Interestingly a paper attempting to argue that God as conceived by openness theorists is morally better (roughly) than the God as conceived by Molinists (Luke Gelinas, University of Toronto) actually reduced my discomfort with Molinism.
Like Hasker, it has always seemed to me that God gets *just* the world he wanted and--considering the world--that's morally blameworthy. God carefully plans each act of cruelty. He does it, as Hasker is reported to say, "in cold blood."
In the discussion, I found myself more comfortable with the idea that all the best worlds contain horrendous evils and God just faces a difficult decision. Do I create a world which is sufficiently good (and therefore, I think, on balance good) but which contains horrendous evils and even some personally gratuitous evils (some lives on balance not worth living) or create a lesser world without that stuff? Shieva pointed out that when you frame it that way it seems like it would be blameworthy of God *not* to create the on-balance-good world with the horrendous and gratuitous evils. I find it hard to disagree.
So then I guess for me that takes it back to the possibility of any world with certain kinds of horrendous evils or gratuitous evil being choiceworthy. Can such worlds be choiceworthy? That's the tough question for me. Horrendous evils take a big chunk out of my credence in theism. But I can see this being unreasonable. If I started out with a credence near to 100% then it's plausible that no evil would seem truly horrendous. I've seen people of great faith suffer with equanimity things that I believe would rip me to shreds. And I can see how an infinite and eternal life of beatitude could make up for anything. I can see both these things being true and I think it is reasonable and rational for people not to give up much of their credence to the problem of horrendous evil. However, I can't seem to make these reasons my reasons.
I don't think the Problem of Hiddenness presents much of a problem for theists per se (see Dougherty and Poston, forthcoming, Religious Studies), but in conjunction with the kind of suffering we are asked to endure, it becomes problematic for me. Also, it is not clear to me that the utilitarian considerations involved in the move where we let Heaven cover horrendous suffering is on strong moral footing. Some things, as Ivan forcefully makes us see in "Rebellion", seem to be such as to be intrinsically wrong regardless of how much we "make up for it." [But then again, if those very individuals are glad they exist--after a few year of beatitude--then it is awfully hard for me to disagree with them (and surely they would, right?)] So that's how it works for me. I have doubts about the possible choiceworthiness of worlds like this, but I do grasp the force of some of the replies (as well as a mitigated skeptical theist move) and so I get some of my credence in theism back...but not all of it. On balance, in my cognitive economy, horrendous evils and apparent gratuitous evils somewhat disconfirm theism. How much varies from day to day and sometimes from minute to minute.
This also raises a special problem for Hell, for it seems that as long as Hell is populated there are some lives which are on balance not worth living. (Jon Kvanvig's book on Hell is essential reading by the way.) I really struggle with the possible choiceworthiness of any world which contains such unredeemed lives. On the other hand, though, if all the best worlds have individuals with transworld depravity, it seems wrong for all the good of worlds like ours to be held hostage to such individuals. I think this puts a *lot* of weight on that property. For if it is possible for God to ensure a world has very nearly as much good as t his world, but no one is permanently damned, then that seems clearly obligatory. As far as I can see, the only ways exonerate God here is Molinism + transworld depravity or a truly open future. I have doubts about transworld depravity, so that pushes me in the direction of a view like Swinburne's. My hope is that I can work out my Boethian view which has the result that it's basically "just as if" the future were open, but it's not. So far, though, this idea is very inchoate. There's nothing conceptually I'd rather have, though.
If anyone is interested, Bimal Matilal discusses this kind of problem from an Indian perspective in "Krishna: In Defence of a Devious Deity," in his anthology.
He makes a point similar to the one discussed by you and Shieva, although he notes that Indian theistic traditions do not put a lot of emphasis on God's omnipotence, which makes the problem a bit different in that context. The gist however is that certain events have been put into motion that even God cannot stop, but He will always make sure that people have reason to hope, and those who do and perservere will find rest in Him.
I hope that doesn't sound too trite, but I think that's the most succinct way to put it and still capture the poignancy of the story.
Hi Trent,
It seems to me that IF transworld depravity (TWD) were true, then the Molinist would have a halfway plausible response to the problem of evil. For my part, however, I just can't see how to make TWD plausible. What the Molinist needs is an argument to show why a creature's having libertarian freedom effectively guarantees that it'll sin. The good angels are an obvious counterexample to that, though. So perhaps the Molinist has to retreat to the position that a corporeal creature's having libertarian free will effectively guarantees that it'll sin. Why one should think that, however, is not at all clear.
