The Leveling Argument
February 2, 2015 — 23:47

Author: Michael Almeida  Category: Concept of God Existence of God Uncategorized  Tags:   Comments: 23

Here is an interesting theistic argument that I call the ‘leveling argument’.  The leveling argument takes as a premise the common assumption in (1). I agree that (1) is tendentious.

1. God cannot actualize a suboptimal world.

Now take any level of value v and suppose that every possible world has an intrinsic value no higher than v. If a possible world w has value v, then God could actualize w. God would have optimized in actualizing w. But if w had value v and w’ had value v+, then God could not actualize w. God would have failed to optimize in actualizing w. So, whether God can actualize a world w depends on what other worlds w’ he might actualize. It is the comparative value of worlds that determines whether God could actualize them, not their intrinsic value. Immediately, we can reach two broad conclusions.

2. If there is variation in intrinsic value across the set of all possible worlds, then God does not exist. (follows from (1))

and of course (2) entails (3),

3. If God does exist, then there is no variation in intrinsic value across the set of all possible worlds (the leveling conclusion). (follows from (2))

(3) already seems false, but that’s not the main point. It is also a common assumption that God might fail to create any concrete objects whatsoever.

4. God might fail to create any concrete objects.

(4) is not the claim that God might fail to actualize a possible world. It is the claim that God might fail to actualize a world including certain sorts of objects, viz. concrete ones. But if (1) and (4) are true, then so is (5).

5. God cannot actualize a world that differs in value from the empty world, e. From (1), (4) [I leave it as an exercise to show this]

(5) is a bizarre conclusion; it entails (6), (7) and (8) which are surely false.

6. God cannot actualize a world whose universe is on balance very good.

7. The creation of moral, rational, and happy beings does not improve a world, overall.

8. There is nothing God, you, or anyone else could do to make the world, overall, a better (or worse) place.

We began the leveling argument by assuming that God cannot actualize a suboptimal world and we concluded that, therefore, there is nothing God, you, or anyone else could do to make the world, overall, a better or worse place! That’s, I think, quite obviously false. There are only two assumptions in the argument: (1) God cannot actualize a suboptimal world and (4) God might fail to create any concrete objects. One of them has to be false, and it’s likely (1).

Comments:
  • Heath White

    Mike,

    You can avoid the inference from 1 to 2 if you assume that worlds might have incommensurate value. And this is easy to believe if you think, for instance, that persons have incommensurate value.

    February 3, 2015 — 11:06
  • Michael Almeida

    Hi Heath,

    The fact that worlds include incommensurable values does not entail–I don’t think–that they are incomparable or that they cannot be ordered. For instance, it is probably true that the value of an orange (whatever that is) and the disvalue of a thousand people suffering don’t share some common unit of measure, but it is nonetheless obvious that worlds that include both (and only both) are not on balance good.

    February 3, 2015 — 11:12
  • Dan Linford

    It seems to me that there is an atheistic argument in the works here as well. It might that we should accept that classical theism entails (1) and (4), find (6)-(8) preposterous, and then call this a reductio argument.

    Why should we accept (1)? It seems to me that to deny (1) would entail that God is less than perfect. But the god of classical theism is perfect. And I think it’s clear that if we deny (4), we would be denying some aspect of God’s free-will.

    February 3, 2015 — 11:49
  • Michael Almeida

    Hi Dan,

    That’s an interesting suggestion. But I wonder whether, really, (1) is necessary to God’s perfection. The important thing to notice about (1) is that it does not preclude God from actualizing a horrendous world. All it does is prevent God from actualizing a horrendous world when there’s a better world. So, a perfect being could actualize a world in which everyone suffers horribly? Yes, if that is a feature of all possible worlds. (1) does not preclude that, and so does not appear to be much of a condition on divine perfection.

    February 3, 2015 — 11:59
    • Dan Linford

      Michael — In response to my previous post, you wrote “The important thing to notice about (1) is that it does not preclude God from actualizing a horrendous world. All it does is prevent God from actualizing a horrendous world when there’s a better world. So, a perfect being could actualize a world in which everyone suffers horribly? Yes, if that is a feature of all possible worlds.”

