One Philosopher’s Bug Can Be Another’s Feature: Reply to Almeida’s “Multiverse and Divine Creation”

Abstract

Michael Almeida once told me that he thought we were just a couple of hours of conversation away from reaching deep agreement about some important topics in the philosophy of religion pertaining to God, multiverses, and modality. This paper represents my attempt to move this conversation forward and to seek this common ground. Specifically, I respond to Almeida’s paper entitled “The Multiverse and Divine Creation”. In the first four sections, I record my disagreement with him concerning some smaller matters. In Section 5, I try to persuade him that what he considers a ‘bug’ in the theistic multiverse is actually a feature—and a desirable one at that. In Section 6, I close by identifying some points at which our views seem to converge.

1. The Principle of Plenitude

Almeida begins his paper by saying that an advantage of the theistic multiverse is that it aims to satisfy the Principle of Plenitude. As A.O. Lovejoy states, this principles includes

… not only the thesis that the universe is a plenum formarum in which the range of conceivable diversity of kinds of living things is exhaustively exemplified, but also any other deductions from the assumption that no genuine potentiality of being can remain unfulfilled, that the extent and abundance of the creation must be as great as the possibility of existence and commensurate with the productive capacity of a ‘perfect’ and inexhaustible Source, and that the world is better, the more things it contains

(Lovejoy 1932, p. 52)

Later, Almeida chides Donald Turner, me, and Timothy O’Connor for developing models of theistic multiverses that fail to deliver all of the abundance promised by the Principle of Plenitude. Specifically, Almeida complains that our models do not include on-balance bad or otherwise unworthy universes (8).

But neither Turner, nor I, nor O’Connor ever intended our models to include such universes, and so Almeida’s complaint misses the target. It is true that Turner discusses the Principle of Plenitude favourably in his paper, and that he says that it “motivates” his model (Turner 2003, p. 147). But Turner is quite clear that his multiverse only includes universes that are “above some cut-off line—for example, every [universe] with a favourable balance of good over evil” (Turner 2003, p. 149, and see also (Turner 2015)). As for me, it’s true that I also explicitly harnessed considerations about plenitude when devising principles which posit that God will create and sustain all those universes that are worth creating and sustaining. But I also introduced further principles which posit that God will create and sustain only those universes that are worth creating and sustaining (Kraay 2010, 2011). As for O’Connor, he too thinks that “… presumably there is some goodness threshold τ below which God would not create [universes]” (O’Connor 2008, p. 117).

I suspect that Almeida’s deeper concern here is that there is independent reason to think that on-balance-bad or otherwise unworthy universes really do exist—necessarily—in modal space, and that the multiverses defended by Turner, me, and O’Connor therefore really ought to include them. But, as we will see below, in Section 5, it is highly controversial whether, given theism, modal space includes such universes.

2. The Theistic Multiverse and the Problem of Evil

Almeida says that another advantage of the theistic multiverse is that it furnishes “a powerful theodicy” (1). This is not quite right, and can be a little bit misleading, as I will try to explain. Following Alvin Plantinga, let’s say that a theodicy specifies God’s actual reason for permitting evil or for [actualizing] a world that contains evil (Plantinga 1974, p. 10). Now, Turner’s theistic multiverse includes only universes that are ‘on-balance good’; mine includes only universes that are ‘worth creating and sustaining’, and O’Connor’s includes only those universes ‘at or above some goodness threshold τ’. These phrases represent, so to speak, overall criteria governing God’s choice.