Alan,
Is it clear that the good angels are sinless? I get the idea that a group of them rebelled, and another group remained. However, it isn't clear to me that sin and rebellion are identical. Is there some good textual reason to think that the angels of heaven are completely free from sin? Are they morally perfect?
Alan,
I, too, don't find anything plausible in TWD. But I think there may be a way for the Molinist to draw a relevant, non-ad-hoc distinction between angels and humans here. The Molinist could think that God confirmed the good angels in their goodness after the bad angels fell (Augustine talks about this in The City of God). Since the good angels are confirmed in their goodness, they won't sin with their free will in the actual world, and hence aren't TWD.
So, there's a relevant distinction: good angels are confirmed in their goodness, humans aren't (or, at least aren't until the beatific vision).
It just struck me that Catholics are doctrinally bound to deny TWD. For, Catholics think that Mary was free from all sin -- original and actual -- throughout her entire life (through the grace of Christ). So, there's at least one essence that could be instantiated in a possible world and not sin.
Alan,
Why do you think that "a creature's having libertarian freedom effectively guarantees that it'll sin"? As far as I can see, all Plantinga needs is that libertarian freedom guarantees that, for every libertarian free and right act, there is a free act and world just like the world in which the right act occurred at which the agent who performs said action goes wrong with respect to that action. And that seems to be a just a consequence of libertarian freedom. Am I missing something?
Matthew,
I don't have any textual reasons at hand to give you, but as far as I am aware it is standardly assumed (in evangelical circles at least) that sin=rebellion and that the good angels (e.g., Gabriel, Michael, etc.) are w/o sin. Strictly speaking, of course, a Molinist could dispense with angels altogether. Belief in their existence is not essential to the position. But it is a traditional belief among Christians that there are angels and that some of them were, at least at one point, free in a libertarian sense and did not sin. Insofar as TWD is in tension with that, it's going to be harder for a traditional angel-believing Christian to accept.
Tim,
I see your point about God's 'confirming' the good angels in righteousness, but then I wonder how a Molinist would explain why God didn't create human beings who would initially freely refrain from sin just like the good angels presumably did and then 'confirm' them in righteousness as well. If God can do it for the angels, then why not for us?
Moveover, if there are feasible libertarianly free creatures that upon being created would freely refrain from all sin for a given span of time, say N minutes, then it's hard to see why there wouldn't also be feasible creatures that would freely refrain from sin for N+1 minutes, and so on. Consequently, it's hard to see why it would not be feasible for God to create a world populated only by free creatures that would always freely refrain from sin. But that conflicts with TWD. I conclude, then, that the defender of TWD must hold that it is somehow inevitable that libertarianly free creatures sin, which strikes me as very implausible.
Tom,
I don't believe that "a creature's having libertarian freedom effectively guarantees that it'll sin", but I do think that the Molinist who wants to use TWD to deflect the problem of evil is committed to that claim.
As for your proposed interpretation of Plantinga, I gather that you're drawing on the Molinist distinction between possible worlds and feasible worlds. Libertarian free will requires that there be a possible world W in which, let us say, creature S freely sins in circumstances C, and also a possible world W* in which S freely refrains from sin in C. But, the Molinist will say, for any such pair of worlds at most one is feasible because of the counterfactuals of creaturely freedom (CCF's). Suppose the only feasible world is W. My question, then, is why? More to the point, why is it the case for all possible (corporeal) free creatures that only worlds in which they freely sin are feasible worlds? Why does the distinction between feasible and unfeasible worlds happen to fall there? Doesn't that strike you as exceeding odd and implausible? Ex hypothesi, it's not logically necessary, nor is it settled either by God's nature or his will or by actual creaturely choices. The only possible explanation I can see the Molinist giving is that somehow having libertarian free will necessitates sin. Does that collapse the possible/feasible distinction? Perhaps. In the end I suppose my objection reduces to a version of the grounding objection. The possible/feasible distinction is only tenable if there can be ungrounded CCF's.
Regarding angels and sin vs. rebellion, Linda Zagzebski once explained that the primary difference between humans sinning and angels sinning was to do with knowledge.Humans sin either out of malevolence or ignorance, but angels are not ignorant when it comes to God's law. Thus, for an angel to sin, they must really mean it.