      The trouble is that you do seem to be committed to the view that God could create a world without any suffering whatsoever. Given that you accept (4), it is false that all worlds God could possibly actualize are worlds that contain horrendous suffering. This is because a world without any concrete objects is a world without any suffering at all (unless one supposes that abstract objects suffer, but that seems incoherent to me).

      So (4) entails that God could create a world without suffering; the conjunct of (1) and (4) would entail that God would create a world without suffering.

      February 3, 2015 — 12:30
  • Ken

    I think your reasoning depends upon an equivocation over ‘possible world.’ Is it a necessary condition of a possible world that it be one that God could actualize or is it merely one that we (or God) could conceive of? (2) follows from (1) only if ‘possible world’ implies ‘could be actualized by God,’ but then the antecedent in (2) is empty and the conditional is true in virtue of having a false antecedent. So the conditional would be true but it doesn’t prove that God doesn’t exist since there is no variability in the value of possible worlds since there are no possible worlds that God cannot actualize. If on the other hand, ‘possible world’ means rather one that we or God could conceive of (without making any claim of whether God could actualize it) then (2) does not follow from (1).

    February 3, 2015 — 12:01
  • Michael Almeida

    Hi Ken,

    Of course, a possible world is possibly actual (setting aside certain cases that Prior and Adams point up). I make a big deal over the point that God does not deliberate over which possible worlds to actualize here (http://prosblogion.ektopos.com/2015/01/27/adams-on-creating-the-best/), since he can actualize any one of them (assuming he exists). But it is not true that a possible world is possibly actualized by God, since possible worlds might exist and God not exist. So, I don’t see the problem with the inference from (1) to (2). The supposition in the antecedent of (2) is that possible worlds vary in intrinsic value. If that is so, then there are worlds that are sub-optimal. But then, if God did exist, he could actualize a sub-optimal world. But he cannot actualize a sub-optimal world (as stated in (1)). So, if there is such variation, God does not exist.

    February 3, 2015 — 12:19
  • Michael Almeida

    Dan,

    Ok, modalizing is tricky. Your original point was that we could not reject (1), since (1) is somehow central to God’s perfection. I wanted to call that point into question. So, I wanted to point out that (1) does not do much by way of ensuring God’s perfection, since (1) does not preclude our discovering that God actualizes horrendous worlds. How could we discover that? We could discover that, from 2017 onward, there is nothing in the actual world but complete and utter suffering and desolation till the universe collapses. And we could discover that every other world is the same way. One would think that, upon the discovery of that, we would conclude that a perfect being does not exist. But that conclusion does not follow from (1). In fact, that discovery is perfectly consistent with (1).

    This was my way of weakening the claim that (1) is somehow necessary to God’s perfection. If (1) is consistent with such utter desolation, it hardly seems necessary to God’s perfection.

    February 3, 2015 — 12:37
    • Dan Linford

      Michael — I understand you to be saying that (1) is not necessary to God’s perfection. I don’t understand how this could be. (1) refers to God generating a “suboptimal world”; by ‘suboptimal’, I understand you to mean a less perfect world than could be created. Another way of stating (1) might be that given possible worlds w1 and w2, where w2 is worse off than w1, God would actualize w1. I’m rather unclear on why a perfectly benevolent being would choose to create a world that was less perfect given a choice to create a world that was more perfect. Typically, we would understand such an action to be a moral failing, would we not?

      February 3, 2015 — 14:21
  • Kris Rhodes

    I’m sorry to be dense but I’m not grasping the move from 1 to 2. I think (think?) the move is supposed to turn on the observation that “it is the comparative value of worlds that determines whether God could actualize them, not their intrinsic value.” But just because God’s being able to actualize a world doesn’t _turn_ on the intrinsic value of a world, it doesn’t follow that there _is no_ difference in intrinsic value between worlds.