But these criteria could be filled out in various ways. Some might hold, following J. L. Mackie (1955), that only universes featuring no evil whatsoever meet these criteria—and evidently, such a strict variant could not furnish a theodicy in Plantinga’s sense.1 Presumably, however, Almeida has something different in mind. Suppose that a proponent of the theistic multiverse holds that some universes that meet these general criteria do indeed contain evil. In what sense could such a view furnish a theodicy? Clearly, it would not itself constitute a specific account of God’s goals within a universe, or what goods God aims to bring about within a universe (etc.) by permitting any type or token of evil. At most, such a view could offer a highly abstract and formulaic account of why God actualizes a world containing evil: the theistic multiverse is such a world, and all of its universes that contain evil nevertheless meet the stated overall axiological criteria. But this is a theodicy only in a very limited sense.2

Moreover, the claim that theistic multiverse theory furnishes a theodicy is liable to be read as suggesting that it can successfully be invoked in responses to arguments from evil.3 And indeed, some of its proponents have held exactly this, although they differ about how significant a contribution the view can make to such responses. Some think that its contribution will only be modest (e.g., O’Connor 2008). Others think it has the resources to significantly enhance existing response strategies (e.g., Hudson 2005; Schrynemakers 2015). The limit case is Megill (2011), who believes that the bare epistemic possibility of a theistic multiverse completely defeats all arguments from evil, past and present. But all these claims are controversial. Draper (2004), Almeida (2008, chp. 8), and Monton (2010) have argued, in various ways, that theistic multiverse theories cannot defeat arguments from evil, and I have argued likewise (Kraay 2011, 2012).

Here is my way of seeing the matter. Defenders of theistic multiverses posit that if God exists, then the actual world is a multiverse that includes only those universes that meet or exceed their preferred axiological criteria. Most arguments from evil, meanwhile, involve an a posteriori claim to the effect that our universe contains (or probably contains) types or tokens of evil that disconfirm God’s existence. In the context of the theistic multiverse, such claims can be taken to assert that our universe fails, or probably fails, to meet the axiological standard preferred by the critics of theism. And so the discussion begins. As I have written elsewhere:

Defenders and critics of multiverse-theism can work together to find a mutually-agreeable threshold [at or] above which universes should be deemed worthy of inclusion in a theistic multiverse. They may well subsequently differ on the a posteriori question of whether our universe surpasses the agreed-upon threshold. Considerations about the existence, variety, magnitude, duration, scope, distribution, types, or intensity of evil in our universe could be appealed to in defending the claim that our universe is (probably) not worthy of inclusion. And defenders of multiverse-theism could either try to show that our universe (probably) is worthy of inclusion, or—more modestly—they could try to defeat or undermine arguments to the contrary. In short, the typical moves in the debate concerning the problem of evil can easily be reframed to apply to multiverse theism. But this, by itself, will not furnish an advantage to either side

(Kraay 2012, pp. 157–58.)

For this reason, theistic multiverse models alone cannot defeat, undermine, or otherwise diminish the probative force of arguments from evil.

3. Axiological Properties of Universes and of Worlds

Almeida criticizes Turner and me for assuming that the best possible world will contain all and only those universes that surpass the relevant axiological threshold. With respect to Turner, Almeida says:

If God necessarily actualizes the theistic multiverse, then he actualizes the best possible world no matter how good or bad the universes happen to be that compose the theistic multiverse. If God necessarily actualizes the theistic multiverse, then God necessarily actualized the best possible world. The intrinsic value of universes composing the multiverse is irrelevant to the question of whether the multiverse is the best possible world (5).

And with respect to me, Almeida says:

If God necessarily actualizes the theistic multiverse, then he actualizes the best possible world no matter how worthy or unworthy the universes happen to be that comprise the theistic multiverse. If God necessarily actualizes the theistic multiverse, then God necessarily actualizes the best possible world. The intrinsic value of the universes composing the multiverse is not relevant at all to the question of whether the multiverse is the best possible world (5).

Unsurprisingly, I disagree. Here are two arguments for my preferred way of seeing the matter. First, consider these four principles, which I have discussed elsewhere (Kraay 2010, 2011):4

P1

If a universe is creatable by an unsurpassable being, and worth creating (i.e., it has an axiological status that [meets or] surpasses some objective threshold t), that being will create that universe.

P2

If a universe is sustainable by an unsurpassable being, and worth sustaining (i.e., it has an axiological status that [meets or] surpasses some objective threshold t), that being will sustain that universe.

P3

If a universe is not worthy of creation (i.e., it has an axiological status that fails to [meet or] surpass some threshold t), an unsurpassable being will not create that universe.

