# Recently in Open Theism Category

## A moderately smart being that knows all necessary truths can know everything

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.

To make this pointed, note that those open theists who think that there are facts about the future that God doesn't know tend to think that God knows all necessary truths.

## The New Collection

Seems that describing it as "shameless self-promotion" absolves one, though I doubt it. But that's the line so I hereby use it, whatever purgatory consequences... My new collection, in draft form, LaTeX'ed to beautiful purposes by Oxford's document class, is here.

Any thoughts welcome, of course--would love to minimize the errors!

## Foreknowledge of free actions

I think the following yields a pretty good formulation of the argument for incompatibility of foreknowledge and free will. Start with the principles:

1. If x freely chooses A at t, and p is a truth solely about what happened prior to t, then p does not entail that x freely chose A at t.
2. <God believes at t* that x freely chooses A at t> entails <x freely chooses A at t>.
3. <God believes at t* that x freely chooses A at t> is solely about what happens at t*.
Now note that if I will freely choose A tomorrow, and God has foreknowledge, then God now believes that I freely choose A tomorrow, and <God now believes that I will freely choose A tomorrow> is a truth purely about what happens today that entails that I freely choose A tomorrow, contrary to (1). So if (1)-(3) hold, then God lacks foreknowledge or we don't choose freely.

But here is a criticism of (1) that I don't remember seeing, though it's obvious enough that I expect it's there somewhere. Claim (1) is supposed to capture our intuition about alternate possibilities. But it fails to capture these intuitions. Consider this case. Suppose the laws of nature are necessary, and you simultaneously deterministically cause me to have an irresistible desire to do a Hitler salute and push me into a time machine so that it is nomically necessary that I perform the Hitler salute in the year 3000 BC. Next thing I see, it's the first moment of the year 3000 BC, and I am doing a Hitler salute. Intuitively, here is a violation of alternate possibilities. But (1) does not indicate this. Let p be a complete description of the universe at the time you push me into the time machine. Then p entails that I do a Hitler salute in the year 3000 BC. But p is not a proposition about what happened prior to the year 3000 BC. Hence, (1) does not rule out my freedom, even though it is surely meant to.

Here's a second, less weird case. Simultaneous causation is at least imaginable. Imagine the laws are necessary, and there is some state of the world that deterministically causes me to simultaneously raise my arm in a Hitler salute. Again, (1) does not tell me that the action is unfree, even though the alternate-possibilities intuitions that led to (1) surely do. So (1) does not capture these intuitions.

## What does an open-theist non-open-future deity know?

Suppose that the future is not open, so that there are non-trivial truths about what people will freely do. (If we want more precision, we may suppose unrestricted bivalence, excluded middle and the rule: (exists(t) & t>now & ~will-hold-at(p,t)) → will-hold-at(~p,t).) According to ot, God does not know all such truths. Thus, according to non-open-future open theism (nofot), God knows some but not all truths. If one accepts nofot (as van Inwagen and Hasker seem to), then when defining the range of omniscience (there are several aspects to omniscience: the range aspect specifies what truths are known by the omniscient being; but there is also the inerrance aspect, the justification aspect, and maybe a modal aspect), we cannot simply say that God knows all truths. Something else needs to be said.

Some have said things like this:

1. God knows p iff p is true and in some possible world p is known by somebody (cf. van Inwagen).
That doesn't work. Under uncontroversial assumptions, it can be proved that (1) implies that God knows every truth. The argument is very simple. Suppose tomorrow I will freely mow the lawn. In some worlds, God knows that tomorrow I will freely mow the lawn or Obama is not president, since in those worlds God knows that Obama is not president. But then by (1), in the actual world, God knows that tomorrow I will freely mow the lawn or Obama is not president. But in the actual world God knows Obama is not president. Closure principles apply to divine knowledge, so in the actual world God knows that tomorrow I will free mow the lawn.

Anyway, Bill Hasker and I have had an extended email discussion on the question of how to define the range of omniscience, and Bill kindly let me comment on that discussion in public, as long as I included "the statement that [Hasker's] personal concern is primarily with the question, 'What truths must God know, if God is omniscient?'" I take this to mean that Bill's focus is on the issue of the range of omniscience.

