Suppose Open Theism (OT) holds. There is a possible world where a demon is better off doxastically than God in respect of future free actions of creatures. On some views of inductive knowledge, there is a possible world where a demon is better off epistemically than God in respect of future free actions of creatures. Hence OT is false. This may be all old hat. But, hey, it's fun to reinvent the wheel–the thrill of discovery, of seeing it roll, etc. Now I need to argue for my above claims.
Argument. Suppose OT is possible. Then:
- There is an infinite set W1 of worlds w which contain the God of OT, and many free creatures that perform many free choices, and exactly one very big book, in Chinese, residing on Pluto, where that book purports to describe the complete history of all the free actions of creatures over all the time during which free actions are done.
- There is an infinite subset W2 of W1 consisting of worlds such that every sentence of that book either ends up being true.
- There is an infinite subset W3 of W2 consisting of worlds w such that a logically consistent and very smart demon has got hold of the book before most of the free actions of creatures in w were performed, where that demon was instantly convinced that every sentence of the book is true, and where that demon formed no beliefs about the free actions of creatures besides the claims in the book.
Let w be a world from W3, let D be such a demon, and let B be the book. Then D has correct beliefs about all future free creaturely actions, and these beliefs fully specify all future free creaturely actions. Now the God of OT in w only has probabilistic beliefs abouts these actions. These are all true, but the true beliefs of D about these actions are much more specific. Then, in w, D is doxastically better off than God vis-a-vis future free creaturely actions. He has true beliefs about many specific things about which God has only probabilistic beliefs.
It does not follow that D is epistemically better off than God is. Indeed, it seems as if D does not know any of these true propositions in the future. But it is theologically bad enough that D is doxastically better off than God, especially if it is in an area where the tradition holds that God's knowledge is paradigmatically impressive (think of how impressed we are at correct prophecy). And, as Socrates notes, all we need to successfully guide our actions is true belief, not knowledge. The God of OT will be deeply surprized at D's uncanny correctness of beliefs about future free action, and will have been outdone doxastically by D in this respect. The possibility of outdoing God doxastically in such a total and impressive way is deeply repugnant theologically. Hence OT is false.
But maybe D's unreasonableness in accepting B makes him doxastically poorly off. I am not sure. The telos of the doxastic faculty is grasp of the truth. One is worse as an epistemic agent in being unreasonable, but if the unreasonableness actually contributes to the telos of the doxastic faculty, this unreasonableness does not decrease doxastic welfare. There are circumstances where by being imprudent one will end up better off, and there are circumstances where by being unreasonable one will end up better off doxastically.
Now suppose that D gets the book early on in the world's career, and instead of believing it is right from the outset, he carefully compares the book's predictions to actual events, and finds they match. He forms an inductively justified belief that all of the book's predictions of actual events are true. The evidence is incredibly impressive here. Now, D is no longer unreasonable in accepting the predictions. In fact, he would be unreasonable not to. So we can no longer excoriate D for his intellectual vices.
Moreover, arguably, this is knowledge. It is a plausible claim about induction that if all Fs hitherto observed have property P, and if all future Fs will in fact end up having P, and if the class of Fs is not gerrymandered, and if there is no undefeated defeater available, then one knows that all future Fs will end up having P. Here let the Fs be free creaturely actions, and let P be the property of having been correctly predicted by the book B.
might object that the demon has a defeater for his belief in the reliability of B. For the arguments for OT, if sound, will establish that the future is inherently contingent and essentially unpredictable, so that if B has been right so far, it has been right only by a fluke, and there is no reason to suppose the flukish rightness will continue.
However, the demon may have never thought of these arguments for OT. Moreover, the demon has a defeater for these arguments. The arguments for OT contain controversial premises. These premises may be plausible (I don't think so myself) but they are not indisputable. If these controversial premises are true, then the success of B so far is incredibly improbable if, say, a billion described well-balanced choices have been verified (as we may suppose; a choice is "well-balanced" if the agent has reasons and desires well-balanced on both sides; I am simplifying some inessential technical issues here). This success gives good reason to reject at least one of the controversial premises. If the plausible claim about induction holds, then D knows that B is always going to end up being right. And so D is epistemically better off than the God of OT.
That D should be epistemically better off than God in connection with future free action is theologically repugnant. (Query: Why can't the God of OT use the same inductive argument as D does? Because the God of OT unshakably knows the premises of the arguments for OT to be true.)