Tense Logic, Bivalence, and Open Theism
In previous blog posts I've discussed two opposing tense logics: (a) Ockhamist and (b) Peircean. Ockhamist tense logic takes as its characteristic axiom the claim that
(O) □(∀p)(∀t)(∀u: u<t)(IS(p,t) → WAS(WILL(p,t),u))In contrast, Peircean tense logic insists that (O) is a non sequitur, and replaces it with:
i.e., necessarily, for all propositions p, and for all times t and u such that u is prior to t, p is the case at t, then at u it was the case that p will be the case at t
(P) ◊(∃p)(∃t)(∃u: u<t)(IS(p,t) ∧ ¬WAS(WILL(p,t),u))The basis of the disagreement turns on whether the future tense operator, WILL, carries determinative force. In other words, if one is speaking strictly (not loosely) and predicts that something will happen, is it implied that the predicted event is necessitated by what obtains at the time the prediction is made? If so, then the Peircean is right. Otherwise, the Ockhamist is right.
i.e., possibly, for some proposition p and some times t and u such that u is prior to t, p is the case at t and it was not the case at u that p will be the case at t
Without trying to resolve that particular issue right now, I'd like to note that there are three possible results if the Peircean is correct, depending on how one answers two questions: (1) are there any propositions about the future that carry absolutely no determinative force whatsover, i.e., Ockhamist-style predictions? (2) If so, are these propositions bivalent, i.e., must they be either true or, if not true, then false?
- Option 1: Yes on (1). Yes on (2). This means that the future is alethically settled, i.e., there is an unchanging set of true Ockhamist-style predictions that completely characterizes the future as of any given time.
- Option 2: Yes on (1). No on (2). The future is alethically open (i.e., not alethically settled), but some Ockhamist-style prediction (those pertaining to future contingents) are neither true nor false.
- Option 3: No on (1). The future is alethically open and bivalence is preserved because there simply are no Ockhamist-style predictions.
- Version 1 - Involuntary Partial Nescience: God knows all that can be known, but there are truths about the contingent future that simply cannot be known, not even by God. (Richard Swinburne and William Hasker have espoused this view.)
- Version 2 - Non-bivalentist Omniscience: God is fully omniscient, i.e., knowing all and only truths. Ockhamist-style propositions about the contingent future are neither true nor false. (J.R. Lucas, among others, has espoused this view.)
- Version 3 - Bivalentist Omniscience: God is fully omniscience. There are no Ockhamist-style propositions about the contingent future. (Greg Boyd has espoused this view.)
posted by Alan Rhoda @ 11:05 PM
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19 Comments:
Great articulation Alan. I agree, of course. I'd only add one thing, a Version 4 to your three versions:
Version 4: Voluntary Partial Nescience--God chooses what to know and what not to know.
I don't think this version is really plausible, so I can see why you left it out. But it is one of the versions floating out there at the popular level at least. I've even had educated theologians offer it to me. They want to insist that the truth about what we shall do is "out there" but that God is free to choose not to know it. It allows us to keep God in 'control' of what he knows and doesn't know. I think some are troubled by the idea that God's not knowing something would be in any sense determined by realities outside of God. So if God 'chooses' to not know X, God's still in control of it all. But whatever those holding this version 4 believe its explanatory power to be, I think they're entirely misconceiving things.
Gotta go,
Tom
Thanks, Tom. You're probably right that I should have included that fourth version as well. The primary reason I didn't, as you noted, is that it really hard to see how divine voluntary partial nescience can be made plausible. If God voluntarily decides not to know that p, then either he subsequently knows that he decided not to know that p or he doesn't. If he knows that he decided not to know that p, then he still knows that p after all since that can be deduced from the fact that he knows that he decided not to know that p. But if he neither knows that p nor knows that he doesn't know that p nor has any other higher-level knowledge from which p could be deduced, then God could never voluntarily recover his knowledge since he no longer knows that it's there to be known.
Hi Alan,
Nice post.
You say, “The proponent of version 3 needs to make a persuasive case that Ockhamist-style predictions are not really propositions.”
Is this a new strategy to get out of the problem re: retroactively predicating truth of predictions? From what I remember of your papers, you didn’t argue that such predictions weren’t propositions, but that (amongst other things) usually such ‘predictions’ are best thought of as not predictions at all. I’d be quite interested in hearing what you’ve got in mind here.
(Oh, and sorry about the above-deleted comment; the format was all messed up.)
