I set out to prove that God morally ought not to actualize the best possible world. I conclude that, since God ought not to actualize the best possible world, the existence of no best world presents no interesting problem for theists. This should be very good news for theists, since the prevailing view is that there is no best world.
Let E be the state of affairs of Smith having hurt himself in some minor way. Let G be the state of affairs of N + 1 persons being deliriously happy (for non-negative N). Suppose the conjunctive state of affairs (E & G) is on balance good or positive (even for N = 0). Here’s a proof that (G & E) cannot fail to obtain in the best possible world, despite the fact that E is an instance of gratuitous evil.
- W is the best possible world and contains no instances of gratuitous evil E. Assumption for Reductio
- (G & E) is an on balance positive state of affairs. Assumption
- W contains N deliriously happy people. Assumption
- Let W’ = W + (G & E). Assumption
- W’ is better than W. (i.e., W’ contains N + 1 deliriously happy people + E, W contains N deliriously happy people). From def. of (G & E).
- Therefore, premise (1) is false. From 5.
- Therefore the best possible world cannot fail to contain the conjunctive state of affairs (G & E). From 4, 5, 6.
- Therefore the best possible world cannot fail to include an instance of gratuitous evil, E.From 7.
- God cannot (morally) actualize a world that contains any gratuitous evil. Standard View
- Therefore, God ought not to actualize the best possible world. From 8,9
It follows as well from the proof above that E might be an instance of gratuitous evil even if (11) is true.
- Necessarily, God actualizes the best possible world only if God permits evil E.
If there is no best of all possible worlds, doesn't it follow, trivially, that God ought not to create it? How can you ought to create something that is impossible?
Suppose N and G are both infinite in the best of all possible worlds? can you
"add" G + E to an infinite G?
If there is no best of all possible worlds, doesn't it follow, trivially, that God ought not to create it? How can you ought to create something that is impossible?
No, I don't think it follows trivially. The atheological argument from no best world aims to show that God fails to exist in any world. The argument is based on the assumption that,
1. Necessarily, if God exists then he actualizes the best possible world.
The argument aims to show that since there are infinitely many ever-improving worlds and (1) is true, it follows that necessarily God fails to exist. That's not an unreasonable line of argument.
Suppose N and G are both infinite in the best of all possible worlds? can you "add" G + E to an infinite G?
Sure, there are several non-Cantorian representations of infinity on which addition/subtraction etc. make perfect sense.
Counterpoint: Heaven is a possible world that contains no evil (gratuitous or otherwise).
Mike D.,
Heaven is not a world; it's part of a world (perhaps part fo this world). For discussion, take worlds to be maximally consistent states of affairs. Associated with each world is a maximally consistent set of propositions describing that world. If it is true that there exists a heaven, that proposition will be in that set and the state of affairs of there being a heaven will be part of the world.
Isn't there a cardinality problem? Perhaps it is only true that it is better that there be N+1 deliriously happy people than that there be N of them when N is finite.
Actually, it's trickier than that if one thinks that goods to different persons are always incommensurable, but let me just leave it as is.
I missed your remark about non-Cantorian stories about infinity. Could you be more explicit?
Here's a thought. Either there can or there cannot be a best of all possible worlds. If there cannot, then of course it is trivially true that every best world contains gratuitous evil (and that every best world lacks gratuitous evil).
Suppose now that there can be a best of all possible worlds. Then this world is one that is not improved by the addition of another deliriously happy individual--otherwise, it wouldn't be the best of all possible worlds. Hence this must be a world that has that kind of infinity of individuals that adding one more does not increase the count, or else is such that more individuals can't be added without decreasing value for some reason. In both of these cases, your argument fails, I think.
In both of these cases, your argument fails, I think.
That wouldn't be good. Note that this argument is a response to those who assume there is no best world in their refutations of theism. No doubt, the premises of the argument together entail that there is no best world. But here's a non-trivial claim, wouldn't you say?
A. A perfect being cannot actualize a world that contains gratitous evil.
But (A) together with one conclusion of the argument (8),
8. The best possible world cannot fail to include an instance of gratuitous evil,
entail two non-trivial claims,
B. A perfect being morally ought not to actualize a best possible world.
C. It is not necessary that a perfect being actualizes a best world.
I don't take claims that follow trivially to be themselves trivial claims. They can have important consequences, as in (A) and (B)
"Heaven is not a world; it's part of a world (perhaps part fo this world)."