So the short answer to the question of whether good angels are sinless would be "yes." I suppose another possible source of sin could be weakness of the will, but I'm not sure that would apply to angels, anyway.
I think we are broadly in agreement, although I think the Molinist can certainly claim that there are worlds in which there are creatures with libertarian freedom who nevertheless do everything right and hence never sin.
Yet to make such a claim, she will need to avail herself of counterfactuals of freedom. And I share your reluctance to accept such things; that is, I think the grounding objection is serious. In fact, it is the combination of my thinking that if God give us libertarian freedom then, in some sense, which world turns out to be actual is not strictly up to him, together with my skepticism about counterfactuals of freedom that pushes me hard in the direction of open theism.
Tom,
I'm less sure what the problem is for CCF's. I'm not even sure the grounding problem is much of a problem; it seems question-begging to me. Anyway, suppose (strong) centering on worlds is true. This amounts to the claim that, for any world w, no world w' is as close to w as w. Or every world is most similar to itself. Let C be a fair coin. There is some indeterministic world w in which it is true that were C flipped, it would come up tails or F []-> T.
Can we prove it?
1. Centering, Assume
2. Possible(F & T), Assume
3. For some w, (F & T) is true at w. From 2
4. For some w, F []-> T, From 3, 1
So, though the chances are by hypothesis even that C comes up heads/tails, there is an indeterministic world in which were C tossed it would come up tails. It is easy to generalize this to libertarian free action. What makes the counterfactual true in the coin case is the simple fact that tails is what happens when the coin is tossed, nothing more. Why not heads instead? There's no reason. There is often no contrastive explanation for events in indeterministic worlds. Same for CCF's in the case of libertarian free action.
The only way to avoid this is to give up centering. But I doubt that any world w' can be as similar to w as w is to itself. So it is quite reasonable not to give up centering.
Mike,
I can see how this gives us an account of some *subjunctives* of freedom but this can't the whole story for the Molinist, right? For while this explains how to get true subjunctives of freedom for what an agent will actually do, it doesn't (as far as I can see) explain the truth of counterfactuals of freedom--those conditionals with contrary to fact antecedents. And without those won't the Molinist position end up being (for all intents and purposes) the simple foreknowledge view?
Tom,
I'm not sure. It seems to present no major obstacle to let w be the closest world to w* at which F is true. In that case 'F []-> T' is true in both w and w*. Again we have the question, "why does T happen (rather than H) in the closest world to w where F happens"? My reaction to this "objection" is that it wrongly assumes there's always a (contrastive) explanation available (or there must be one). The right response is that, "there is no reason why T rather than H in indeterministic worlds; either one could well have happened". The counterfactual is true in w* because T is what did happen in w. Same goes for CCF's. I understand that it bothers those committed to some versions of PSR that T occurs inexplicably in w. But this is just part of what it is for a world to be indeterministic.
Hi Trent,
I'd like to hear more about why the paper reduced your discomfort in Molinism. The reason you give here seems to be that it's somehow less troubling for you to think of God as simply faced with a tough world-actualization decision; all the best worlds regrettably contain nasty evils, etc.
I agree with you and Shieva that, in this situation, God is perfectly justified in bringing about a world w/ horrendous evils, and that failure to do so might even be blameworthy (given that all the best worlds contain such evils). But I don't see how this makes Molinism any more palatable. Is it just because the Molinist God knows what he's getting when he actualizes a world, whereas the open God doesn't?
If so, I can understand. The risk factor involved in the open model is an issue for sure. Even so, the point of my paper wasn't to argue that, with respect to initial world actualization, the open model is better off than Molinism. I admit it might not be.
The point of my argument was just that the fact that the Molinist God knowingly and willingly actualizes a world that includes moral evils precludes him from responding to those evils (when they in fact come to pass) in a way that is as morally praiseworthy as the God of open theism. If we think that how agents respond to moral evil is morally relevant, it follows that the open God is in at least one sense morally better off than the Molinist God.
Mike,
On the assumption that a subjunctive conditional is true if the closest possible world in which the antecedent is true is also one in which the consequent is true, your use of 'centering' to license the move from 1 and 3 to 4 trivializes subjunctive conditionals by reducing them to mere material conditionals. But that's ridiculous. If we can assess the truth of subjunctive conditionals without consulting any other worlds, then modal logic is useless.
No, the relevant notion of world-similarity requires that we look at not the closest possible world (full stop), but the closest distinct possible world. On that construal, however, the inference from 1 and 3 to 4 does not go through.