## An Advantage of Open Theism?

I am tempted by the claim that open theism is in a better position to respond to the problem of evil than is Molinism. Consider some particular evil e1 that has occurred at a particular time t2. A group of innocent German Jews is gunned down before a mass grave they have been forced to dig themselves, let's say. On the open view, God knew at some time before t2 that e1 would occur. But God did not know that e1 would occur from time immemorial. It won't be as if God has built e1 into the basic structure of the world, as it appears God does on Molinism. Intuitively, it seems to be easier to defend God's failure to prevent e1 given that God becomes aware of its forthcoming occurrence at t1 rather than prior to the creation of the world. That, at least, is how it has seemed to me.

Against this intuitive appeal comes the "Molinist Retort". The basic idea behind it is that whatever resources are available to the open theist to justify God's permission of e1 at t1 are equally available to the molinist to justify God's permission of it from before the creation of the world. Presumably the open theist will have to appeal to some kind of balancing of goods contingent upon free will over against the amount and gruesomeness of evils parasitic upon the goods. The molinist can claim to make appeal to these self-same considerations. I think this retort fails.

## Adams and "The Virtue of Faith"

I recently finished Robert Adams' old article "The Virtue of Faith" (chapter 1 of the book The Virtue of Faith), and I found a really interesting point. Uncertainty and faith are necessary for a certain sort of special good in a relationship. I think it's worth quoting Adams on this:

## Problems for the standard view of an everlasting God

The standard view of an everlasting God is that God has existed in time for an infinite amount of time and will continue to exist for an infinite amount of time, and a finite amount of time ago, creation sprang into being. Thus, God existed a year ago, a billion years ago, a trillion years ago, and so on. (I think, though I shall not argue for this here, that if one denies God's atemporality, one should adopt the standard view on pain of believing something theologically much worse, such as that God has a finite age or that creation is infinitely old. So if the standard view of everlastingness is false, then God is not atemporal.)

I shall talk of the universe springing into being a finite amount of time ago rather than its' being created a finite amount of time ago, to disambiguate between the time of the cause (God's act of creating) and the time of the effect (the universe's springing into being).

Problem 1 (Augustine's problem): Why did God wait this infinite amount of time before the universe sprang into being, rather than, say, making the universe spring into being a hundred years earlier? Augustine records the old chestnut that God was busy preparing a hell for those who ask such questions. His own answer that time began with the universe's springing into being is not available to the defender of the standard view. One might take a relational view of time on which the question does not make sense--the world where God create a hundred years earlier is the same world. Only a B-theorist can say that, and not every B-theorist can.

Problem 2 (Deliberation and omniscience): Suppose God at t0 is deliberating what should spring into being and when it should do so. But God being omniscient already knows what will spring into being and when it will do so. How can one deliberate over what one already knows?

## Excluded middle

Some, but not all, open futurists deny excluded middle for future contingents. Thus, they deny that either there will or there will not be a sea battle tomorrow. Here is an inductive argument to the contrary: A sea battle typically requires a conflict between naval powers that has been brewing for some time. Such a conflict is probably not brewing right now. Therefore, probably, there will be no sea battle tomorrow. But if there will be no sea battle tomorrow, then there will or will not be a sea battle tomorrow (disjunction-introduction). Hence, there will or will not be a sea battle tomorrow. But if there will or will not be a sea battle tomorrow, views that deny excluded middle for future contingents are false.

## Omniscience

Consider two claims about God's knowledge.

1. For all p, if p, then God knows p.
2. For all p, if p, and possibly God knows p, then God knows p.
It is an interesting fact that (2), combined with two uncontroversial premises, entails (1). I said this in an earlier post, but now I have a more elegant argument. Here are my uncontroversial premises:
1. Necessarily, God's knowledge is closed under conjunction and tautological implication (i.e., if God knows p and God knows q, then God knows (p and q), and if God knows p, and p tautologically implies q, then God knows q).
2. There is at least one proposition p such that possibly God knows p and possibly God knows not-p.
Obviously, the proposition p in (4) is contingent, since knowledge entails truth.

Here is the argument that (2)-(4) entail (1). Fix any true p. By (4), let q be any proposition such that possibly God knows q and possibly God knows not-q. If q holds, then let r=q. If q does not hold, then let r=not-q. Note that r is true. Observe that possibly God knows not-r (if r=q, then this follows from the fact that God possibly knows not-p; if r=not-q, then this follows from the fact that God possibly knows q as well as (3), since q tautologically implies not-r). Let s be the proposition (p or not-r). Then, God possibly knows s. For God possibly knows not-r, and in any world where God knows not-r, God also knows (p or not-r) by (3). Now, s is true as p is true. Therefore, s is a proposition that is true and possibly known by God. Therefore, by (2), God knows s. Moreover, r is a true proposition, and God possibly knows r (since God possibly knows q and God possibly knows not-q). Therefore, God knows r, by (2). But s is (p or not-r). By (3), it follows that God knows p, since (s and r) tautologically implies p.