    But quite possibly I’m wrong to think the move is supposed to turn on that observation. If it doesn’t turn on that observation the way I’m thinking, then I need the inference from 1 to 2 to be explained to me in a little more detail.

    February 3, 2015 — 13:12
    • Michael Almeida

      Hi Kris,

      Here’s how the move goes from (1) to (2). The inference is truncated, so don’t sweat not seeing it right off. I’ll do it by conditional proof.

      1. There is variation in intrinsic value across worlds (Assume: the antecedent of (2))
      2. Some possible worlds are worse than others. From (1)
      3. Some possible worlds are sub-optimal From (2)
      4. God exists. Assume for Reductio
      5. If God exists, then it is possible that he actualize any possible world. Fact (note I don’t say ‘able’)
      6. God can actualize a suboptimal world. From (3), (4), (5)
      7. God cannot actualize a suboptimal world. From Premise (1) in the Leveling Argument
      8. (6) & (7) Contradiction !@#
      9. God does not exist. From (4) and (8) Reductio
      10. If there is variation in intrinsic value across worlds, then God does not exist. (1), (9) Conditional Proof

      February 3, 2015 — 13:51
      • Kris Rhodes

        From your elucidation of the inference from 1) to 2) (and thanks by the way for expanding it)

        5. If God exists, then it is possible that he actualize any possible world. Fact (note I don’t say ‘able’)
        6. God can actualize a suboptimal world. From (3), (4), (5)
        7. God cannot actualize a suboptimal world. From Premise (1) in the Leveling Argument

        Am I right in thinking that your note (“(note that I don’t say ‘able’)”) is meant to signal that the word “possible” in line 5 is not meant to denote the same modal operator as the word “can” (in “cannot”) in line 7?

        February 4, 2015 — 11:34
  • Michael Almeida

    Michael — I understand you to be saying that (1) is not necessary to God’s perfection. I don’t understand how this could be.

    Yes, I understand your resistance. Here’s what I’m saying, I think. (1) together with (4) have consequences that are plainly false. What to do? (1) is a purely formal requirement, entails nothing whatsoever about the nature or content of possible worlds. (4) is substantive. It tells me that God can actualize a world without concrete objects. How could that be false? The subtraction arguments for this claim are pretty powerful (http://prosblogion.ektopos.com/2014/12/28/a-note-on-substraction-arguments/), and I think they are strengthened on the assumption that God exists. I’m not anxious to give up (1), but it looks like it’s got to go.

    February 3, 2015 — 15:22
  • Anthony

    It seems to me that neither of (7) nor (8) are logically entailed by (5). After all, I could be an atheist who thinks that all worlds are sup-optimal (or non-optimal) because I think that for any world w there is a more valuable world w*. Accepting atheism and this thesis allows me to accept (5) and deny both (7) and (8).

    One might also think (though I am inclined to say falsely) that (5) fails to entail even (6) if the value of the contents of what you call “the empty world” is in part derived from its very emptiness. Maybe the contents (I assume that something at all exists in the empty world) of the empty world possess the value they do only in relative terms. That’s not totally clear, but by this I mean that maybe creating an on net valuable universe diminishes accordingly the value of the contents of the empty world, and that creating a crummy universe correspondingly enhances the value of the contents of the empty world.

    February 3, 2015 — 15:26
  • Michael Almeida

    Accepting atheism and this thesis allows me to accept (5) and deny both (7) and (8).

    Not so. (1) and (4) are both de re modal claims, so both entail that God exists. But I’m not sure I follow the objection anyway. On your assumptions, (2) is false. I don’t deny that if the premises of the argument are false, then the conclusions might not follow. To get (2) true under the assumption of atheism, you have to assume that there is no variation in intrinsic value across the set of all possible worlds. And that alone entails (7) and (8).