P4

If a universe is not worthy of being sustained (i.e., it has an axiological status that fails to [meet or] surpass some threshold t), an unsurpassable being will not sustain that universe.

Jointly, these principles suggest that that God will create and sustain all and only those universes that meet or surpass a certain axiological threshold. The result, I have argued, is the best possible world.5 But of course this means that, contra Almeida, the best possible world simply cannot feature any unworthy worlds.

A second way to motivate my way of seeing the matter is by considering connections between the axiological properties of universes and of worlds. I have argued that the axiological status of universes can be expressed as some complex function of the universe-good-making-properties (UGMPs) and universe bad-making properties (UBMPs) that universe exhibits, and the degree to which it exhibits them. I have also argued that the axiological status of worlds can be expressed as some complex function of the world-good-making-properties (WGMPs) and world-bad-making properties (WBMPs) that world exhibits, and the degree to which it exhibits them (Kraay 2010). I take it that, ceteris paribus, worlds are better to the extent that they include more universes at or above the relevant axiological threshold. I also take it that, ceteris paribus, worlds are worse to the extent that they include universes below the axiological threshold. So it is a mistake to think, as Almeida does, that the axiological status of a multiverse has nothing to do with the axiological status of the universes it contains. For the same reason, I disagree with Almeida’s claim that “If God necessarily actualizes the multiverse, we have no idea which universes are parts of that multiverse” (2). On my view, principles P1–P4 give us a rather good idea.

I should clarify three small additional points about the axiological properties of universes and of worlds, in order to forestall any confusion. First, I do not hold that the theistic multiverse contains only universes and nothing else. Worlds can and do contain non-spatiotemporal entities, and clearly these cannot be housed inside universes, which, after all, are concrete spatiotemporal entities. Paradigmatically, of course, God is a non-spatiotemporal entity, and so God cannot be said to inhabit a universe, but can be said to exist in a world.6 Some non-spatiotemporal entities, (like God and numbers) exist necessarily. Others (like angels, perhaps) are continent beings. The fact that worlds can include non-spatiotemporal objects matters because it helps to underscore the point that there is an important distinction between WGMPs and UGMPs (and, equally, between WBMPs and UBMPs). After all, some WGMPs and WBMPs have nothing whatsoever to do with universes, since they refer to the presence or absence of non-spatiotemporal entities in a world, and the resulting axiological effects in that world.

Second, while the overall axiological status of a world depends upon the WGMPs and WBMPs it exhibits, it may that be certain good-making properties cease to make worlds better past a certain point, or in certain combinations. (The same goes, mutatis mutandis, for WBMPs.) So, while the goodness of a world or a universe depends upon the axiological properties it exhibits (or fails to), this dependency may not be simple.

Third, someone might object to theistic multiverse theory on the grounds that universes should not be treated as the primary locus of value in our axiological theorizing. This complaint might hold, for example, that persons, or perhaps creaturely lives, should be treated as the primary locus of value, and should accordingly be given greater prominence than universes in axiological theorizing. I would respond by saying that an account of WGMPs, WBMPs, UGMPs and UBMPs could be developed to harness these intuitions. Someone might say, for example, that a universe is worth creating, or a world is worth actualizing, only if the persons it contains lead lives that are overall worth living. To generalize the point: talk of the good- and bad-making properties of universes and worlds represents only a sort of schema that can be fleshed out in various ways to accommodate different axiological and ethical views.

4. Almeida on O’Connor

Almeida claims that O’Connor holds that “God would elect to create that superuniverse containing every single universe at or above some goodness threshold τ” (7, emphasis added). But, although O’Connor does include this very proposition in his book (O’Connor 2008, p. 117), it is not quite right to characterize his considered view in this fashion. First, we need some context. O’Connor prefaces this claim by saying merely that it is more likely—more likely than the scenario he set out immediately beforehand, namely that God would create every possible universe. Let’s set likelihoods aside, since it’s difficult to know how to construe this claim probabilistically. I take it that O’Connor really means to say that it is more plausible to think that God will create every universe at or above axiological threshold τ than it is to claim that God will create every universe simpliciter. (I agree, and will say about this below.) But, of course, it doesn’t follow from the fact that an author regards position X as more plausible than position Y that the author’s considered view is indeed X.

