According to classical theism, God necessarily actualizes the best possible world and only the best possible world. It is a consequence of God’s perfect nature that divine creation satisfies the principle of plenitude and the principle of the best. I show that God necessarily actualizes the best possible world w only if (i) the resulting world w’ satisfies both the principle of the best and the principle of plenitude and (ii) w’ is worse than w. That is the paradox of best worlds.
KeywordsClassical theismprinciple of plenitudeprinciple of the bestparadox of best worldsIntroduction
It is a consequence of God’s perfect nature, according to classical theism, that divine creation satisfies the principle of plenitude. The principle of plenitude is most closely associated with Arthur Lovejoy. According to Lovejoy, the principle states that no genuine potentiality can remain unfulfilled.
… the extent and the 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 … the world is the better the more things it contains. (A.O Lovejoy, 1932, p. 52)
The principle of plenitude is an ontological principle about the number and variety of possibilia in creation. A creation that is in proportion to the power of an infinite being must itself be infinitely or limitlessly large. The principle of plenitude entails that all genuine possibilities are actual at some time or other. 1
Another consequence of God’s perfect nature, according to classical theism, is that creation must satisfy the principle of the best. The principle of the best is an axiological principle according to which God necessarily actualizes the best possible world. William Rowe follows Leibniz and Clarke in arguing that a maximally great being necessarily chooses the best possible world.
Let’s suppose along with Leibniz and Samuel Clarke that the series of increasingly good worlds culminates in the best possible world, a world than which no possible world is as good or better… Faced with choosing from among these two series of worlds the world he shall create, it is obvious that an infinitely good being would not, indeed could not, create one of the bad worlds. Which good world would he then create? Again, it seems obvious that he would create the very best world, the best of all possible worlds. (Rowe, 2002, p. 409. my emphasis)
Recent work on the theistic multiverse aims to show that divine creation satisfies both the principle of plenitude and the principle of the best. According to multiverse theorists, God creates every on balance good universe just if divine creation satisfies the requirements of both principles.
Pushed to their logical limit, these considerations suggest that an unsurpassably powerful, knowledgeable, and good deity will create every universe that is worth creating. I suspect that this way of thinking is motivated by a principle of plenitude …2 (Kraay, 2011, p. 362.)
In section (2) I argue that objects, persons, and events might persist across concrete universes and worlds in the same way that objects, persons, and events might persist across times in a single universe. I argue that overlapping possible worlds are compossible and so are overlapping possible universes. The intrinsic properties of objects enduring across possible worlds are exemplified-at various universes and worlds. So, it is possible that Smith is a concrete, spatiotemporal object existing in world w and also existing in world w’. There are no violations of Leibniz’s laws provided that the intrinsic properties of Smith stand in the exemplified-at relation to worlds w and w’.
In section (3) I present the argument from classical theism that God necessarily actualizes the best possible world. I show that God necessarily actualizes the best possible world only if God actualizes a metaphysically isolated world. Metaphysically isolated worlds are accessible only to themselves and no other possible world is accessible to them.3 Since every metaphysically isolated world satisfies the principle of the best and the principle of plenitude, it follows that God necessarily actualizes a world w only if w satisfies the principle of plenitude and the principle of the best. It’s an interesting and unanticipated consequence of the argument that the classical God can necessarily actualize any number of possible worlds.
In section (4), I present the paradox of best worlds. According to the paradox, the result of God necessarily actualizing the best possible world is a world in which there are no significantly free moral agents. So, when God necessarily actualizes w he makes it worse. It is therefore better if God does not necessarily actualize w. I offer some concluding remarks in section (5).
On Compossible Worlds
Universes are understood as regions of spacetime that include the spatiotemporal objects, events, and states of affairs in a world.4 We will say that a possible world w is a multiverse just if w includes multiple universes. We will say that the pluriverse - the totality of metaphysical space - includes every region of possible worlds.
We allow that universes - and so also possible worlds - might overlap with respect to their inhabitants. Objects, persons, and events might persist across universes in one world, for instance, in the same way that objects, events, and persons might persist across times in a single universe. And objects, events, and persons might persist across worlds.
The endurance of objects across worlds is ensured through indexing property exemplification - in this case, indexing the copula, is-at or exemplifies-at - to spacetime regions in worlds. (cf. Haslanger 1989; Johnston, 1987; Miller, 2006) Given the exemplification-at relation, universes in a world might together constitute one domain of quantification in which the same individuals exemplify various intrinsic properties in various universes.5 It might be true, for instance, that God exemplifies-at-u the monadic property of being incarnate and God exemplifies-at-u’ the monadic property of not being incarnate.6 God might exist in every universe in a multiverse and God might exist in multiple possible worlds. Finally, God might exist in “one big world” - multiple possible worlds all of which are spatiotemporally isolated (though not metaphysically isolated) and all of which are actual.7 (cf. Lewis, 1986, pp. 76-85, 97 - 99)
Possible worlds all include regions of spacetime. The spatiotemporal isolation of w0, w1 and w2 in general ensures the individuation of those worlds. Possible worlds nonetheless stand in certain relations to other possible worlds and to themselves - relations of relative possibility, for instance, and various logical relations - though diverse possible worlds cannot stand in any causal or spatiotemporal relations to one another.