Hi Patrick,
You're right that I haven't brought up this issue in my papers. That's because I wasn't aware that it was an issue until about two weeks ago. While working on revising my "Defense of Prior's 'Peircean' Tense Logic" paper it occurred to me that an Ockhamist could concede the point that Ockhamist-style "predictions" aren't really predictions and go on to argue that's irrelevant as far as tense logic is concerned because Ockhamist-style "predictions" still count as propositions and thus need to be accommodated by tense logic. If that charge is right, then the Bivalentist Omniscience view collapses into either the Involuntary Partial Omniscience view or the Non-Bivalentist Omniscience view, depending on whether those Ockhamist-style "predictions" are bivalent or not.
As this point I can think of two different strategies for arguing that Ockhamist-style "predictions" are not even propositional.
(1) Following Peirce and Arthur Prior, argue that "the merely possible is invariably general". If that's right, then there are no singular propositions about future contingents, only general propositions. The drawback of this approach for an open theist is that it considerably lessens the prospects for a robust theory of divine providence. Instead of the infinitely intelligent Chess Master who can foresee ever possible move and board position, we'd instead have a Chess Master who can plan general strategies (like if my opponent attacks my kingside, then I'll try counterattacking on the queenside) but not work out specific move sequences.
(2) Develop and defend a general criterion of propositionality, like the CAD criterion I proposed a couple posts back, and show that Ockhamist-style "predictions" fail on that criterion. This approach offers better prospects for a robust theory of providence, but it will need to be strongly defended, ideally by showing how it can be used to help solve other philosophical problems (like the Liar's Paradox and such). Otherwise, the Ockhamist is just going to reject the criterion of propositionality on the grounds that it just seems "obvious" to him that Ockhamist-style "predictions" are propositional.
In short, there's a lot of philosophical work to be done here, and any insights you have to offer would be most welcome. I should have a revised version of my "Defense of Prior's 'Peircean' Tense Logic" paper ready by the end of the month. It's gonna be considerably expanded and, I think, improved.
Hi Alan,
Let me see if I’m following you. If I am, whether I’ll have any insights here remains to be seen!
You say, “it occurred to me that an Ockhamist could concede the point that Ockhamist-style "predictions" aren't really predictions and go on to argue that's irrelevant as far as tense logic is concerned because Ockhamist-style "predictions" still count as propositions and thus need to be accommodated by tense logic.”
Take the roulette example from your paper: “It is doubtful, then, that we should construe the utterance as a prediction at all. It may be more plausibly construed as autobiographical (“I’m guessing the ball lands on 20” or “I hope it lands on 20”) or as a performative (“I bet on 20”).”
If you’re right here, then even if such “predictions” count as propositions, then it doesn’t seem like the content of those propositions will be *the ball will land on 20*. Rather, won’t it be something like, *Patrick chooses 20* (which is presumably true or false) or something along these lines? In short, I’m not sure why you’re worried here. If the Ockhamist grants that the ‘predictions’ aren’t really predictions, then wouldn’t he also grant that the propositional content (if any) of such ‘predictions’ aren’t future contingent propositions (and hence, not propositions the truth or falsity of which would threaten the bivalentist OT)?
You raise a good point, Patrick, and maybe that's enough to defend bivalentist OT. I'll have to think about it some more, but let me try to restate my worry.
Granting that my assertibility argument is correct, then expressions like "E will occur at T" ought to be construed either as genuine predictions, in which case they carry causal or (more broadly) modal force, or not as genuine predictions at all. Suppose an Ockhamist concedes this much and then says, "OK, I can't rationally assert that E will occur at T without supposing that what now obtains makes probable E's occurring at T, but I can still entertain the possibility of E's occurring at T. I can hope that, fear that, suppose that, etc. E obtains at future time T. Since each of those is a propositional attitude, that E obtains at future time T is a proposition; hence it must have a truth value, etc."
Make sense to you?
Hi Alan,
I guess I’m not seeing it, which is probably a good thing! :)
You say (on behalf of the Ockhamist), “Since each of those is a propositional attitude, that E obtains at future time T is a proposition; hence it must have a truth value, etc."”
So the proposition in question is supposed to be *E obtains at future time T*. Now, why not say what we’ve been saying, namely that this is false at the present time, supposing that E’s occurrence is contingent at that time?
So just grant that there’s a proposition here on which the Ockhamist entertains certain attitudes, and say that the proposition is false. Am I missing you?
