are impossible to explain. PSR requires that every proposition that could be explained should have an explanation. Since there are lots of contingent propositions like R, we can have our cake and eat it too. We have every proposition explained that can be explained, and we have contingency in the world. And we avoid all of the unwanted implications of the loss of contingency noted above.