Second, and contra Almeida, the next few moves clearly reveal that it is not O’Connor’s final view that God would create every universe above threshold τ. After noting that God could achieve infinite overall aggregate value by creating every threshold-surpassing universe, O’Connor immediately points out that God could achieve the same result by creating every second, third, or n-th universe at or above threshold τ. O’Connor regards these all as “adequate choices” (p. 117). But then O’Connor notes that there is no highest transfinite cardinal, and, hence, no upper bound on how many universes God could create. So while there are many ways for God to bring about infinite aggregate value in creation, none of these would bring about maximal aggregate value. This does not trouble O’Connor, however, since he thinks it “…doubtful that a perfect being would desire to pursue maximal aggregate value at all” (p. 119).7 O’Connor ultimately favours the view that universes can be grouped into kinds or value-types (p. 120), and he thinks that God would create at least some universes from each of these, without attempting to creating all of the universes that there are in modal space. In the end, then, O’Connor’s considered view comes to this:

I have argued that all the possibilities deemed creation-worthy by a perfect creator would conform to a rich structure. Even so, an infinity of options satisfies these constraints, and there is no reason yet uncovered to suppose that any highly particular sort of universe will be deemed necessary. Hence, for all we’ve seen, the extent of alternatives open to a perfect creator will be wide indeed (120).

So, Almeida is mistaken when he claims that O’Connor’s God will create every universe at or above threshold τ. But, Almeida is quite correct to say that there are some things that O’Connor’s God cannot do. In particular, O’Connor’s God cannot: (a) refrain from creating;8 (b) create any universe whose axiological status is below threshold τ; (c) actualize a possible world that contains only one universe—in other words, he cannot refrain from creating a multiverse; (d) create a multiverse comprised of merely finitely many universes; and he cannot (e) refrain from creating at least one universe from each kind or value-type.

5. “It’s not a Bug; it’s a Feature!”9

I now turn to the central disagreement between Almeida, on the one hand, and Turner, O’Connor, and me on the other. Almeida states:

It is nonetheless an important criticism of the theistic multiverse that it is not plenitudinous. It nominally satisfies the general principle of plenitude, but there are many ways things non-skeptically might have been that are not represented in the theistic multiverse. There are, for instance, no on balance bad [universes] in that multiverse ... And there are no [universes] in which the level of goodness falls just below the standard of goodness for universes in the theistic multiverse (8).10

So, Almeida thinks that these theistic multiverses are not fully furnished, since they fail to include universes that really do exist, necessarily, in modal space. As a result, Almeida further objects that theistic multiverse models incoherently represent God as choosing some universes over others to create and sustain. In particular, if God necessarily chooses only those universes that meet or surpass some axiological threshold, then universes below the threshold are in fact metaphysically impossible, and so cannot coherently be represented as possible objects of God’s choice. All of this is the chief ‘bug’ that Almeida detects in theistic multiverse theory.

This ‘bug’ is sometimes referred to as ‘modal collapse’—the idea that on a given theoretical model or ontology, modal space turns out to be rather less capacious, or more restricted, than it really ought to be.11 Now, one philosopher’s ‘bug’ can be another’s ‘feature’, so to speak—and indeed, can be a desirable feature. In the remainder of this section, I will explain why I think that the restriction that Turner, I, and O’Connor agree on—namely, that God will not create worlds below a certain axiological threshold—should be thought a desirable feature, rather than a bug. The central idea begins with this simple modus tollens:

(1)

If God creates and sustains any universe that is below a plausible axiological threshold, God is not essentially unsurpassable.

(2)

God is essentially unsurpassable.

(3)

It’s not the case that God creates and sustains any universe that is below a plausible axiological threshold.