Well, if you like, God has created a region of the world -- viz., Heaven -- that does not obviously supervene on the regions of the world in which evil obtains. So it would appear that there is a possible world that is Heavenly.*
Be that as it may, I think you've persuasively argued for two claims:
(i) At least arguably, there is no best possible temporally finite world, since aggregate happiness is additively infinite.
(ii) Aggregate happiness can be increased in any world by states of affairs in which gratuitous evil obtains.
The problem is that those two lemmas do not support the conclusion that
(iii) Aggregate happiness can only be increased by states of affairs in which gratuitous evil obtains.
God could better W by adding (E & G). But that doesn't show that W "cannot fail to contain the conjunctive state of affairs (G & E)" (your premise (7)). After all, God could also better W by adding just G, or (G & G), or (G & G & G), or.... So I don't see how your argument goes through without something like (iii).
Side Note: It might be worth noting that no one in the grip of the problem of evil is concerned about "evils" like Smith's "having hurt himself in some minor way." The evils of genuine concern are things more like 18,000 children dying of starvation every day. (A purely formal model can help keep things clear, but considerations outside the model can help keep it real.)
________________
* This ties in with Alexander's point a bit. The value of world W in which one deliriously happy person lives eternally is the same as that of world W’ in which two deliriously happy persons live eternally, namely, infinite. (I'm assuming W and W’ are otherwise value neutral or net positive.)
(iii) Aggregate happiness can only be increased by states of affairs in which gratuitous evil obtains.
I don't know what you're talking about. That claim is nowhere in the proof.
God could better W by adding (E & G). But that doesn't show that W "cannot fail to contain the conjunctive state of affairs (G & E)" (your premise (7)). After all, God could also better W by adding just G, or (G & G), or (G & G & G), or.... So I don't see how your argument goes through without something like (iii).
Yes it does. Let God do all you suggest that he do (aside from adding (G & E) and as many times as you'd like him to do it. Let the resulting world be W. W is not the best possible world, since W + (G & E) is better. No matter what else God does in improving a world, it is always true that he can add (G & E) on top of all of that and make the world better.
The worry about infinite value has been answered above. Such concerns reflect Cantorian representations of infinite values. There are better representations (See for instance John Conway On Numbers and Games Academic Press, 1976) on which addition/subtraction etc. are all perfectly coherent with infinite quantities: so that, for instance, (oo + 1) is greater than oo. Al Hajek employs these representations recently in 'Waging War on Pascal's Wager' Phil Review (2003).
Side Note: It might be worth noting that no one in the grip of the problem of evil is concerned about "evils" like Smith's "having hurt himself in some minor way."
Whether this is true or not is irrelevant to anything I say or even attempt in the post. I obviously agree that people suffer and need solace.
"That claim is nowhere in the proof."
That's my point.
"it is always true that [G]od can add (G & E) on top of all of that and make the world better"
But by parity of reasoning it is also true that for any arbitrary betterment of W by the addition of (G & E), God could simply have added G instead. Therefore there is no marginal betterment of W such that it "cannot fail to contain the conjunctive state of affairs (G & E)."
"[The nature of evil] is irrelevant to anything I say or even attempt in the post."
Formally, yes. Pragmatically, not so much. It is much easier to see that things like paper cuts are part of a morally acceptable world (given the nature of the putative creator) than that 18,000 children dying daily of starvation is part of a morally acceptable world. (If you want an example of how socially salient content modulates our ability to reason logically, cf. the Wason selection task.)
I don't think it's a good idea to use non-standard arithmetic for counting up cardinalities.
That's my point.
What's your point? That some conclusion that I do not argue for, do not assume, and have no concern with, is not in the proof?
These red herrings waste a lot of time and, just to be fully up front, I'm going to be less generous in posting them.
But by parity of reasoning it is also true that for any arbitrary betterment of W by the addition of (G & E), God could simply have added G instead
I agree and never denied it. But, again, what's the point? It has nothing to do with what the proof shows. It has nothing to do with either the validity or soundness of the proof.
Formally, yes. Pragmatically, not so much.
The proof draws conclusions about what theses can be asserted truthfully about a perfect being. It has nothing to do with any pragmatic claims. You are concerned with the practical side. That's nice. I'm not worrying those issues here.
I don't think it's a good idea to use non-standard arithmetic for counting up cardinalities.
We thoroughly disagree on this point. Nonstandard arithmetic is very old news by now. I follow Howard Sobel (Logic and Theism) and Al Hajek on modeling infinite values/disvalues. It helps avoid conclusions that are closer to theft than honest toil. You spend more time cautioning about models than I do!
