Tuesday, October 19, 2010

Open theism and divine error

  1. (Premise) If p is overwhelmingly probable on the balance of God's evidence, then God believes p.
  2. (Premise) If open theism is true, then some of the propositions that are overwhelmingly probable on the balance of God's evidence are false.
  3. Therefore, if open theism is true, God believes some falsehoods.
  4. (Premise) God believes no falsehoods.
  5. Therefore, open theism is false.
I think (2) is not that hard to argue for on the assumption that there will be infinitely many approximately independent free choices made in the future. Here is a plausibility argument for that assumption: at least some persons will live forever (this follows from divine goodness), and it is plausible that they will always be choosing freely (this follows from the value of freedom). To argue from this to (2), I will make the simplifying assumption that by law the choices are always between options A and B, and that the nth choice occurs exactly n years from now. For any prime number k, let pk be the proposition that the choice made k years from now, or the choice made k2 years from now, or the choice made k3 years from now, ..., or the choice made k100 years from now will be A. The probability of pk is 1−2−100 given the setup. Then pk will be overwhelmingly probable on the balance of God's evidence if open theism is true. But it is also all but certain that at least one of the propositions pk, where k is a prime, is false. For they are independent, and given infinitely many independent propositions of probability 1−2−100, it is all but certain that at least one is false. Hence some overwhelmingly probable proposition is false.
What about (1)? This is tougher. It is false that rationality requires us to believe everything that is overwhelmingly likely. We have to be careful not to clutter our minds with junk beliefs, because our minds are limited. But this concern does not apply to God. But, maybe, we could say that God should be very careful to avoid false beliefs. However, it would be a sign of irrationality, of an undue punctiliousness, to withhold belief simply because there is some tiny non-zero probability of the belief being false. God is not irrational. So God will believe what is overwhelmingly likely.


Heath White said...

If I were an open theist, I would deny (1). I would start by saying that God has credences matched to probabilities, and acts on those, like a good Bayesian perhaps. It might be pointed out that he would need evidence for these probabilities. Then maybe God has some range of uncertainty in his beliefs. I am not sure if this solution works in full.

Alexander R Pruss said...

But it seems plausible that to attach an overwhelmingly high credence to a proposition is to believe the proposition.

Richard H said...

"(Premise) If p is overwhelmingly probable on the balance of God's evidence, then God believes p. "

The temporality of p can be ambiguous. P as a current state of affairs seems different than p as a possible future state of affairs. Different types and amounts of evidence (or credences) pertain to each, leading to different shades of meaning in "believe." If p is conceived as a future state of affairs, it would make sense to understand "God believes p" as equivalent to "God expects p." This equivalence doesn't work if p is a present state of affairs.

I have seen instances of God's activity in scripture that can be read as frustrations of God's expectations (regarding future states of affairs). I do not remember any frustrations of God's believing of present states of affairs.

#1 seems to presuppose then, a commitment to a version of divine timelessness that Open theists would deny.

Heath White said...

You could go that direction, in which case (1) becomes more or less trivial. Then the burden shifts to (4): we can translate it as "God never attaches overwhelming credences to states of affairs which wind up not obtaining." Presumably the OT will deny this. Though we might wonder if this just saves omniscience at the price of God being, not *wrong* precisely, but *fooled* occasionally.

I think this highlights the degree to which omniscience is interesting mainly for its implications for divine providence.

Anonymous said...

I wrote on my own site about this post that I think the open theist could simply deny (4) at the price of saying that God can believe falsehoods. Do you think this is implausible?

Eric said...

I agree with Heath, if I were an open theist (which I am not) I would say that God holds beliefs with probabilities in proportion to their likelihood.

I think Alex's suggestion that "to attach an overwhelmingly high credence to a proposition is to believe the proposition" is not quite correct.

Attaching an overwhelmingly high credence to a proposition is functionally the same as believing it for less than perfectly rational creatures like ourselves, but I think anything like an omniscient divine being (even the open theist version of Him) would distinguish between the two categories.

Alexander R Pruss said...


Suppose that attaching a sufficiently high credence is the same as believing. Then we have two basic ways of erring:
1. We attach a credence that is not justified by our evidence.
2. We believe, but it's false.

Type 2 errors can arise in two ways:
2a. The false belief is there because we don't follow the evidence (we commit a type 1 error).
2b. The false belief is there because the world doesn't follow the evidence.

If Open Theism is true, God isn't subject to type 1 errors, and hence he isn't subject to type 2a errors. But he is subject to type 2b errors, just as we are, only more rarely. I suppose it does make sense to call type 2b errors as cases of "being fooled". But they are errors, nonetheless. (Though I don't think I'd call them "mistakes".)

The Open Theist may even have to say that God's beliefs are contradictory, as in the preface paradox. For if my argument is sound and Open Theism is true, then God will also have overwhelming evidence for the claim that some of his beliefs are false. So he will both have some large finite set B of beliefs about future choices and he will believe that at least one of the beliefs in B is false.

Brandon said...

I'm inclined to agree that (1) is the obvious one for the open theist to reject, and rightly so: if p is overwhelmingly probable on the balance of God's evidence, it is certainly (and in a sense trivially) true that God regards p as overwhelming probable; but this is simply different from believing p. If I buy a lottery ticket, I would, of course, regard it as overwhelmingly probable that I would not win the jackpot; but there's no clear sense in which this means that I believe that I won't win it. In fact, it's obvious that I don't believe p here, even though I do believe that p is overwhelmingly probable.

Alexander R Pruss said...

I think there may be a difference between believing that a proposition Q has probability p on my evidence and assigning credence p to Q. In the lottery case, you believe that Q has very high probability on your evidence, but maybe you don't actually assign that high credence to Q? Though you really should assign that high credence and believe the proposition, unless doing so unduly clutters your mind or some other such pragmatic consideration applies. :-)

I should say I am not that committed to the identification of belief with high credence.

But whether the two are identifier or not, wouldn't the following be a weird thing to say? "I know P. I also know that Q is more probable than P on my evidence, but I don't believe Q." It would be OK to say this if one had some pragmatic reason, like not cluttering one's mind (which wouldn't apply to God), but otherwise it just doesn't sound rational to me. Yet, unless we implausibly want to say that the only things we know are ones that have probability 1, some of the lottery propositions will be more probable than some of the things you know.

I know this is well-worked over in the literature, and a lot of smart people like John Hawthorne disagree with this line of thought. But it still seems right to me. :-)

Kief said...

I thought that open theists would deny (2). This is what I gathered from Greg Boyd's chapter in: http://www.amazon.com/Divine-Foreknowledge-James-K-Beilby/dp/0830826521

He says that propositions about future states are neither true nor false because they don't yet exist. If that's the case, then (2) is a misrepresentation of open theism. Maybe I read him wrong, though. I'm no professional, haha.

Kief said...
This comment has been removed by the author.
Alexander R Pruss said...

The cost of that view is that he has to say that some states are probable even though they certainly don't have truth value. But then he has to say that "p is probable" means something other than "p is probably true".

Kief said...

Couldn't he say something like "p will probably be true"? But then I wonder what he would do with the truth value of that statement...