On Lewisian truth-conditions, for instance, propositions of the form ◻︎B are true at a world w just if B is true in every world w’ accessible to w.8 That is, just if B is true in every relatively possible world. If the relatively possible worlds include every possible world, then there is no difference between what is relatively possible and what is absolutely possible - or possible simpliciter.9
We will say that God actualizes a possible world w just if God creates the regions of spacetime in w and every contingent object, event, and state of affairs in w.
Actualization is creation rather than instantiation on this account. 10 We take the created or actualized part of possible worlds to be concrete.11 In actualizing any world God creates all of the objects and events and states of affairs in the universe. All possible worlds share the same necessarily existing objects, events, and states of affairs.
According to classical theism, divine creation satisfies a principle of plenitude and a principle of the best. The principle of the best requires that God actualize a world unequalled in overall value. We formulate the principle of the best as follows.12
B. ◻︎(∀y(w ≠ y ⟶ w >G y) ⟷ (God actualizes w))
The principle states that, necessarily, w is the best possible world if and only if God actualizes w. The biconditional entails that God actualizes the best possible world and only the best possible world. We take B to express an axiological requirement on the classical God. (cf. Hintikka, J. (1980), pp. 259 – 286).
The simplest formulation of the principle of plenitude entails that every genuine possibility will be actual in the fullness of time. Everything that is possible is, at some time or other, actual. The principle of plenitude requires that God actualizes a world w if and only if w includes, over time, the greatest compossible number and diversity of possibilia. We let S be the most inclusive compossible set of universes as determined by the number and diversity of objects in each universe.13 And we read two-placed predicate ‘Ixw’ as universe x is included in world w.
P. ◻︎((God actualizes w) ⟷ ∀x(x ∈ S ⟶ Ixw))
Principle P states that, necessarily, God actualizes a possible world w if and only if the most inclusive compossible set of universes S is included in w. We take P to be an ontological requirement on the classical God.
The principle P permits contingent objects in w to exist in diverse universes at diverse times, and does not require that objects exist permanently in w. w is a plenitudinous world, but objects might also come into existence or go out of existence in w. (Cf. Williamson, 2002; 2013)
An Argument from Classical Theism
Divine creation must ultimately satisfy the principle of the best and the principle of plenitude. We assume that the values determining the axiological status of possible worlds are objective and necessarily existing. For the sake of discussion, we set aside epistemological limitations that depend on the incomparability of objective values. And we assume that the objective values determine a strict ordering >G of possible worlds.14
God’s ordering of possible worlds >G is based on the overall value of worlds. Since values are objective and necessarily existing, they do not vary from world to world.15 If it is true in some world that w is better than any other possible world according to >G then it is true in every world that w is better than any other possible world according to >G. The first premise in the argument states that >G determines a best possible world.
◻︎∀y((w ≠ y) ⟶ (w >G y))
According to (1), necessarily, w is better than any other world according to the ordering in >G. The second premise in the classical argument is principle B. Necessarily, God actualizes w just if w is the best possible world according to >G.
◻︎(∀y(w ≠ y ⟶ w >G y) ⟷ (God actualizes w))
According to (2), necessarily, God actualizes the best possible world and only the best possible world. From (1) and (2) we derive the conclusion in (3).
◻︎(God actualizes w)
The classical argument’s conclusion states simply that God necessarily actualizes w. The argument from (1) and (2) to (3) is valid. The central question for the classical theist is whether (3) entails that divine creation satisfies the principle of the best and the principle of plenitude.
God necessarily actualizes the world w. But it does not follow from this argument that there exist no worlds in the pluriverse other than w. It follows rather that w is a metaphysically isolated world.16 w sees no possible worlds other than itself and so no other worlds are metaphysically possible from the point of view of w other than itself. Since God necessarily actualizes w, every object and event in w necessarily exists or occurs and every state of affairs in w necessarily obtains. So, w is a metaphysically isolated world.
As noted, metaphysically isolated worlds see only themselves and no other worlds. But it is also true that no other worlds see metaphysically isolated worlds.17 If w and w’ are metaphysically isolated, then w includes some fact that is metaphysically impossible relative to w’. For example, it might be true in w’ that H2O = water and true in w that H2O ≠ water. Each of these facts is logically possible, but they cannot both be true in any single cluster of possible worlds. So, these are worlds from the point of view of which there exist no other metaphysically possible worlds. All other worlds - and all other clusters of worlds - in the pluriverse are relatively impossible or metaphysically impossible relative to w. We assume that all worlds, including every absolutely possible world, is a normal world. There are no worlds in which a contradiction is true.