I am still trying to mull this argument over. However, I'm not sure I follow you on why (5) is true. I get that W' contains one more deliriously happy person. But why does that make W' better than W? Both worlds seem pretty good to me.
You cited that it follows by the definition of G & E, but I'm not sure it does, in fact, follow by definition. Perhaps if we alter G to be something like "N + 1 happier state of affairs"? Thus W would contain N happy state of affairs. But then W, if it is the best possible world, would need to have the happiest state of affairs possible, without E would it not? But this would lead to even more difficulties because then the newly defined G would be extremely odd, "N+1 happiest state of affairs possible", but that makes no sense.
Anyways, you have probably thought this through more than I; so hopefully you can clear up at least my first point. I'm not sure the second point is entirely clear.
Hi Raymond,
I get that W' contains one more deliriously happy person. But why does that make W' better than W? Both worlds seem pretty good to me.
Right, well, I've been assuming that the values of worlds increase in direct proportion to the numbers of happy people in them. I would say that the value of a world decreases in proportion to the number of suffering or unhappy people. I guess there's a philosophical problem to worry about here, but these are pretty standard assumptions about the value of worlds.
You cited that it follows by the definition of G & E, but I'm not sure it does, in fact, follow by definition. Perhaps if we alter G to be something like "N + 1 happier state of affairs"?
I'm not sure I follow. For each additional deliriously happy person there is another, better state of affairs: viz. the state of affairs of there being N deliriously happy people (rather than N-1 deliriously happy people). There is also the state of affairs of S (the latest happy resident) being deliriously happy. As you add happy residents, you also add states of affairs (in all but the actual world, some would say, all you add are states of affairs. Talk about adding happy people is shorthand for talk about states of affairs.)
Hi Mike,
I like this line of argument. I'm interested to hear how you respond to the following two questions:
(1) The 'No Best World' premise in typical arguments from improvability are, or should be, restricted to feasible worlds. But, on premise 9, W' isn't feasible, and shouldn't be included in the sequence. Even if your argument shows that there's no possible world that doesn't contain pointless evil, does it show the same for feasible worlds? That for any world that doesn't contain gratuitous evil, there's no slightly better feasible world?
(2) I wonder if we could take something like this as a reductio of the standard view on God's permitting pointless evil, expressed in premise 9. Consider an overwhelmingly good world, full of blissful creatures living in right relation to each other, God, and their, environment; lots of fine Belgian ale; the '86 Celtics win the Finals every year; whatever. The only imperfection is that it contains one pointless toe stubbing, which causes minimal, fleeting pain. It often seems to me that God would be permitted to create a world like this.
But, on premise 9, W' isn't feasible, and shouldn't be included in the sequence. Even if your argument shows that there's no possible world that doesn't contain pointless evil, does it show the same for feasible worlds?
I don't think it can be denied that W' is a better world,since it contains more net value than W. I agree that it's not feasible--it is not among those that God can actualize--but that is another way to my point, sort of: viz. that God ought not to actualize the best possible world.
(2) I wonder if we could take something like this as a reductio of the standard view on God's permitting pointless evil, expressed in premise 9. Consider an overwhelmingly good world, full of blissful creatures living in right relation to each other, God, and their, environment; lots of fine Belgian ale; the '86 Celtics win the Finals every year; whatever. The only imperfection is that it contains one pointless toe stubbing, which causes minimal, fleeting pain. It often seems to me that God would be permitted to create a world like this.
This is a great question. I imagine the response would be that, if the evil is gratuitous, then there is a world just like the one you describe except for the toe stubbing.
There is Rowe's concern, you recall, that God is not required to actualize the best world in cases where there isn't one. Rather God must fulfill P.
P. God cannot actualize a world w if there is another w' such that w' is better than w.
The response to Rowe, I think, in this context, is that we can show (B) is true.
B. Necessarily, for every possible world w in the sequence, there is a world w' such that w' is better than w and w' contains an instance of gratuitous evil.
From (B) it follows that (C),
C. It is impossible to actualize a world w that satisfies Rowe's principle (P) without actualizing a world that contains an instance of gratuitous evil.
And it follows from (C) that,
D. Rowe's principle (P) requires that God allow an instance of gratuitous evil.
Since God cannot allow a single instance of gratuitous evil, it follows that Rowe's principle (P) is false. So, God can actualize a world that w when there is a better world w' that he can actualize instead.
'I don't think it can be denied that W' is a better world, since it contains more net value than W.'
