Modal realism and God
August 24, 2012 — 10:54

Author: Alexander Pruss  Category: Concept of God  Tags: ,   Comments: 27

According to David Lewis’s modal realism, every possible world exists as a concrete universe, and a proposition is possible provided it holds at some universe. But this seems incompatible with theism. For necessarily God believes every truth, and we can now run the following argument.

Necessarily, if p is true, God believes p. So, if p is possible, possibly God believes p. Thus, possibly, God believes that there are no horses, since the proposition that there are no horses is possibly true. So there is a universe, say u1, at which God believes that there are no horses. Now God either actually has this belief or not. If he actually has this belief, then he actually has conflicting beliefs, since he actually believes that there are horses. But God does not have conflicting beliefs. So we have to say that while at u1 God believes there are no horses, actually God instead believes there are horses. Thus, what propositions God believes differs between universes. But how could that make any sense? Granted, perhaps our beliefs can be localized to brain hemispheres and then at a location in my left hemisphere I believe p and at another I don’t. If that can be made sense of, then one could give a sense to the locution “believes p at x“. But God’s beliefs surely do not have any such localization. Wherever God is present, he is wholly present. He is not a material being to have partial presence of the sort that might allow for a spatial distribution of our beliefs.

  • Jay

    Why could you not not say that God has, say, a divine and extremely sophisticated number system by which he assigns a unique identifier to every possible world? Is believing that there are horses-in-w1 and no-horses-in-w2 really so different from believing that Pontius Pilate is alive-in-30AD and dead-in-300AD?

    August 24, 2012 — 12:02
  • Well, that there are horses-in-w1 and no-horses-in-w2 are necessary truths. So on this picture, what God believes are all necessary truths. But since God believes all truths, it follows that all truths are necessary truths, and that’s what fatalism says.

    August 24, 2012 — 13:36
  • I am told that Richard Brian Davis in “God and Modal Concretism” Philosophia Christi 10/1 (2008) discusses very similar arguments.

    August 24, 2012 — 13:36
  • John Alexander

    Alexander: Why can’t each possible world have its own necessary Being (God)? Why is it necessary that if God knows p that He believes P? Some recent work in experimental epistemology suggests that this might not always ne the case.

    August 24, 2012 — 17:44
  • Matt B.

    Alex: to say ‘that there are horses-in-w1 and no-horses-in-w2 are necessary truths’ is to go meta-modal, in a way I don’t quite understand. For one of those to be a necessary truth, it would have to be true at all worlds that it is true at, say, w2 that there are no horses, right? But I just don’t understand what it would be for it to be true at w1 that it is true at w2….
    Or to put the matter differently: why not say that these truths are contingent, rather than necessary? Why not say instead that no-horses-in-w2 is contingently true, because w2 could’ve contained horses? After all, a world very similar to w2 (eg, w1) may have horses, and that’s all we need to secure the contingent possibility.

    August 24, 2012 — 19:05
  • JJ

    Presumably, since Counterpart Theory is an integral part of Lewis’s modal realism, one could resolve the proposed incompatibility between modal realism and theism by affirming that God – like the rest of us – has a discrete counterpart in each possible world at which “God” exists. In that case, God1 (God’s counterpart in w1) correctly believes there are no horses, while God2 (God’s counterpart in w2) correctly believes there are horses. “Necessarily, God believes all truths” would simply mean that, for any GodN, GodN believes all truths true at wN.
    Of course, a theist might prefer not to apply Counterpart Theory to God. Since this requires the a priori rejection of important features of Lewis’s modal realism as formulated, however, it generates ambiguities not inherent in the system itself. If one affirms, pace Lewis, that a single entity, GodTrans, can be the subject of beliefs at both w1 and w2 and thus presumably exists at both w1 and w2, then both w1 and w2 are equally actual from the perspective of GodTrans.
    It does not seem to follow from this that all truths are necessary truths. Instead, it follows that some of the propositions true at w1 are not true (simpliciter) for GodTrans, because truths like there-are-no-horses are true at w1 as quantified only over a frame of reference for actuality more limited than that which is indeed actual to GodTrans. GodTrans believes “There-are-no-horses is true at w1 and false at w2” at both w1 and w2; this truth is necessary at both w1 and w2, but there-are-no-horses itself remains contingent at both.
    This does not, of course, amount to a denial of omniscience. The “truths” GodTrans does not believe are true only from within discrete worlds; GodTrans does his believing with reference to the whole world system because the whole world system is actual to him.