Now, given theism, nobody but God is in the business of creating and sustaining universes, and no actual universes lack a creator and sustainer. It follows that, given theism, no universes below the threshold are possible. They are, in fact, logically self-contradictory, because, from the vantage point of those universes, they both have and lack a creator and sustainer who is essentially unsurpassable.12 Given theism, then, modal space just cannot be as capacious as it might, meta-modally speaking, otherwise be. In Thomas Morris’ phrase, God is “a delimiter of possibilities” (Morris 1987, p. 48); as Brian Leftow puts it, God leaves a “modal footprint” (Leftow 2005, p. 96; Leftow 2010, p. 30).

Now, of course, Almeida may wish to insist that the universes below this axiological threshold really are logical possibilities. But I think it is illicit, in this dialectical context, to rely solely on, or even privilege, modal intuitions that bracket God. Here is Thomas Morris again:

If there is a being who exists necessarily, and is necessarily omnipotent, omniscient, and good, then many states of affairs which otherwise would represent genuine possibilities, and which by all non-theistic tests of logic and semantics do represent possibilities, are strictly impossible in the strongest sense. In particular, worlds containing certain sorts of disvalue or evil are metaphysically ruled out by the nature of God, divinely precluded from the realm of real possibility

(Morris 1987, p. 48)

Alvin Plantinga, incidentally, holds a similar view:

[A]ll possible worlds … are very good. For God is unlimited in goodness and holiness, as well as in power and knowledge; these properties, furthermore, are essential to him; and this means, I believe, that God not only has created [i.e., actualized] a world that is very good, but that there aren’t any conditions under which he would have created a world that is less than very good … The class of possible worlds God’s love and goodness prevents him from actualizing is empty. All possible worlds, we might say, are eligible worlds: worlds that God’s goodness, mercy, and love would permit him to actualize.

(Plantinga 2004, p. 8)

Morris and Plantinga here speak of worlds, rather than universes, but of course this makes no difference, since they would both hold that worlds that include universes that fail to surpass a plausible axiological threshold are not genuine possibilities.

So, why is this a desirable feature rather than a bug? Well, it is desirable for the defender of theistic multiverses, since it neatly avoids casting God—an essentially unsurpassable being—as the creator and sustainer of any worlds below the relevant axiological threshold. It is also desirable for those with a high view of divine sovereignty, because there is an important sense in which God is sovereign over modal space on this view.

6. Modelling Possibility With and Within the Theistic Multiverse

Toward the end of his paper, Almeida says this:

In the theistic multiverse, every possible object, event, etc. exists at some time or other where the existence of these possible objects, events, etc. does not differ ontologically from the existence of actual objects, events, etc. There is no ontological difference between possible objects and actual objects, since the possible objects just are the actual objects. The theistic multiverse does not make the distinction between actual worlds, objects, events, states of affairs and possible worlds, objects, events, and states of affairs. The theistic multiverse is the only existing possible world, so God [trivially] actualizes every possible world (8).

I have three points to make in response.

First, this is not an accurate description of O’Connor’s theistic multiverse. O’Connor thinks that there are no universes below threshold τ in the theistic multiverse. But, as we have seen, O’Connor takes pains to argue that God can still sensibly be thought to choose between genuine metaphysical possibilities, despite this constraint. This is because there is no greatest transfinite cardinality, and, accordingly, there is an infinite array of metaphysically possible super-universes (each including only universes at or above axiological threshold τ) from which God can choose, while still bringing about infinite value in creation.

Second, strictly speaking, my view does not require me to say that the theistic multiverse is the only possible world. Technically, my view is just that God will create and sustain all and only those universes that are worthy of being created and sustained. Perhaps there are several worlds that all meet this description, but that nevertheless differ with respect to the contingent non-spatiotemporal entities they lack or contain. But I won’t insist on this point—in fact, I will ignore it in what follows.13

So, on Turner’s view, and mine, it is the case that God necessarily actualizes the theistic multiverse, and so Almeida’s description here might seem apt. But, again, perhaps not entirely—and this is my third point. One might follow Donald Turner (and others) by distinguishing between two sorts of possibility. As Turner puts it, the first sense holds that “the internal consistency of a world is determined without reference to whether it is a world the actualization of which is consistent with God’s character” (Turner 2015, p. 121). In this sense, worlds other than the theistic multiverse are possible. But in the second sense, according to which the internal consistency of a world is determined without bracketing considerations pertaining to God’s character, such worlds are not possible. Relatedly, one might picture possible worlds in the former sense as mere ideas in God’s mind—really and truly there for inspection, but not really and truly furniture in modal space. If a move like along these lines is plausible, then Almeida’s description above will not be entirely accurate.