Suppose I disagree that worlds should be ranked in terms of intrinsic value. They should be ranked in terms of right violations, or unjust distributions of well-being, or in terms of how much pointless evils they contain (or the conjunction of all three). I'm thinking of anti-consequentialist attempts (Foot, in particular) to deny that it's always better to bring about more intrinsic value than less; which might involve the claim that there’s no intelligible sense of ‘better’ on which a state of affairs that contains injustice is better than one that doesn’t.
'I imagine the response would be that, if the evil is gratuitous, then there is a world just like the one you describe except for the toe stubbing.'
Though it might not be a world God can actualize. It depends on the type of evil, and what you think about CCFs. Suppose the only imperfection in the otherwise perfect world is not a pointless toe-stubbing, but some analogously insignificant pointless moral evil e. If e is tied to some libertarian free choice of Joe's, it might not be possible for God to actualize a world as good as W-minus-Joe's-evil, depending on the CCFs. Maybe every world as good as W contains Joe freely causing e.
'P. God cannot actualize a world w if there is another w' such that w' is better than w.'
It seems P should be read with a parenthetical 'and w' is actualizable by God (or a god-like being)' at the end. If W' isn't actualizable, we shouldn't think that there's anything wrong with God actualizing W when W' exists (that is, we should think P is false)--since it's not possible for God to actualize W'.
I guess I’m not convinced that we know, or are really all that justified to believe, that W’ exists and is actualizable for a god-like being. For all I know, the CCFs might be such that every world better than W contains gratuitous evil; for all I know, they might not. In the context of Rowe’s argument, you could still use your basic story as a way out; since all we need there is a just-so story.
Suppose I disagree that worlds should be ranked in terms of intrinsic value. They should be ranked in terms of right violations, or unjust distributions of well-being, or in terms of how much pointless evils they contain (or the conjunction of all three). I'm thinking of anti-consequentialist attempts (Foot, in particular) to deny that it's always better to bring about more intrinsic value than less. . .
I'm just not inclined to let my response depend on major changes to the proposed hypothetical cases. I go with my initial intuitions that the problem is genuine as it is stated. Maybe your suggestion is the way to go, finally, but I'd like a solution somewhere short of that.
If e is tied to some libertarian free choice of Joe's, it might not be possible for God to actualize a world as good as W-minus-Joe's-evil, depending on the CCFs
I guess that's right, but we no longer have a gratuitous evil, do we? It sounds like the evil is a tradeoff for the exercise of freedom.
'P. God cannot actualize a world w if there is another w' such that w' is better than w.'
It seems P should be read with a parenthetical 'and w' is actualizable by God (or a god-like being)' at the end.
You have to be careful here. It is obviously not true that God could actualize w' instead, at least not without reformulation, since it would follow that God could actualize a world in the sequence (viz., w'), contrary to Rowe's conclusion. Second, the question is which worlds could God actualize, if any; we can't easily stipulate what worlds God could actualise in (non-circularly) answering that question.
'I guess that's right, but we no longer have a gratuitous evil, do we? It sounds like the evil is a tradeoff for the exercise of freedom.'
I'm not sure. Wouldn't it depend on how much, if any, intrinsic is value involved with the mere exercise of Joe's freedom? I tend to think that there's very little intrinsic value involved in exercising one's freedom, but lots of possible instrumental value, depending on what one does with it (freely given love, etc). It could be that the positive intrinsic value involved with Joe's merely exercising his freedom is pretty small, or at least not great enough to outweigh the evil he performs; in which case e would still be gratuitous. That's my view.
'You have to be careful here. It is obviously not true that God could actualize w' instead, at least not without reformulation, since it would follow that God could actualize a world in the sequence (viz., w'), contrary to Rowe's conclusion.'
Right, so restrict it to god-like beings who don't necessarily possess the moral (or rational) property in question. Though I suppose this would commit Rowe to such beings. I'm not sure what the best way to formulate P is. But I assume there's some way to capture the intuitive idea without committing Rowe to anything he doesn't want.
'Second, the question is which worlds could God actualize, if any; we can't easily stipulate what worlds God could actualise in (non-circularly) answering that question.'
I'm not sure I follow this. We want a way to express the moral claim without making it the case that a morally perfect being is faulted for doing something it's not possible for that being to do.