    August 24, 2012 — 19:59
  • Adam

    Thank you for the wonderful post! I do, though, have a question (or maybe a misunderstanding):
    I’m going to assume some theory of creationism for now. Would an omniscient God simply know the outcome of future contingent events, especially if this God presumably created every universe and furniture, and not be conflicted?

    August 24, 2012 — 20:10
  • John:
    1. Multiple deities in existence, even if according to Lewis not in actuality, would seem to be contrary to monotheism. And I take theism to entail monotheism.
    2. I don’t know what to make of the suggestion that God knows without believing. I can see a pull to saying that there can be knowledge without belief in some cases, but I don’t know that this can happen across the board.
    1. A proposition is true iff it is actually true.
    2. A proposition is actually true iff it is true at the actual world.
    3. For all s, the proposition that s is true iff s. (Disquotation)
    4. No-horses-at-w2.
    5. So, it is true that no-horses-at-w2. (3,4)
    6. So, it is true at @ that no-horses-at-w2. (1,2,5)
    So iterated modals of the form s-at-w2-at-w1 had better make sense, at least in the case where w1=@, but if they make sense where w1=@, why wouldn’t they make sense for other values?
    Now, I think Lewis himself adopts identity, rather than counterpart, theory for the worlds themselves. Thus, when we evaluate the truth value of no-horses-in-w2 at different worlds, we don’t get to look at counterparts. No-horses-in-w2, thus, is true at all worlds if it is true at any world–it can’t be contingent.
    But what if we take counterpart theory? Then no-horses-in-w2 is true at w3 provided that at w3 there is a counterpart w2′ of w2 and no-horses-in-w2′ is true at w3. But what could the counterpart w2′ of w2 at w3 be? Normally, the counterpart of x at a world w3 would be an entity x that exists at w3. But if we said then, then we would have to say that the counterpart of w2 at a world w3 would have to be something that exists at w3. And plausibly the counterpart of a world will be a world. But presumably worlds, like their parts, exist only at themselves. So the counterpart of w2 at w3 is going to be a world that exists at w3, and hence the counterpart of w2 at w3 is going to be w3 itself. If that’s right, then no-horses-in-w2 is true at w3 iff no-horses-in-w3 is true at w3. In other words, no-horses-in-w2 is true at a world iff no-horses is true at that world.
    In particular, then, no-horses-in-w2 is false at @, since no-horses is false at @. But this argument works for any w2. So no-horses-in-w is false for every w. So it’s necessary, by Lewis semantics, that there are no horses, on the above counterpart theoretic rendering. And that’s absurd.
    Applying counterpart theory to God is hard to square with monotheism.
    I think your GodTrans suggestion ends up implying that it is not true simpliciter that there are horses. But what is true is true simpliciter, just as what happens is what really happens.

    August 24, 2012 — 21:44
  • JJ

    Once modal realism is granted (for the sake of argument), I am not sure what an adequate account of contingent truth more straightforward than the one I employed might look like, even before theism enters the equation. There-are-no-horses-at-w1 is a necessary truth, as you point out, and no possible world is ontologically privileged over another. So, if there-are-no-horses is to be true at all, it must be so as a result of a frame of reference for its truth which is restricted to w1 alone. If counterpart theory is comprehensively adopted, then this has fact has little bearing on *belief* as such, since any believing entity will be part of only one possible world (which is rendered indexically ‘actual’ by the entity’s existing in it rather than in another). The GodTrans suggestion raises the issue of how such “restricted” truths might relate to truths which take the whole ontologically equal world system into account, but it doesn’t – as far as I can see, anyway – employ an account of contingent truth fundamentally different from that which modal realism itself implies. How else might you characterize the relevant distinction among truths under modal realism?

