Theism, Axiarchism and Restricted Actuality
June 19, 2015 — 14:12

Author: Adam Taylor  Category: Uncategorized  Tags: , , , , ,   Comments: 8

Guleserian (1983) presents a version of the Problem of Evil that attacks the conjunction of theism and modal realism. Like the traditional Problem of Evil, Guleserian’s argument begins with a set of initially plausible, but mutually inconsistent, propositions, which Kraay (2011) reconstructs as follows:

1. Necessarily, there exists a being (God) who is essentially unsurpassable in power, knowledge, and goodness.

2. Every possible world is actual at itself.

3. Necessarily, if w is a possible world, then it is true in w that God permits w to be actual.

4. Necessarily, if it is true in w that God permits w to be actual, then it is morally acceptable for God to do so.

5. There is at least one on-balance-bad world, w.

6. It is not morally acceptable that, in w, God permits the overall bad world w to be actual when it is within God’s power to prevent this.

(1) and (2)  state the primary ontological commitments of theism and modal realism respectively. (3), (4), and (6) state plausible consequences of the conjunction of theism and modal realism. (5) reflects a common modal intuition had by many philosophers, namely that we can conceive of at least some some possible world that is full of misery and altogether lacking in redeeming value.

One strategy for resolving the inconsistency is to reject (5). This the move endorsed by Morris (1987). Thomas argues that nature of an Anselmian God (one that is unsurpassable in greatness) would rule out the possibility any on-balance-bad worlds existing. The Anselmian God is, thus, “a delimiter of possibilities.” Another strategy, favored by Almeida (2011) is to reject (6). On Almeida’s view, the necessity of the on-balance-bad worlds exculpates God from moral responsibility for their existence. Finally Kraay (2011) also rejects (5). He argues for a Theistic Multiverse account of possibility on which (i) there is only one possible world (the actual world), (ii) it is the best possible world, and (iii) it is a multiverse.

What all of these positions have in common is a commitment to (2), the claim that all possible worlds are actual at themselves. This is a core principle of Lewisian modal realism. On Lewis’ account the term ‘actual’ works like the term ‘here’. Just because some things are real here it does not follow that other things cannot be real elsewhere. Likewise, for the denizens of other possible worlds, on Lewis’ theory, their worlds are just as concretely real for them as our world is for us.

Here’s another strategy for resolving the inconsistency. This one allows us to keep (1), (3), (4), (5), and (6) by modifying (2). On the view in mind, we accept an axiological restriction on actuality. We thus replace (2) with

(2′) All and only on-balance-good worlds are actual at themselves.

If this substitution is made, then the inconsistency in the proposition-set is resolved. Why accept such a restriction? The Anslemian theist will argue that such a restriction is merited by the nature of God. While a Lesliean axiarchist might argue that such a restriction is an abstract ethical constraint upon the space of possibilities.

Traditional modal realism holds that there is nothing special about actuality. Ersatz views take actuality to be a special property that only applies to one world, the one that obtains. The view in mind here takes a middle position. Many worlds (perhaps infinitely many) have the property of being actual at themselves. In this way the proposed view is akin to the modal realists position. But not every world, on this view is actual. Some worlds fail to obtain. But the failure is not entirely ad hoc. They either fail because they are inconsistent with the nature of an Anselmian God, or because of an abstract ethical requirement that only on-balance-good worlds exist.

(cross posted from Persons and Value)

  • Derrick

    Could you be more specific on why we should buy (3)? Given a Lewisian analysis of actuality, the mere possibility of a world entails that it’s actual. Accordingly, given this definition of actuality, it seems that God has no control over which worlds are actualized. The mere possibility of the world entails that it’s actual at itself, which Lewis took to be what actuality per se was. Am I missing something?

    June 20, 2015 — 4:33
    • Adam Taylor

      Derrick… Thanks for the comment. I am coming to the issue only recently myself, so others here might be able to fill in the detail better than I can, but here is my take fwiw.

      According to Kraay (2011) “all sides in this debate grant (2), (3), and (4).” I am take it to be the case that (3) is seen as an implication of of the conjunction of theism (1) and modal realism (2). You’re correct to point out that on Lewisian modal realism being possible for being actual. As I understand it, Theistic modal realism adds a new fold: since God is a necessary being, it follows that God exists in all possible worlds. Furthermore God is omnipotent in those worlds. Thus God would have the power in each world to determine whether that world is actual or not.