    February 3, 2015 — 15:43
    • Anthony

      Hi Michael,

      First thing, with regards to (1) being a de re modal claim. Fair enough, I was taking (1) to be using “God” as a kind term with (1) coming out as “A god cannot actualise a sub-optimal world” (the assessment of this proposition’s truth-conditions will depend on whether or not god-hood can be a contingent property, so I was likely taking (1) to be “Nothing can be a god and actualise a sub-optimal world”). I don’t want to dwell on this point but I imagine that my understanding is the more common. But I’m happy to be corrected.

      Second thing, (2) doesn’t affect anything I say. I was taking (5) on its own and assessing its implications. Maybe we’re talking past each other. You wrote that (5) entails (6)-(8). Were you rather claiming that (5) & (1)-(4) entail (6)-(8)? If not then my ability to endorse or deny (2) is irrelevant to anything I said.

      Third thing, (2) says “If there is variation in intrinsic value across the set of all possible worlds, then God does not exist.” Atheism alone guarantees the truth of this proposition, so why would atheism + my other thesis cause me trouble in accepting (2)?

      February 3, 2015 — 16:20
  • Michael Almeida

    Right, Anthony, (2) presents no problem for you. In fact, nothing prevents you from reading (5) de dicto, ignoring (1) and (4) (or, for that matter, reading them de dicto, too) and reaching the desired conclusion. But, as i said, (1) and (4) are de re (and that reading, as far as I can see, seems the natural one in this context), and so the derivation of (5) is de re too. But all of this naturally points up that I should re-label (7) and (8) as following from (1), (4) and (5). That’s a reasonable point. Of course, since (1) and (4) are de re modal claims, the rest is more or less academic.

    On second thought, perhaps it is not obvious that the argument is an attempt to draw conclusions about the principle of sub-optimality on the assumption that God cannot actualize a suboptimal world. Since I’m worried about whether God would be governed by that principle, I see no problem in assuming that God exists. Hence, the de re reading.

    February 3, 2015 — 16:50
  • Brandon

    I think that Lawrence Resnick’s “God and the Best Possible World” is relevant here.

    http://philpapers.org/rec/RESGAT-2

    In it, he lays out an argument similar to your response to Kris to support (1) to (2):

    1. If God exists then this is the best of all possible worlds.
    2. If this is the best of a possible worlds, then worlds worse than this one are logically possible.
    3. A logically possible world is any world the existence of which is compatible with logical necessity.
    4. If “God exists” is necessarily true, then “The world which exists is not the best of all possible worlds” is necessarily false. (That is, if the proposition “God exists” is necessarily true, then any proposition inconsistent with it is necessarily false. But since God’s existence, in Leibniz’s conception, entails that this is the best of all possible worlds, it also entails that “The world which exists is not the best of all possible worlds” is false. Thus, if “God exists” is necessarily true, “The world which exists is not the best of all possible worlds” is necessarily false.)
    5. If “The world which exists is not the best of all possible worlds” is necessarily false, then no world which is not the best of all possible worlds is a logically possible world. (That is, if “God exists” is necessarily true and if it is in His nature to create only the best of all possible worlds, then it is logically impossible that any lesser world could have come into existence–again, assuming that all things depend for their existence on God).
    6. Given that this world is the one God chose to bring into existence, if no world worse than this one is logically possible, then it is not the case that this is the best of all possible worlds.
    Conclusion: If this world was created by a necessarily existing Perfect Creator, then it both is and is no the case that this world is the best of all possible worlds. Therefore, it is not possible that the world was created by a necessarily existing Perfect Creator.

    It seems that the above is entailed by the idea of God as normally defined, more precisely, as a being that both necessarily exists and is morally perfect. Regarding moral perfection, it seems that a morally perfect being cannot help but will to actualize the best options available to them. For instance, I consider myself a mostly moral being(by no means perfect), and part of why I consider myself as such is because if I have the choice to will either “my stabbing my friend” and “my not stabbing my friend” I choose to will the latter. That choice to will a better of possible options is part of what it means for me to be a good person. Now, it seems to follow that if I can speak of myself being a pretty good person partially because of the above reasons, that a morally perfect being would just have what I have(willing to actualize better of multiple options) to the maximum capacity. It seems that to now deny that facet(willing to choose the better of options) of what it means to be good, in regards to a morally perfect being like God, would mean that I should deny that for me. Then why should I regard my choice to stab or not to stab as anything more than choosing to eat pizza or mac and cheese? I mean, it surely cannot be a moral choice for me if it also isn’t for a morally perfect being.