    August 24, 2012 — 22:41
  • Dennis Kavlakoglu

    @ Alex
    “And plausibly the counterpart of a world will be a world.”
    This can be resisted. Worlds are simply possible individuals unified in a certain way (if you take Lewis’s word as gospel, by spatio-temporal relations).
    Worlds can contain counterparts of other worlds as a part (consider Lewis’s brief discussion of one-way eternal recurrence worlds containing exact duplicates of proper parts of itself on p. 102 of OPW).
    A world, w1, bears a counterpart relation to a proper part (p1) of an eternal recurrence world, w2. In that case, p1 is a counterpart of w1 though not a world itself, since for p1 to be a world would require that p1 inhabits two worlds and that would contradict P2 of counterpart theory.
    To see that this is the case, consider that every world inhabits itself, so p1 inhabits p1. By assumption, p1 is a part of w2 so p1 inhabits p1 and w2, contradicting P2 of counterpart theory. Since w2 is a world (by hypothesis) it follows that p1 cannot be a world. But then p1 is a counterpart of w1 although p1 is not a world. So the principle “the counterpart of a world is a world” does not hold generally.

    August 25, 2012 — 1:25
  • Chad Carmichael

    Alex, you say that monotheism is hard to square with counterpart theory. Presumably you’re thinking of monotheism as the view that there is (quantifier wide open) exactly one God. But that’s not the natural way for the counterpart theorist to understand ‘monotheism’, is it? It seems to me that the counterpart theorist should understand ‘monotheism’ as designating the view that exactly one divine being exists in the actual world. And that’s easy to square with the thesis that God has many counterparts.

    August 25, 2012 — 10:11
  • John Alexander

    It would seem that all statements that do not involve a contradiction, statements that are possibly true, would be necessarily true if Lewis is correct, in so far as, according to him, as reported by you, there has to be an actual (concrete) world for each possible statement. This being the case, the statement ‘there are no horses in w2’ is true in all possible worlds if there are no horse on w2. I assume that there must be facts that we are unaware of, and always will be such, as there being ‘wegnots’ on w3. Let us assume that w3 is a world with no beings, except (it’s) God, capable of understanding facts, modalities, etc. Leaving God aside for a moment, in this world there would be facts but no knowledge (or beliefs) regarding these facts. The statement ‘there are wegnots on w3’ is true, but not known to be true. But, ‘there are no horses on w2’ is also true on w3 because it is a possible statement and all possible statements are true, and necessarily so, because there is a concrete world corresponding to that statement. So there is a concrete world for all possible statements, and possible combinations of statements, that do not result in a contradiction or disagreement with the facts regarding that world.
    Now the question becomes is there a statement that is true of all possible worlds? If I understand what commentators on Prosblogion have been saying over the years regarding modal terms like ‘necessary’ and ‘possible,’ and ‘contingent,’ then the statement ‘there is a necessary being’ is true in all possible worlds. I take it that this necessary being would know all possible statements and that all possible statements have concrete worlds corresponding to them and would also know all the facts concerning these possible worlds. If Leibniz is correct then there is only one necessary being. So, it would seem that there is one necessary being but a whole lot of possible worlds that are also concrete worlds.
    Let us assume that there are possible worlds that are concrete worlds. These worlds must not be interactive or there would be only one world. So if there are possible worlds they must be ontologically separate. But there must be necessary being for each for each of these worlds. These necessary beings are identical except that they also do not interact. Each possible world is therefore monotheistic even though there is a plurality of deities.
    Here is my confusion. I take it that theists believe that there must be a necessary being in order for there to be possible and/or contingent beings. If there is a necessary being then possible/contingent beings, then there is only one possible concrete world – the word of facts. Isn’t this Spinoza’s position?