Tom,
I'm glad to see we're on the same page.
Alan
On the assumption that a subjunctive conditional is true if the closest possible world in which the antecedent is true is also one in which the consequent is true, your use of 'centering' to license the move from 1 and 3 to 4 trivializes subjunctive conditionals by reducing them to mere material conditionals. But that's ridiculous.
It would be ridiculous, but nothing I say remotely entails that. Centering (indeed, strong centering) is a condition on both Lewis and Stalnaker semantics for counterfactuals (Lewis discusses weak centering for might-counterfactuals). So the condition is not mine.
Second, centering does not reduce counterfactuals to material conditional; really, not even close. What centering validates is (1):
1. []((A & B)-> (A []-> B))
Centering also validates (2),
2. []((A []-> B)->(A -> B))
It does not validate (3),
3. []((A -> B)->(A []-> B))
So there is nothing remotely reductive about the condition. What centering reflects is the metaphysical assumption that each world most similar to itself. That metaphysical assumption is pretty hard to deny. It turns out true on centering that if the antecedent of a "counterfactual" is true, then the counterfactual is not true unless the the consequent is also true. But it is consistent with centering that neither the antecendent nor consequent are true in the actual world (but true where the consequent holds in all of the closest (non-actual) antecedent-worlds).
No, the relevant notion of world-similarity requires that we look at not the closest possible world (full stop), but the closest distinct possible world.
On what semantics for counterfactuals? Certainly not Lewis or Stalnaker and, for that matter, no semantics for counterfactuals that I know of. Even if you relax the centering condition, the world in which the counterfactual is evaluated remains among the closest worlds to itself. The suggestion that the world of evaluation does not count as one of the closest worlds to itself is simply untenable.
Mike,
Okay, I think I have a clearer idea now on what you're proposing.
Frankly, I have no problem with centering. Every world is most similar to itself. That's obvious. What I don't buy is the move in your argument from (1) and (3) to (4).
If a flipped coin is indeterministic, then we can suppose that there is one possible world, w1, in which the coin lands head, and another, w2, in which it lands tails. So we have
w1: F & H
w2: F & T
Now, I say that all one can validly infer from this scenario is a pair of 'might'-counterfactuals:
F --> H (true)
F --> T (true)
And I deny that either of the corresponding 'would'-counterfactuals follows:
F []--> H (false)
F []--> T (false)
My rationale turns on my understanding of the natural semantics of this sort of counterfactual. The antecedent "if the coin were flipped" tells us that the relevant possible worlds are those in which the coin is in fact flipped and all other factors that might after the outcome of the toss are kept as they are in the actual world up until the time of the toss. What happens after the toss is irrelevant for determining which worlds count as "closest", though it is relevant for determining whether the counterfactual is true. Since w1 and w2 are equivalent in all the relevant respects, both are members of the relevant set of "closest" possible worlds. Consequently, since the coin lands heads in one and tails in the other, neither 'would'-counterfactual is true.
The general point that I would insist on, is that we cannot simply say that because the actual world is the unique closest world to itself all things considered (it's absolutely closest) that we need not consult other worlds in assessing the truth of counterfactuals. What matters is not which worlds are absolutely closest, but which worlds are relevantly closest, where that class is determined by the antecedent and anything else about the actual world that bears on the consequent while abstracting from the truth or falsity of the consequent.
The suggestion that the world of evaluation does not count as one of the closest worlds to itself is simply untenable.
You're right, Mike. I didn't express myself correctly. The point that I was trying to make here, but apparently botched, is given in the final paragraph of the immediately preceding previous comment above.
PS. My 'might'-counterfactuals in the above comment didn't come out right. They're supposed to have a diamond-arrow, not a simple arrow.
Hi Alan,
I might not be following you. Initially, you seem to concede that each world is most similar to itself. For my part, I can't see how that could not be true, even if there are (though I'm not sure there are) indiscernable worlds.
If you concede (strong) centering, then the inference just goes through. In the smallest sphere surrounding w there is just {w}. The truth-conditions for counterfactuals C make C true just in case the consequent is true through all of the worlds in the closest sphere. If the antecedent of C is in fact true, all or the antecedent worlds include just w itself.
Later it seems like you want to replace centering with weak centering. It is weak centering that will make your two might-counterfactuals come out true. It gets you the result you want, but it has a metaphysical cost: you have to say that there might be a world w' that is as similar to w as w is to itself. That seems false to me. Maybe not to you.