      June 20, 2015 — 6:13
      • Derrick

        Thanks for your response, Adam. I still feel like I’m missing something. Specifically, I’m not seeing how bringing in God’s necessity and omnipotence helps. On a Lewisian analysis of actuality, how could even an omnipotent being determine what is actual or not? That a world is actual at itself is a necessary truth, hence, truth that not even an omnipotent being could change. As powerful as God is, he couldn’t change that any world w is actual at itself. Moreover, it seems unclear how he could MAKE that the case either. Again, I have to wonder if I’m missing something.

        June 23, 2015 — 5:28
  • Andrew

    Hi Adam,

    Is this a view on which we retain the modal realist view about the nature of possible worlds, so that even worlds that don’t have the special property of actuality are mereological sums of maximally, spatio-temporally related things?

    If that’s the view, I wonder about the following:

    (1) Lewis considers the view that actuality is an absolute, non-indexical property of worlds as he thinks of them and worries that we would have no way to know that our world is in fact actual, whereas its supposed to be a sort of trivial truth that this world is actual. Are you thinking that the view you’re suggesting isn’t subject to that sort of worry, or that there is some easy response?

    (2) Lewis also worries about whether the sort of view you’re suggesting gets the contingency of actuality right. That is, it should turn out to be a contingent fact, varying from world to world, which world is actual. Here’s one way to bring out that point, I think. Take some world, w*, which does not have the property of being actual – because it’s not on balance good, I guess. For any world, w, it should be a trivial truth that things might actually have been as they are in w. That is, that w might have been actual. But, that’s no so on this view.

    (3) This view gets some of the facts about actuality wrong. Suppose at least one of the on-balance-good worlds includes talking donkeys. Then, there are are actually talking donkeys. But, that’s not true.

    (4) I don’t really see how it helps with the problem. Can’t we reformulate the supposedly inconsistent set of sentences so that they just concern what worlds (as thought of as Lewis thinks of them) exist, rather than in terms of actuality? The tension is between the thought that God would allow worlds of this sort to exist (with real suffering and torture, etc) and the thought that God is perfectly good, right? I don’t see how any particular view of actuality plays some important role. Suppose I endorse the view you’re suggesting. I’m still stuck with the thought that there are these worlds out there with on-balance-badness, whether or not they have this peculiar property of absolute actuality.

    June 20, 2015 — 13:30
    • Hi Andrew… thanks for the marvellous and thoughtful reply!

      On the view that I have in mind, possible worlds that fail to meet the axiological criterion of being on-balance-good are not actual at themselves, they do not obtain, and ex hypothesi they are not concrete. They are ersatz possible worlds. Only worlds that are on-balance good are actual at themselves and obtain. This is what I mean by “restricted actuality”.

      This position is inspired by the recent development of the Hybrid Modal Realism account impossible worlds. Berto and other take impossible worlds to be ersatz constructs while they take possible worlds to be concrete. I would make the same move with with on-balance-bad or on-balance-neutral worlds. Only, instead of ruling such worlds out on logical or metaphysical grounds, my theory rules them out on axiological grounds. They feel to meet the threshold of being on-balance-good and thus they do not obtain. (N.B. I’m inclined to think that on-balance-goodness is not sufficient to meet the axiological requirement. It may be the case that a world must be on-balance-uniquely-good to meet the requirement, thus ruling out duplicate on-balance-good worlds).

      Thoughts on your enumerated comments:

      1. On my view there is little doubt that our world is actual, sense it is clearly the case that our world obtains. The upshot of this is that our world is also on-balance-good.

      2. I am not sure I quite follow your comment here. My view still allows for each on-balance-good possible world to be actual at itself. amongst those worlds it will very from world to world which world is actual. All the adds is the set of axiologically impossible worlds, which will not be actual. If this requires me to give up on the triviality of things being as they are in a world, I suppose I bite that bullet. But then, so would any theist, if I understand the point correctly.

      3. I take your point here to be that there may be on-balance-good worlds that are impossible for metaphysical or logical reasons (since talking donkeys are impossible). I do not see any reason why I should have to accept this. If a world is metaphysically or logically possible, then it cannot be on-balance-good. We could see this as a part of the abstract axiological requirement that determines whether a world obtains.

      4. I don’t think I have endorsed “absolute actuality” so I will reserve the right to reply to this comment later.

      June 20, 2015 — 19:06
  • Michael Almeida

    Guleserian’s argument does not assume modal realism, and does not need that assumption. Indeed, his argument assumes a roughly Plantingan picture of possible worlds. Plantinga is a realist about worlds too, but presumably not the sort of realist you have in mind.

    July 24, 2015 — 11:25
    • AP Taylor


      Thanks for the comment. After writing this initial post, I spent several weeks getting more deeply into the issue. And I think the point you make is important. Guleserian does not need modal realism to be true to motivate his argument. He only needs the framework (borrowed from Plantinga’s view of modality) that allows to generate a reductio of (1) . I think perhaps I was mislead by my reading of the way in which Kraay formulates the MPE.