Alan: Suppose an Ockhamist concedes this much and then says, "OK, I can't rationally assert that E will occur at T without supposing that what now obtains makes probable E's occurring at T, but I can still entertain the possibility of E's occurring at T. I can hope that, fear that, suppose that, etc. E obtains at future time T. Since each of those is a propositional attitude, that E obtains at future time T is a proposition; hence it must have a truth value, etc."
Patrick: So the proposition in question is supposed to be *E obtains at future time T*. Now, why not say what we’ve been saying, namely that this is false at the present time, supposing that E’s occurrence is contingent at that time? So just grant that there’s a proposition here on which the Ockhamist entertains certain attitudes, and say that the proposition is false. Am I missing you?
Tom: That’s how I would treat it, Patrick. If the Ockhamist wants to rationally assert E at T without supposing that what now obtains makes E at T probable [not sure why you only said ‘probable’ here Alan; wouldn’t ‘inevitable’ be more consistent with the Ockhamist’s worldview?] by, say, hoping, fearing, supposing that, planning for, etc. E at T, all he’s doing is (a) positing the ‘logical possibility’ of E at T and then (b) admitting that he doesn’t ‘know’ whether E at T is in fact causally ruled out because of present reality. But open theists just argue this is how things really are anyhow. So we can ‘rationally fear, hope, suppose’ regarding the future can do so without being an Ockhamist. All doing so requires is the truth value of “possibly and possibly not E and T.” That’s enough to rationally fear, hope, etc. regarding the future. After all, “might and might not E at T” is the proposition a bivalent OT argues for, right?
Tom
Patrick,
I take you to be suggesting that whether Ockhamist-style "predictions" are propositions or not is irrelevant as far as Peircean tense logic goes because either (a) they are not propositions, or (b) they are propositions, but false ones just insofar as the corresponding Peircean-style prediction is false. So if the Peircean's "E will obtain at T" is false b/c E might not obtain at T, then the Ockhamist's non-causal, non-modal "E will obtain at T" is also false.
That's an interesting thought, and it may work, but here's the difficulty: As far as Ockhamist-style "predictions" are concerned, "will" and "will not" are contradictories because "E will obtain at T" and "E will not obtain at T" (a la Ockham) are equivalent to "E does obtain at future time T" / "E does not obtain at future time T", and "does"/"does not" are contradictories. So, if we say that Ockhamist-style "predictions" express propositions and are false insofar as the event "predicted" is a future contingent, then the Ockhamist is going to accuse us of inconsistently affirming that both parts of a contradiction can be false at the same time.
Tom,
I think you may be making a slightly different suggestion than Patrick, one that is more in line with my thought that us BOT's need to deny that Ockhamist-style "predictions" express propositions. For to insist on incorporating the modal character of the propositional attitude into the content of the propositional object of that attitude is, effectively, to deny that there can be anything like the non-modal or amodal "predictions" that the Ockhamist wants.
Here's the big difference between the Peircean and the Ockhamist: The Peircean wants to locate all talk about the future on a probabilistic continuum from "will not" (probability=0) to "will" (probability=1). The Ockhamist doesn't want to do this. He wants to speak directly of future actualities as though they were present. The only probabilistic implication of the Ockhamist's "will" is that the probability is >0. The only probabilistic implication of the Ockhamist's "will not" is that the probability is <1. Despite these implications, the Ockhamist's "will" and "will not" cannot be reduced to "possibly will" / "possibly will not". They are equivalent, rather, to something like "possibly will" + "actually does" / "possibly will not" + "actually does not". That there are such propositions is central to the Ockhamist's position. On that rests his hopes of reconciling "will" and "might not". If we try construing them just as "possibly" claims, the Ockhamist is going to cry "foul".
Alan,
Yes, that seems to be what I’m suggesting, though I’m not sure why you think it is just an interesting thought – I think I’m not understanding. You say, “So if the Peircean's "E will obtain at T" is false b/c E might not obtain at T, then the Ockhamist's non-causal, non-modal "E will obtain at T" is also false.” But isn’t this pretty straightforward? That is, if “E will obtain at T” is false, then it is false, period, whether in the mouth of a Peircean or an Ockhamist.
Concerning (b), I also had in mind to say, “Yes, perhaps the Ockhamist “predictions” are propositions, and here’s the sort of propositions they express: *Patrick chooses 20*, *Patrick has the attitude of liking 20 more than the other numbers*, etc.” So when someone “predicts” that the ball will land 20, the proposition there isn’t one that, if true, would even be about the future contingent event of the ball’s landing on 20, and hence, isn’t one that, if we retroactively predicate truth of, would threaten the OT. If the Ockhamist wants to argue against the BOT that we retroactively predicate truth of predictions, then she’ll have to also argue that the propositional content of such predictions are future contingent propositions. But it seems to me that, in granting that the ‘predictions’ are really not predictions at all, but rather statements of what someone chooses or some such, she grants that the predictions don’t express those propositions. (Hope that is clear).