I realize that you want to contrast similarity (all-in) with relevant similarity. This point engages a problem that Lewsi spent a lot of time discussing (largely in response to the famous review of Counterfactuals by Kit Fine), viz., what makes one world similar to another. Lewis's paper on the arrow of time has a fascinating discussion of this problem.
Hi Mike,
From your most recent comment, I gather that the difference between strong and weak centering consists in this:
Strong: For any w, the set of possible worlds that is closest to it is a singleton set that includes only w.
Weak: For any w, the set of possible worlds that is closest to it includes w and, possibly, other worlds as well.
Given those definitions, I'm with you on strong centering. Where we differ is on the relevance of centering (strong or weak) to the truth values of subjunctive conditionals. And this issue hinges on how we interpret the standard semantic rule for evaluating such conditionals:
(SR) Subjunctive conditional C is true just in case the consequent is true in all possible worlds closest to the actual world in which the antecedent is true.
In my view, it is a mistake to read the word "closest" in (SR) as meaning "absolutely closest" or "closest (all-in)". I believe that this is the wrong reading in part because I accept strong centering. For it seems to me that the absolute reading gives the wrong results for subjunctive conditionals in which the antecedent happens to be true in the actual world. In such cases, given strong centering, only one possible world, the actual one, would need to be consulted. But it seems quite obvious to me that when we reason subjunctively we are always considering how thing would stand in other, putatively non-actual, situations. Thus, in your coin flipping scenario, what is at issue is not any fully determinate particular situation, but a general situation-type, one in which a coin is flipped and in which all relevant laws of nature and relevant initial conditions are kept as they are in the actual world. Other details, including how the coin does land in the actual world, are, in my view, completely irrelevant to specifying the appropriate situation-type. It's to the worlds exemplying that situation-type - and because it is a type we are concerned with there will always be more than one such world - that we need to look to assess the truth of the subjunctive conditional. Those are the worlds that, in my view, ought to count as "closest" for purposes of applying (SR).
Hi Alan, you write,
For it seems to me that the absolute reading gives the wrong results for subjunctive conditionals in which the antecedent happens to be true in the actual world. In such cases, given strong centering, only one possible world, the actual one, would need to be consulted. But it seems quite obvious to me that when we reason subjunctively we are always considering how thing would stand in other, putatively non-actual, situations.
Here are some imagined exchanges that might persuade you. X= "if a table had one leg, it would topple over". Y= "that's not true. Lots of tables have on leg and do not topple over."
Note that Y refers what has occurred in one world alone, ours. Again, X= "if Smith had gone to the party, it would have been a disaster". Y = "not so! Smith went to the party and it was a lot of fun".
These kinds of examples suggest that we can consider what happens in the actual world alone in demonstrating that a counterfactual with a true antecedent is false. We don't have to consider any other worlds. Now I concede that this won't be persuasive for someone urging weak centering (since you get the same results on weak centering). But it does tell against what seems like the stronger view you're advancing. I think you want to say that, when A is the true antecedent of counterfactual A[]->B, the actual world is not in general counted among of the closest A-worlds to itself. You don't merely want to say, I think, that it is sometimes counted along with other A-worlds. If your view is right, then it ought to be the case (right?) that observing that the actual world is an (A & ~B)-world is not in general relevant to the evaluation of 'A[]->B'. But the exchanges between X and Y above suggest the contrary.
Alan, you also write,
. . . how the coin does land in the actual world, [is], in my view, completely irrelevant to specifying the appropriate situation-type.
It is irrelevant on my view too. I did not include how the coin landed in my description of the situation type. Rather I included how the coin landed in my assessment of the counterfactual, C[]->T. Let H & C be everything that actually occurs up to and including the coin toss C. I say that any world w that includes H & C is relevantly similar to @. @ is such a world, therefore @ is relevantly similar to @.
Hi Luke,
The basic idea was just an acceptance of the possibility of it being a hard reality that God is stuck with horrendous evils if he wants to make worlds of great value. I started to worry that my reading of Dostoevski had caused a failure of nerve or something like that.
Before I became Catholic I was Baptist for awhile and I still recall fondly a lot of little stories I heard in homilies, erm, sermons. One was about the bridge-master who had to raise the bridge to save all the people on the ship even though he knew his son was playing amidst the gears. This was supposed to illustrate God's sacrifice of His own Son for us. Of course, God loves all so each is as precious. I just don't think I could do it, but this could be a fault and not a virtue.