    August 25, 2012 — 11:05
  • Chad:
    That is, of course, how a Lewisian might understand monotheism. But (a) this feels no more to be monotheism than it is monotheism to say that there is one God for Israel and another for Egypt (that’s henotheism, perhaps); and (b) Donald Turner who originated theistic multiverse theorists doesn’t want a different a God for each world.

    August 27, 2012 — 10:55
  • Chad Carmichael

    Lewisian worlds are supposed to be causally isolated from one another, unlike Israel and Egypt. One might think that this is highly relevant to the question, e.g., which God you would pray to, worship, etc. If one thinks of monotheism as the idea that there is one God in the sense that there is one person who deserves our worship and so on, this might be monotheism enough. Of course, on this view, when one is doing serious metaphysics, one will have to admit that there are many gods. But not in ordinary English, and not in any sense that is relevant to actual religious practice. That’s what I was thinking, anyway.

    August 28, 2012 — 20:21
  • “Of course, on this view, when one is doing serious metaphysics, one will have to admit that there are many gods. But not in ordinary English, and not in any sense that is relevant to actual religious practice.”
    I think monotheism is a seriously metaphysical doctrine. It tells us that every being, other than the First Being, is in some deep way grounded in that First Being.

    August 28, 2012 — 22:17
  • Chad Carmichael

    Alex: The question I wanted to address is whether counterpart theory and monotheism can work together. We shouldn’t argue about what monotheism is *supposed* to be, or what it *really* is; rather, we should simply distinguish various theses that could be regarded as monotheistic sorts of theses, and ask whether any of them or all of them can be squared with counterpart theory. So far it seems to me that we have the following:
    Monotheism-1: There is exactly one God.
    Monotheism-2: There is actually exactly one God.
    Monotheism-3: There is exactly one First Being and everything is grounded in that First Being.
    Monotheism-4: There is actually exactly one First Being and, actually, everything is grounded in that First Being.
    Maybe there are others as well. In any case, my conjecture is that the Lewisian Theist could accept 2 and 4, reject 1 and 2 (though accepting both when they are voiced in ordinary language or in a religious text), and also claim to vindicate most any reason that has ever been given for any version of monotheism. If this is right, then it seems to me a mistake to say that counterpart theory fails to square with monotheism. (For the record: I dislike counterpart theory.)

    August 29, 2012 — 0:35
  • Well, ordinary monotheistic talk is often highly metaphysical, because ordinary believers defer to experts and tradition for the meaning of the theological terms they use, and the experts and tradition are often (this is most obvious in the Catholic case) highly metaphysical.
    In any case, there a maximalism about God at the heart of monotheism that appears incompatible with counterpart theory.

    August 29, 2012 — 7:40
  • David Alexander

    I realize that the following can be given Lewisian paraphrases, but I am not sure that they will relieve the discomfort.
    Given something like Lewisian modal realism (plus other relevant assumptions) the following appear to be true:
    A. The God I correctly worship is different from the God my counterpart correctly worships.
    B. There are things that the creator and sustainer of our universe neither created nor sustains.
    I think we can generate many more statements like A and B.

