I just came across a quote from Leibniz that I must have read before but it never impressed itself on my mind: “no reason can be given for the ratio of 2 to 4 being the same as that of 4 to 8, not even in the divine will” (letter to Wedderkopf, 1671).
This makes me feel better for defending only a Principle of Sufficient Reason restricted to contingent truths. :-)
It may seem initially slightly surprising, but there are necessary truths that are explained by contingent ones. For instance, it is a necessary truth that Obama is president or 2+2=4. And this necessary truth can be explained by the fact that the majority of the electoral college voted for Obama, or, perhaps even better, by facts about the way the Democrats and Republicans campaigned. Another necessary truth that can be explained in the same way is that it is or is not the case that Obama is president.
That the necessary can sometimes be explained with the contingent is, I think, a rather more trivial claim than that the contingent can be explained with the necessary.
Suppose Fred knows all necessary truths and is at least as smart as the author of this post. Fred wants to know whether a proposition p is true. So Fred says: "I stipulate that P is the singleton set {p} and that S is the subset of all the members of P that are true." But sets have their members essentially. So S is necessarily empty or necessarily non-empty. If S is necessarily empty, then Fred knows that, and if S is necessarily non-empty, then Fred knows that, too. Since Fred is at least as smart as the author of this post, if Fred knows that S is necessarily empty, he can figure out that therefore S is empty, and hence that all the propositions in P are false, and hence that p is not true. And if Fred knows that S is necessarily non-empty, then Fred can figure out that therefore S is non-empty, and hence that p is true. In either case, then, Fred can figure out whether p is true.