Hi Trent,
I see where you're coming from now. It seems to me that the open theist is going to need to face up to the same difficulty you're wrestling with, though in a slightly different way. Denying exhaustive foreknowledge gets God off the hook at the outset, so to speak, but the opennist must still come to grips with the fact that God lets the show go on, doesn't intervene more, etc., and that presumably God does so for some greater good, in the interest of an overall very good world. Then there's going to be all kinds of questions about how the open God, given that he doesn't know exactly how the world will turn out, could be justified in permitting everything he does; whether the justifying goods are necessarily subsequent (and not contemporaneous) to the evils in question, etc.
Your comments about utilitarian considerations set me thinking a bit too. If appealing to a consequentialist (or generally teleological) normative theory is good enough to get God off the hook for allowing horrendous evils, why think it's not good enough in human matters as well? Should Xians who play the heaven-trumps-all-evil card be consequentialists? If not, it seems they'll need to tell some story about why consequentialism works for God but not for us.
If, on the other hand, we think there are deontological constraints on what God can do (perhaps obtaining by virtue of God's nature), this makes our acceptance of such constraints in human morality easy for Xians to explain (which I think is a very good thing!). It also points in the direction of a response to Rowe's no-prime-world argument. It could be possible that the reason God doesn't (and indeed can't) create a better world than the actual world, a world with more good in it, is because all the worlds with more good in them contain such horrendous evils that God is, by virtue of the presence of deontological constraints, not able to actualize them. If an essentially morally perfect is constrained from actualizing a world with more good in it than our world, on the grounds that all the better worlds contain horrendous evils God is constrained from actualizing, Rowe's argument fails. Of course, given what God in fact allows, we might wonder how bad evils would need to be before constituting a genuine constraint.
Mike: Here are some imagined exchanges that might persuade you. X= "if a table had one leg, it would topple over". Y= "that's not true. Lots of tables have one leg and do not topple over." Note that Y refers what has occurred in one world alone, ours. Again, X= "if Smith had gone to the party, it would have been a disaster". Y = "not so! Smith went to the party and it was a lot of fun". These kinds of examples suggest that we can consider what happens in the actual world alone in demonstrating that a counterfactual with a true antecedent is false.
Alan: You’re right, Mike, that considering what happens in the actual world alone can show that a subjunctive (‘would’) conditional with a true antecedent is false, but it does not follow that considering what happens in the actual world alone can show that such a conditional is true. The latter is what you need to be able to pull off your inference from (1) and (3) to (4) in your above argument. Consider your first example. “If a table had one leg, then it would topple over” tells us to consider all the possible ways in which a table could have one leg and then, assuming the same laws of nature that obtain in the actual world, to check whether all of those one-legged tables fall over or not. The response that “lots of tables have one leg and do not topple over” suffices to falsify the conditional because it only takes one possible world with a standing one-legged table and relevantly similar laws of nature to accomplish that and, as it so happens, the actual world suffices. In contrast, to show (counterfactually) that the conditional is true would require consulting a vast number of possible (and non-actual) worlds. It would have to be the case that no worlds containing one-legged tables and relevantly similar laws of nature (and there are quite a few of those) have standing one-legged tables.
Now, you might want to argue that this is unnecessary because in order to show that A [] B is true all one has to do is show that A [] ~B is false. But that would be mistaken. As the above discussion shows, the falsity of A [] B (i.e., ~(A [] B)) is equivalent to there being some possible world in the relevant class C that is an A & ~B world. C may include the actual world, as in the example, but it need not include only the actual world (the conditional would still be false even if there were no standing one-legged tables in the actual world). Likewise, the falsity of A [] ~B (i.e., ~(A [] ~B)) is equivalent to there being some possible world in C that in an A & B world. Now, the logical opposite of “some possible world in C is an A & B world” is clearly “no possible world in C is an A & B world”, which is not equivalent to “some possible world in C is an A & ~B world”. Consequently, A [] B and A [] ~B are not contradictories. Hence, you cannot establish the truth of one by establishing the falsity of the other. The logical opposite of a ‘would’-conditional is not a ‘would not’-conditional, but a ‘might not’-conditional. And the logical opposite of a ‘would not’-conditional is not a ‘would’-conditional but a ‘might’-conditional.