    August 29, 2012 — 11:54
  • Mike

    As some have noted above, the problem you mention seems to be generated by the assumption of overlap for God. While Lewis does not entirely deny overlap (universals, for instance) and does not explicitly deny overlap for God, the problem is removed if we do deny that worlds overlap wrt God. In that case, it is true that necessary God exists, though that modal proposition is made true by the existence of counterparts of God in each world. Bigger problems arise from Lewis’s rejection of essentialism, which would also have to be rejected in the case of God.
    But let’s assume that worlds do overlap with respect to God. How exactly does the inconsistency arise? God believes there are no horses (in w) and God believes there are horses (in @). God does not thereby have inconsistent beliefs and he does not believe only necessary truths. Compare the following: Jones in Tokyo is speaking to Smith in Waco. Jones says “it is raining here” and Smith says “it is not raining here”. Do their beliefs conflict? No, they express consistent propositions since ‘here’ designates a different location in the two utterances. Now suppose Jones is bilocated in Waco and Toyko. He utters the two sentences ‘it is raining here’ and ‘it is not raining here’. Does he utter inconsistent propositions? No, he doesn’t, for the same reason. Now take God uttering ‘there are horses here’ (or ‘there are acrtually horses’ and ‘there are not horses here’ (or, ‘there are actually no horses’). These are not inconsistent since ‘actual’ is an indexical like ‘here’ and works the same way. These propositions are not inconsistent to utter or to believe.
    [Sorry I was not able to login. This is Mike Almeida]

    August 29, 2012 — 12:26
  • Mike:
    There is no problem with God uttering different things in different places. But how does an immaterial God believe different things in different places?

    August 29, 2012 — 15:10
  • Mike

    The beliefs are consistent, Alex. Since he is present in w, he believes of w that (1) there are no horses here or (no important difference) there are no actual horses. In @ he believes, (2) there are actual horses. He can believe (1) and (2) in both worlds, since ‘actual’ varies in its reference in the same way that ‘here’ does. Both of those propositions is contingent, and both might be true at the same time.
    Maybe I’m missing your worry.

    August 29, 2012 — 19:26
  • Mike:
    I am not clear on what you mean by “believes of w that p”.
    Here is a plausible account of “x believes of A that F(it)” (e.g., “Sam believes of the tallest woman in the world that it (or, better, she) is smart”): x believes of A that F(it) iff there is an expression “e” that in fact refers to x and x believes F(e) (thus, if if the tallest woman is identical with the smartest woman, and Sam believes that the smartest woman is smart, he believes of the tallest woman that she is smart).
    Suppose I try to fit your locution into this mold. There is some expression e that in fact refers to w and God believes that at e there are no horses. (I am taking “here” and “actual” to function like “it”.) But what is this expression? If it refers rigidly to w, then what God believes is a necessary truth. If it refers non-rigidly to w, then presumably there is some world at which e has no horses in it, and so God’s belief is one that is true at some but not at other worlds.

    August 30, 2012 — 9:14
  • Justin

    “There is no problem with God uttering different things in different places.”
    Why is this? I would have thought the problem was equally pressing.

    August 30, 2012 — 10:07
  • Well, by “different things”, I meant different sentences, not different propositions.
    Suppose I am a long snake with a mouth at each end, and one end of me is in Texas and the other is in Arkansas. Then I can correctly say out of one mouth “Here it is Texas” and out of the other “Here it is not Texas” at the same time. But when doing so, I express propositions that are equally true in Texas and in Arkansas.

    August 30, 2012 — 11:22
  • Justin

    The snake pulls it off by having spatial parts. But, God isn’t like that. “Wherever God is present, he is wholly present. He is not a material being to have partial presence of the sort that might allow for a spatial distribution of [his sayings].”

    August 30, 2012 — 11:40
  • I could make my voice come out of two different megaphones, and then “here” would probably refer to the location of the megaphone (or at least could, depending on context) rather than my location.

    August 30, 2012 — 12:30
  • I’m glad to see some serious discussion of the notion that God has distinct counterparts at other worlds. If there are many worlds, this entails that there are many Gods, and thus it’s a type of polytheism. I’ve held this very position for several years (with some articles now starting to appear). It settles an enormous number of old problems, though for Christians it raises many more. Although I would not say that I’m a Christian, Peter Forrest has argued that a similar type of polytheism (tho not quite Lewisian) is compatible with Christianity. Maybe, maybe not. But when this type of theistic modal realism is fully developed, it seems to me to be a novel type of theology. It certainly is not monotheistic.

    November 3, 2012 — 23:07
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