Next, you say, “"E does obtain at future time T" / "E does not obtain at future time T", and "does"/"does not" are contradictories.”
Incidentally, I’ve just been having a discussion concerning this point over at Show-me the argument. (http://www.missouri.edu/~philwww/show-me/?p=229) But I took the line you and Tom take in the *OT, Omniscience, and the Nature of the Future* paper; are you backing off of that? That is, there you argued that *does* and *does not* aren’t contradictories, i.e. that the truth conditions for “X does obtain at T” is that it’s either true that X has obtained at T, is obtaining at T, or will obtain at T. And where X is a future contingent, it won’t have obtained and isn’t obtaining, so what’s left is that it will obtain, and then we’re back to the original claim re: ‘will’. So where X is a future contingent “X does obtain at T” (or “X obtains at T”) is false, and likewise for “X does not obtain at T”. Hence, they can both be false, so aren’t contradictories.
One thing I’m worried about, though, and I brought this up in the post at Show-me, is what the contradictory of ‘does obtain’ is in ordinary English. In other words, it would be great to show that both “X does obtain at T” and “X does not obtain at T” can both be false (and as of now, I think that can be done), but it’d be quite nice to say something more concerning what the contradictory of “does obtain” is if not “does not obtain”. That is, we can say that the contradictory of “will” is “might not” rather than “will not”, and that sounds pretty plausible. So what can we say for “does”?
This seems to me to be the weakness of the response to the tenseless proposition objection to the BOT. We say that “will or might not” is p v ~p. So what should we say for “does”? That is, if we want p v ~p, what do we put in the blank here: “does or _____”.
Patrick,
I agree with you that Ockhamist-style "predictions" are not really predictions at all. I just don't think our Ockhamist friends are going to be so easily convinced of that. What I'm trying to do is anticipate responses to my rational assertibility argument. I think the one I've suggested is likely to strike many Ockhamists as quite appealing, and I'm pretty sure they will fiercely resist any attempts on our part to respond with "But what you're really saying is this ..." Even if such a response is technically correct, it's likely to strike them as condescending and question-begging and consequently may prove counterproductive in the effort to sell BOT.
So, what I think the rational assertibility argument does show is that Ockhamism does not emerge naturally out of actual predictive discourse. That's a serious blow, because many of them have wanted to claim that their tense logic is the natural one. But it's not a decisive blow. Indeed, it may only prove to be more of a glancing blow if the Ockhamist can plausibly respond with an "OK, so what?" by claiming that Ockhamist-style "predictions", even if they don't naturally occur in normal discourse, are nevertheless propositional expressions and thus need to be accommodated by a tense logic.
On the 'does'/'does not' thing, no, I'm not retracting my earlier views on tenseless propositions. In my previous comment when I tried to express the Ockhamist's "E will obtain at T" with "E does obtain at future T" I wasn't thinking of tenseless discourse at all but just trying to capture as best I could what the Ockhamist seems to mean by "E will obtain at T".
Regarding the contradictory of "does obtain", if does here is present tense, then the contradictory is clearly "does not obtain". If, however, "does obtain" is supposed to be tenseless then what we get is a proposition like "E obtains (tenseless) at T" that represents E's obtaining at T as a determinate fact without giving any indication of whether T is past, present, or future. Thus, "E obtains (tenseless) at T" says, essentially, "Either E has obtained, is obtaining, or will obtain at T". The contradictory of this is the logical negation of each of the disjuncts, thus, "E neither has obtained, is obtaining, nor will obtain at T". Since there are two ways in which "E will obtain at T" can be false, this is equivalent to "E has not obtained at T. E is not obtaining at T. And either E will not obtain at T or E might and might not obtain at T."
Now that's certainly a mouthful, but it's complexity does not, in my opinion, reflect any inadequacy in the analysis, but rather reflects the unnaturalness of tenseless discourse. Outside of philosophy, hardly anyone adopts a tenseless mode of discourse. I suspect that comfortableness with tenseless talk reflects a corrupted semantic sensitivity.