Finally, I turn to concerns judgments of possibility within the theistic multiverse. Elsewhere, I have written:

If the only possible world is the theistic multiverse, the claim “nothing could possibly be other than it is” is ambiguous. Taken to mean that there could not possibly have been anything other than the array of universes worth creating and sustaining, this claim is true. But expressed from a vantage point within a universe, and taken to refer to that universe, it is false. From this perspective, to say that things could be otherwise is just to say that there is another spatiotemporally distinct universe in which things are otherwise. Universes … can vary in all sorts of ways. They may differ in their laws of nature and in their histories, and these variances can perhaps anchor many of the familiar modal claims whose intelligibility seemed threatened by the claim that there is only one possible world. In fact, this picture of modality—on which modal claims are understood to refer to concrete, spatiotemporally isolated universes—is strikingly similar to a well-known theory of modality: David Lewis’ modal realism. So while the claim that there is only one possible world on theism seemed an affront to our modal intuitions, once it is seen that this world is the theistic multiverse, it may be that familiar modal claims can be parsed in terms of universes instead of worlds. Modal collapse may not be so bad after all.

(Kraay 2011, pp. 366–67)

Almeida considers the idea that in actualizing the theistic multiverse, God creates all of metaphysical reality. Echoing Lewis, he dubs the result “the one big world” (Almeida 2017, p. 9; and see (Lewis 1986, 70 ff)). And, interestingly, Almeida then quickly offers the following suggestion:

However the one big world is structured, it would include infinitely many world- like objects. Those world-like objects are parts of the vast, temporally infinite, universe. The defender of the theistic multiverse might argue that—contrary to what we might have thought—the one big world comprises all of metaphysical reality, and the totality of the world-like objects in the theistic multiverse represent[s] every way things non-skeptically might have been (9).

This suggestion seems very similar in spirit to my proposal, and so I welcome it, with only two small caveats. First, I must quibble with the second sentence, since I don’t see why the ‘one big world’ should be regarded as either a universe (it’s a multiverse) or as temporally infinite (it is not a spatiotemporal entity at all, although it contains spatiotemporal entities). Second, I would add the modifier “given theism” to the end of the final sentence, to capture the idea, discussed in Section 5, that God leaves a footprint on modality.

Almeida imagines a critic insisting that there must be possible worlds other than the theistic multiverse that represent ways things might have been. He then suggests the following reply:

The multiverse theorist might argue … that if you thought there was a possible world for every way things non-skeptically might have been, how do you know you are not thinking of world-like objects [within the multiverse]? How do you know that you are not thinking that there is a world-like object for every way things non-skeptically might have been? If the theistic multiverse includes an infinity of world-like objects, and if the theistic multiverse—the one big world—is all there is to metaphysical reality, then we might be moved to conclude that metaphysical reality is in fact plenitudinous or close enough (9–10).

I welcome this idea as well, although I again want to underscore the constraint that theism places, in my view, on plenitude.

It remains to be seen, of course, whether this conception of metaphysical reality is robust enough to meet our modal requirements. But it strikes me as promising—and as desirable for the theist. Moreover, it is not really that different from Almeida’s own view: theistic modal realism. On my view, concrete spatiotemporal world-like objects—universes—are created by God and can plausibly anchor many familiar modal claims. On his view, concrete spatiotemporal objects—worlds—exist in modal space and ground familiar modal claims. While we differ on how many of these objects there are, given theism, there does seem to be some important convergence between our views. Perhaps Almeida and I will ultimately find agreement after all.