So if one attempts to limit omniscience by saying that omniscience only means that God knows things that God can know, or that God only knows things that possibly are known by someone (which also entails (2)), one hasn't limited omniscience at all: God still ends up knowing all true propositions, assuming (3) and (4). Is there some other way of non-arbitrarily limiting omniscience? I am not sure. But, fortunately, there is no need to limit omniscience. God knows all truths.

If open future views are true, I think it is puzzling that we have so many propositional attitudes about future propositions that we are in a position to know for sure are not true. We intend, fear or hope (or al three at once!) that something will happen, though the propositions that are the objects of our intentions, fears or hopes are typically ones that, according to open future views, either lack truth value or are false, and sometimes even necessarily false (thus, on the view of Rhoda et al., propositions saying that someone will freely do something are necessarily false). In fact, much of our life is spent dealing with these allegedly non-true propositions. These propositional attitudes are sometimes inappropriate, but sometimes quite appropriate. If one has the intuition that our lives as emoters and agents should be centered on reality, the sheer amount of life appropriately spent in concern about the future will be in tension with open future views.

## Modality and open future

I've been thinking what open future (OF) views can say about the modality of statements about the future. There are two OF semantics, which I'll call N and F. Suppose Curley now exists, and that Curley's freely taking the bribe is open. On the N semantics, Curley will freely take the bribe is neither true nor false. On the F semantics, it is false that Curley will freely take the bribe. The N semantics requires denial of excluded middle. The F semantics requires denial of the principle that, basically, not(will(p)) iff will(not(p)).

Suppose now that we say that a proposition p possibly/necessarily/impossibly is V iff p is V in some/all/no worlds, where V is a truth value or a logical combination of truth values like "neither true nor false", which I will abbreviate "ntnf". Let p be the proposition that Curley will freely take the bribe. On the F semantics, p is false in every world. For in some worlds Curley's freely taking the bribe is open, and in those worlds p is false by that semantics. And in all other worlds, it is determined that Curley won't freely take the bribe (e.g., because it is determined that there is no Curley, or that nobody will ever offer Curley a bribe, or whatever). So, in every world, p is false, and so p is necessarily false.

On the N semantics, things are more interesting. In worlds where Curley's freely taking the bribe is open, p is ntnf. In worlds where Curley's freely taking the bribe is not open, p is false. Therefore, on the N semantics, p is possibly ntnf and possibly false, and necessarily not true.

So what's wrong with this? Well, one thing is that as Geoff Pynn pointed out in the previous discussion of open futurism, the open futurist surely wants to say that p is a "future contingent". But if p is necessarily false, as it is on the F semantics, then that's endangered. And if p is necessarily not true, then it's also in a bit of trouble.

## Counterintuitive Consequence of Open Theism

I was talking w/Alan Rhoda at the Central APA, and I discussed with him the following counterintuitive implication of versions of open theism which say that all future contingents (or sentences about freely willed acts) are not true.

me: I bet that Curley will take the bribe tomorrow.
Alan: I don't think he will.
me: let's bet!
Alan: okay.

Tomorrow comes. Curley takes the bribe.

me: I was right!
Alan: I guess you were!

It seems that when I say "I was right!" I am ascribing truth to the sentence I uttered the day before. And intuitively, I speak truth when I ascribe truth to the sentence I uttered the day before. And if it is true that I correctly ascribe truth to the sentence I uttered the day before, then I did speak truth the day before. But some versions of open theism are committed to the counterintuitive implication that I did not speak truth the day before (i.e., utter a true sentence).

Two points: not all versions of open theism have to deal with this (e.g. Hasker's). Secondly, I take this only to be some degree of negative evidence against open theism; perhaps there is more positive evidence for open theism.

I've heard this objection a lot in conversation, though I haven't seen it in the literature. If I were an open theist, I'd just say that ordinary people have false views about the future, and so they are speaking incorrectly in these cases. Are there better ways out of this problem? Has there been any literature on this?

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