Alan,
Thanks. Concerning the “does” (tenseless), I think you’re right, and I’m glad I asked. It wasn’t occurring to me that tenseless verbs either rarely or never come up in ordinary talk, and hence that it’s not strange that we don’t have an easily specified ordinary-language contradictory of “does” (tenseless).
Concerning the rational assertibility argument, you say, “it may only prove to be more of a glancing blow if the Ockhamist can plausibly respond with an "OK, so what?" by claiming that Ockhamist-style "predictions", even if they don't naturally occur in normal discourse, are nevertheless propositional expressions and thus need to be accommodated by a tense logic.” Let me just ask, if I may: what do you think these propositions are, i.e. what is their content, and how does the tense logic we’re going for currently handle them? That is, how is it that the tense logic we’re after fails (or may fail) to accommodate them?
It does seem that the BOT must bite the bullet (at least somewhat) on the retroactively predicating truth of predictions issue. In the roulette case, my saying “the ball will land 20” can perhaps be plausibly construed as a non-prediction, but (as a fellow grad student said to me today), what about a case like the following. A psychic says “the ball will land 20” (or whatever). Sure, “the ball will land 20” is (we’re assuming) not rationally assertible for her (she doesn’t have any special powers), but it does seem odd to say that what she said isn’t properly speaking a prediction; the principle of charity won’t lead us to interpret her saying as something besides a prediction (and in fact, would probably *require* us to construe it as a prediction. We can imagine her as having set up a ‘prediction-booth’ at the casino.). 19 of 20 people would immediately say that, if the ball lands 20, the psychic was right, i.e. she spoke truly. It does seem, that is, that we can irrationally assert genuine predictions.
Maybe the best thing to do here is to simply press a grounding objection on the proponent of the is-was-will principle. That is, say something like, So right now there’s a set of facts exhaustively describing the contingent future? Well, (to put it crudely) where’d those facts come from? Why are they there? What is it in virtue of which they’re true? And thus, when the psychic made her predication, what was it that then obtained that made her prediction true at that time? I’d press these sorts of questions and hence ask for a justification for what’s admittedly the common practice of retroactively predicating truth of predictions, and hope that the lack of grounds for these truths will trump the fact that it matches common ways of speaking. At least that’s part of what I’d do.
Patrick,
I appreciate the ongoing interaction. Thanks.
You ask: "what do you think these propositions are, i.e. what is their content, and how does the tense logic we’re going for currently handle them?"
My reply: You're asking about the propositions that are allegedly expressed by Ockhamist-style "predictions". Personally I doubt that there are any such propositions, but our Ockhamist friends certainly aren't going to let the matter go that easily. So what we have to try to do here is think like an Ockhamist and articulate as best we can what their understanding of a proposition about the future seems to be. From reading my work, you know that I distinguish between two dimensions of meaning that the future tense can carry. I'll call these here "temporal force" and "causal force". Now, for the Peircean, these two dimensions run parallel to each other. In fact, there's really only one dimension for the Peircean - propositions about the future carry temporal force insofar as they carry causal force. For the Ockhamist, however, these two dimensions run orthogonal to each other; temporal force is almost completely independent of causal force. The only causal (or perhaps better, probabilistic) implication of the Ockhamist's "will" is that the probability is > 0. Thus, the proposition expressed by an Ockhamist-style "prediction" that E will obtain at T is simply that E obtains at future T. To the Ockhamist that qualifies as a proposition. To my mind, it's suspicious, but settling the matter requires a detailed theory of propositionality, which is a topic I've barely scratched the surface of. If they are propositions, then the Peircean can only maintain an alethically open future by denying bivalence for such propositions. Thus, the BOT is committed to denying their propositionality.
Regarding the psychic case, I'm inclined to stick to my guns on the assertibility objection and argue that either (a) the psychic believes her own prediction or (b) she doesn't. If (a), then presumably she thinks she's got some special insight (that in reality she doesn't is irrelevant) into the matter that warrants her saying "the ball will land on 20", in which case she is expressing a genuine prediction. If (b), then she's either (i) not expressing that prediction, but a weaker one like "the ball might land on 20" or "the ball is more likely to land on 20 than anywhere else", or (ii) she's not making a prediction at all.
The Peircean can also point to lottery examples to counter the Ockhamist's appeal to retroactive predications of truth. Give a person a lottery ticket. Fill him in on the abyssmally low odds of winning. Then ask him to endorse the statement "My ticket will not win." Nearly everyone in that situation will refuse to make such a statement. Why? Because my ticket might win. Thus, in lottery cases people typically treat "will not" and "might" as contradictories, which is just what the Peircean says they are.