      So, I wonder what you would make of this response to MPE:

      Francesco Berto has defended a position that he calls Hybrid Modal Realism. Roughly, the theory is an attempt to make sense of modal discourse about impossibilia without having to make recourse to impossible worlds as a reduction base for the relevant class of propositions. Berto (2010, p. 482) says

      “Suppose one wants to retain the advantages of both worlds, ersatz and genuine, when it comes to impossibilities…one could then try the following hybrid solution: (1) go realist when it is about possible worlds, and (2) exploit the set-theoretic machinery of modal realism to represent different impossible worlds…as distinct ersatz abstract constructions.”

      Berto’s theory takes concrete, possible worlds to be the basic stuff in our ontology. Basic, atomic propositions (‘bachelors are unmarried males’ or ‘Sally is in the office’) are then reducible to sets of possible worlds. Since there are no impossible worlds, impossible situations are, instead, represented by distinct ‘world-books’ or ‘world-stories’ which are in turn constructed out atomic propositions. The world-stories are sets of sets of genuine possible worlds.

      I want to use HMR as a model for thinking about a response to MPE that allows the theist to avoid modal collapse with having to sacrifice any of the classic attributes of God , and thus to

      I call this view Theistic Modal Hybridism (TMH).

      Here’s how the TMH account deals with MPE :

      (1) Along with HMR we maintain that possible worlds are the basic stuff in our ontology;
      (2) We agree with the Anselmian that God exists in every possible world and is essentially unsurpassably powerful, knowledge, and good;
      (3) We introduce a distinction between merely possible worlds and robustly possible worlds, a merely possible world is a world that is conceivable (but which may contain impossibilia), while a robustly possible world is both conceivable and free of impossibilia;
      (4) We treat merely possible worlds in a manner similar to HMR’s treatment of impossible worlds, i.e., we treat them as ersatz abstract constructs out concrete possible worlds, as sets of sets. God is capable (as we are capable) of representing merely possible in thought, but these need not be concrete worlds;
      (5) We classify all on-balance-bad worlds as merely possible worlds. Thus, on TMH, there are on-balance-bad merely possible worlds, but these are not problematic for the theist because they are not concrete possible worlds, they are ersatz constructs.

      The view has affinity with Thomas Morris’ “Divine Delimitation” view, but differs from Morris in that he takes it to be the case that God’s nature delimits the possible, while the view I have in mind says only that there are no robustly possible worlds such that the world is on-balance-bad and God allows it to be actual.

      July 24, 2015 — 12:13
  • Michael Almeida

    Hi AP,

    Effectively, your suggestion (minus special details) is to argue that the possible worlds that Guleserian talks about (call them the bad worlds) are modal illusions: we think they’re possible worlds, but they’re really impossible worlds or merely possible worlds (what I think you’re calling ‘merely possible worlds’ are actually impossible, aren’t they?). I agree that impossible worlds are objects of thought, as you say, they are intentional objects, in some sense or other. But many people deny that such intentional objects exist; I think there’s no worry at all in saying that impossible worlds exist, since they are (again, if we’re following Plantinga) states of affairs. For Guleserian (Plantinga too) impossible worlds exist every bit as much as possible ones do, indeed they exist necessarily. What impossible worlds cannot do is obtain.

    But the reply to Guleserian can’t stop there. You’ve got to explain the source of the modal illusion. Why does it seem so compelling that there are such bad worlds? Recall Kripke’s explanation of the modal illusion that this desk might have been made of oak. The illusion is generated by the genuine possibility that the desk in the room might have been made of oak. That possible world is confused with a world (impossible world) in which the actual desk is made of oak. That explains the mistake. We’re confusing a possible world (a world where the desk in the room is made of oak) with an impossible one (a world in which this very desk is made of oak). But what is the mistake in thinking that there is a world in which rabbits (Guleserian’s example) suffer terribly? What genuinely possible world am I imagining and confusing with one that’s impossible? Am I imagining a world in which rabbits are simply engaging in pain behavior (possible)–acting as though they are in real pain (possible)–when in fact they’re not? Am I imagining a world in which there are zombie rabbits or quasi-rabbits or rabbits that do not have the neurology to suffer (all possible)? I’m imagining something that sure seems possible. What’s needed is some explanation of the source of my illusion that, possibly, real rabbits suffer terrible pain (impossible).

    Guleserian is at pains to argue that these real rabbits suffering world is no illusion. He thinks our modal intuitions on the matter are epistemically very reliable.

    July 24, 2015 — 14:10
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