Because of this I think we need to restrict the discussion to worlds feasible for omnipotent and omniscient beings (or however you want to formulate the No Best World premise). Which worlds are feasible? We know of at least one type of world that *isn't* feasible: Leibniz's Lapse type worlds. Presumably it's OK to assume that the being in question can't (strongly) actualize these worlds, no? For it's not possible for the being to do so. Thus, the being exhibits no moral or rational fault for not actualizing a Leibniz Lapse type world (even if it's a better world than some alternative), which is what Rowe's argument needs.
Thus, the being exhibits no moral or rational fault for not actualizing a Leibniz Lapse type world (even if it's a better world than some alternative), which is what Rowe's argument needs.
What makes is so diffcult to formulate Rowe's argument is that the very thing in question is which worlds in the sequence God can actualize. As you know, Rowe concludes, none! So, we cannot start the discussion by stipulating that there are some worlds that God can and God cannot actualize. That begs the question at issue.
I'm not sure. I don't think we can begin by putting any *moral* constraints on which worlds are and are not actualizable. We can't let God's moral nature have any role in delimiting the realm of actualizable worlds. That definitely begs the question.
But Leibniz Lapse worlds aren't like that. The reason God can't actualize them has nothing to do with God's moral properties. It has to do with God's inability to bring about contradictions. I don't see how that begs the question. It still might be very plausible to think that, among non-Leibniz Lapse worlds, for each one, there's a better.
I'm thinking of Mackie-like positions that advance forms of compatiblism that make it perfectly possible for God to arrange for caused free action. But the main point concerns the positive side: i.e. stipulations of which worlds are really in the sequence of actualizable worlds. It is difficult to do that w/o begging questions.
Right, you need to assume incompatibilism. But in my experience the vasy majority of theists are already committed to this!
Doesn't your argument above do something similar? Instead of assuming incompatibilism and concluding that some worlds aren't actualizable, it assumes that God couldn't permit pointless evil and concludes that some worlds (at least the best one--but presumably whichever worlds contain pointless evil)aren't actualizable.
Thanks for the discussion. Much appreciated.
Doesn't your argument above do something similar? Instead of assuming incompatibilism and concluding that some worlds aren't actualizable, it assumes that God couldn't permit pointless evil and concludes that some worlds (at least the best one--but presumably whichever worlds contain pointless evil)aren't actualizable.
Yes, my argument makes that assumption. But I'm happy for that claim to be in play. I'd be happy to learn that gratuitous evil does not trump overall value in the cases I describe. Our concept of 'gratuitous evil' seems to me largely untested, so it would not surprise me to discover that it's just hackneyed or poorly understood or poorly thought out.
Doesn't this argument need the additional premise that it's possible that, for any N, there are more than N deliriously happy people? If this is false and W contains the greatest possible number of deliriously happy people, then W' isn't a possible world.
Doesn't this argument need the additional premise that it's possible that, for any N, there are more than N deliriously happy people?
Premise (4) is false unless something like that is true. But two points. First, I really don't need that specific increment in improvablity to be correct. I just need some way or other to improve worlds. Second, those who offer atheological arguments from improvability are happy to concede such a premise, since it is necessary to their own arguments.
A couple different people I've talked to about improvability arguments have told me that you can do some fancy stuff with set theory to positively show that there's a best possible world. The basic idea was that you can take any good-making property you think there is and somehow max it out via set theory; and then combine all the maxed out sets of good-making properties in one world. Something like that.
A couple different people I've talked to about improvability arguments have told me that you can do some fancy stuff with set theory to positively show that there's a best possible world
My guess is that the 'maxing out' involves making it infinitely great and then claiming that no additional increment would increase the value of a world. There are two ways to go here: one is to move in the direction of kagan and Vallentyne on infinite utility theory (where distributions of utility are made to matter) or non-standard arithmetic (which I prefer).
I never understand the claim that an infinitely great set doesn't get greater by adding one more. Is it some sort of law of diminishing returns? But even then, why think it reaches a point where adding one more involves *no* increase in value? Why not just think it involves less and less ad infinitum? I need to read up on this more.
I never understand the claim that an infinitely great set doesn't get greater by adding one more. Is it some sort of law of diminishing returns?
No, it's just that arithmetical operations are not well-behaved when applied to Cantorian infinites. You get all sorts of weird results. For instance, oo + oo = oo and oo x oo = oo, etc. Bill Craig makes much of this in his Kalam Cosmological Argument, where the Hilbert Hotel example illustrates many of the counterintuitive consequences of assuming that there could be an actual infinite series (such as an infinite sequence of moments prior to the current moment). You might look at Craig's discussion to get an intuitive idea.