Finally, Hasker has made the observation that when making retrospective predications of truth we often say that the prediction has "come true", thereby suggesting that it was not true all along. In short, the linguistic data does not unambiguously favor the Ockhamist.
Alan,
No problem, and thank you for the ongoing interaction as well. Allies are hard to find when it comes to this view! By the by, I first read of the BOT view through Shield’s and Viney’s essay *The Logic of Future Contingents* in a rather new volume called “Process and Analysis.” (It’s got essays from analytics on process thought, etc.) They defend Hartshorne’s view. Have you ever given that a look?
I don’t know much about those two, besides that I think Shields is a process theist, but besides you, Tom, Boyd, myself, and perhaps those two, I’m not aware of anyone in the broadly academic world who argues that ‘will’ and ‘might not’ are contradictories. Do we have any friends that I don’t know about?
Concerning Ockhamist predictions, you say (for the Ockhamist), “the proposition expressed by an Ockhamist-style "prediction" that E will obtain at T is simply that E obtains at future T.” But you’re think this may fail to meet the standards of propositionality. Is this because it seems to be tenseless?
However, you say that if they are propositions, then the Peircean will have to deny bivalence for them. But why? Seemingly, we’d have to only if we can’t say that *E obtains at future time T* and *E fails to obtain at future time T* (or, I suppose, *E does not obtain at future time T*, where ‘does’ is tenseless) are both false. That is, we’d have to deny bivalence only if *E obtains at future time T* and *E fails to obtain at future time T* are contradictories. But as our previous discussion re: the contradictory of ‘does’ (tenseless) shows, we can hold the previous two props. (which seem to be going for a tenseless ‘obtains’) are merely contraries. Both can be false. Right?
Good point on the psychic. I’ll think about that some more, but I think the assertibility argument may be stronger than I thought.
Last, I think you’ve got a good point concerning the lottery ticket. But the point seems mitigated by the following. Suppose someone *does* endorse the claim that she will not win (she’s a pessimist, or whatever). And she doesn’t, in fact, win. Almost everyone would say “she was right!”, even though, at the time, it was still true that she *might* win. So it looks like they’d go back to the Ockhamist construal in that case. Still, good point.
Patrick,
I haven't heard of Shield's and Viney's essay. I'll have to get a hold of it. Thanks for the reference.
It's my understanding that Peter Geach defends something very similar to the BOT view in his book "Providence and Evil". I've got a copy coming on Inter-Library Loan. I'm hoping that I'll be able to make use of his work in the cause. I'd also add Prior onto your list, though I'm sure you already know about him.
You make a good point that even if the Ockhamist's "E obtains at future time T" is a proposition, it is only necessary to deny bivalence if both that and the Ockhamist's "E does not obtain at future time T" are contradictories. If such "propositions" turn out to be equivalent to their tenseless counterparts (and I suspect you're right in thinking they are), then we can argue that they are contraries. I'll give that line some more thought, but it looks promising.
I'll grant that lottery examples are not knock-down arguments, but do I think they take most of the wind out of the Ockhamist's sails regarding retroactive predications of truth.
Alan,
If you've not ever read anything from Shields/Viney, then check out the article "process theism" on the SEP: http://plato.stanford.edu/entries/process-theism/#6
Go to the section "Divine Foreknowledge and Future Contingents"; the whole section is great, and the stuff re: bivalence, will/might not comes towards the end of that section. The article I cited doesn't go much beyond what is here. The BOT view was very well articulated by Hartshorne. Though, like Prior, he intially defended the Aristotelian solution.
I should also link you to this article of Viney's: "Does Omniscience Imply Foreknowledge? Craig on Hartshorne"
http://www.religion-online.org/showarticle.asp?title=2771
The only beef I've got with this, though, is that Viney argues that though Hartshorne's view doesn't entail the denial of the law of exc. middle, it does entail the denial of bivalence. I don't think it does, and I'm still surprised that Viney says this. Anyhow, still a relevant piece and one you'd be interested in looking at.
Alan-
I purchased Geach’s Providence and Evil last year. I remember liking it (because he’s obviously an open theist) but not seeing anything special. Hmm. I’ll have to look at it again!
Patrick-
I’d think Hartshorne would have affirmed bivalence where future tense props are concerned. With you, I certainly don't see how his view entails denying bivalence. And Craig (in the article you cited) I think, just misses the point in his review of Hartshorne.
Tom
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