    February 3, 2015 — 17:57
  • Michael Almeida

    Hi Brandon,
    I consider myself a mostly moral being (by no means perfect), and part of why I consider myself as such is because if I have the choice to will either “my stabbing my friend” and “my not stabbing my friend” I choose to will the latter.

    That’s interesting. The principle that God cannot actualize a sub-optimal world does not entail that no terrible things happen. All it entails is that possible worlds do not vary in intrinsic value; that’s of course consistent with all having extremely low intrinsic value (assuming e is not possible). So, Resnick is mistaken that a perfect being necessarily actualizes the best world; he might instead actualize a world, among many others, that share some value v. Further, even if there is a single possible world, there is no reason to conclude that it is any good. It might be horrible. That is perfectly consistent with God existing.

    February 4, 2015 — 7:45
  • Michael Almeida

    It might be worth noting that the argument in the OP can be revised for a de dicto reading throughout. We would need to replace (7) and (8) with (7′) and (8′).

    7. The creation of moral, rational, and happy beings does not improve a world, overall.
    7′. God cannot improve the world overall with the creation of rational, happy beings.

    8. There is nothing God, you, or anyone else could do to make the world, overall, a better (or worse) place.
    8′. God cannot create any rational beings who can do anything at all that will improve or worsen the world.

    February 4, 2015 — 7:59
  • Michael, at first glance, I am tempted to agree with you in denying the truth of (1). However, it strikes me that there is more than one way in which “world” can be read. Depending on the reading (1) takes on at least a couple of different meanings. In particular it can be read as:

    (1a) God cannot actualize a suboptimal universe (where ‘universe’ is understood as a
    discrete euclidean 3-space and its contents).
    or
    (1b) God cannot actualize a suboptimal totiverse (where ‘totiverse’ is understood as being
    composed of the set of all extant euclidean 3-spaces and their contents, as well as all
    abstract entities that might exist.

    If (1) is read in accordance with (1a) then I think it is tendentious. However if (1) is read as (1b) then I am not sure it is tendentious. The difference is that (1b) makes allowance for the possibility that within the totiverse (as I am calling it) there might be suboptimal universes, the existence of which might contribute to the optimality of the overall arrangement.

    If we read (1) as (1b) I think we can avoid the conclusion of the argument in the following way: there may be nothing that god, you, or anyone else can do to make the totiverse better or worse, but this does not mean that there is nothing god, you, or anyone else can do to make the universe better or worse.

    February 4, 2015 — 10:15
  • Michael Almeida

    Adam,

    I don’t mean either (1a) or (1b) by (1). When I say ‘world’ I mean a maximal state of affairs. The maximal SOA includes everything there is according to the world w. Now, w might include one universe, or it might include a multiverse, as you suggest. The multiverse line is taken by many, including Turner, Kraay, O’Connor, Megill, Hudson, Draper, among others. And many say more or less what you say, that a multiverse might include on balance good, but sub-optimal universes. For my part, I think the multiverse line is replete with confusion, among which is the suggestion that God might choose to actualize all of the on balance good universes included in the simple, non-multiverse worlds. But that’s another story. My claim in (1) is that, whatever sort of world, complex or simple, God can actualize that world only if it is not sub-optimal.

    February 4, 2015 — 10:53
  • Michael Almeida

    Kris,

    I want to use ‘S can do A’ throughout the proof to mean ‘possibly, S does A’ and never to ‘S is able to do A’ (though there are cases in which S it is possible that S does A might just as well be replaced with S is able to do A). I don’t know if that helps.

    February 4, 2015 — 12:14
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