There might be other possible worlds - or even clusters of worlds - in the pluriverse, but w has no metaphysical access to those worlds and those worlds cannot access w. Let arrows indicate accessibility and consider the following set of worlds.
none
Here w0 and w1 are both metaphysically isolated worlds. w0 and w1 see only themselves and no other worlds. Of course, w0 and w1 are logically, and perhaps epistemically, possible relative to one another, but that’s irrelevant to the current issue. So, w1 is metaphysically impossible relative to w0 and vice versa. There are two possible worlds in this small model - we will say that there are two absolutely possible worlds in the pluriverse - but from the point of view of each of those worlds, there exists exactly one metaphysically possible world. It is true in each world that it alone is metaphysically possible. The classical God in this case necessarily created each of w0 and w1 and each of the worlds necessarily obtains. From the point of view of each world, w0 and w1, it is the best possible world and it alone satisfies the principle of plenitude. We have in effect two best possible worlds, two possible worlds each of which is better than any other possible world.
If w0 and w1 are metaphysically isolated worlds, then w0 and w1 inhabit distinct, isolated regions of metaphysical space. w0 and w1 are not merely spatiotemporally isolated, they are metaphysically isolated. w0 is metaphysically impossible relative to w1 and w1 is metaphysically impossible relative to w0, though neither is a non-normal world18 Each of these worlds is possible relative to itself alone and metaphysically inaccessible to the other.
Premise (2) ensures symmetry in the metaphysical isolation of worlds. 19 w is metaphysically isolated from all other worlds just if all other possible worlds are metaphysically isolated from w. There might even be infinitely large collections of worlds that are metaphysically isolated from w. It is true from the point of view of w that such worlds are metaphysically impossible, but it is not true from the point of view of every world that such worlds are absolutely impossible. They are relatively impossible but not absolutely impossible.
It is true that God can necessarily actualize some world in the pluriverse. But, as we saw above and we see again below, God can also necessarily actualize several worlds in the pluriverse. The pluriverse might include worlds like w0 – w2 each of which is necessarily actual in its region of logical space and each of which is a metaphysically isolated world. The arrows indicate metaphysical accessibility, so each world sees only itself. Let the rectangle be all of logical space. w0 – w2 are distinct and isolated metaphysical regions of logical space. These are ways the totality of metaphysical space might be.
none
Each of w0 – w2 is an isolated concrete world and each occupies an isolated region of logical space.20 World w0 sees only itself, and similarly for w1 and w2. This entails that, relative to w0, worlds w1 and w2 do not represent genuine metaphysical possibilities. Of course, all of w0 – w2 are possible relative to themselves and so represent genuine possibilities relative to themselves. And all of the worlds are logically possible relative to each other.
None of the worlds w0 – w2 include any inconsistencies or contradictions. They represent epistemic possibilities relative to each other for at least some inhabitants. It is true, for instance, that some inhabitants of w0 regard w1 or w2 as possible, for all they know.
But how can a world be both possible relative to itself and not possible relative to other worlds? Consider an example of how this might happen. Suppose the principle of essentiality of origins is true and the hunks of matter y, z, and w do not overlap.21 It might be true in world w0 that a table x is originally composed of y and true in w1 that x is originally composed of z and finally true in w2 that x is originally composed of w. The example is possible if w0, w1 and w2 are metaphysically isolated from each other, since x is essentially y in w0, x is essentially z in w1 and x is essentially w in w2. All three worlds are possible relative to themselves, but none is metaphysically possible relative to any other world.
It is true in each of these worlds that it is the actual world. Each world is in its own region of the pluriverse - having no access to any other world - and so from the point of view of each world there exist no other metaphysically possible worlds or regions. w0, w1, and w2 are possible relative to themselves and it is true from the point of view of each world that it is the uniquely best possible world. Since there are no other worlds from the point of view of each, each must be the best. It is true from the point of view of w0, for instance, that it is the best possible world on any standard we might apply and, indeed, necessarily the best possible world. It is true from the point of view of each of these worlds that it is itself the only possible world and so the best possible world by any standard. All other worlds are relatively impossible.
There are other ways it might happen that God necessarily actualizes each world w0, w1, and w2. Suppose the ordering of possible worlds varies from world to world. In w0 worlds are ordered according to >G0 and in w1 worlds are ordered according to >G1 and in w2 worlds are ordered according to >G2. The following are true in every possible world, if each of the worlds is the best possible world relative to each ordering >Gn.
◻︎(∀y(w0 ≠ y ⟶ w0 >G0 y)
◻︎(∀y(w1 ≠ y ⟶ w1 >G1 y)
◻︎(∀y(w2 ≠ y ⟶ w2 >G2 y)
And the principle of the best in premise (2) entails that the classical God necessarily actualizes each of these worlds w0, w1, and w2, since each of these worlds is the best metaphysically possible world according to the theses above.22
It follows from premise (2) above that God exists in each of w0 – w2 since it is true in each of these worlds that God necessarily actualized that world. So, the fact that God necessarily actualizes the best possible world does not entail that God exists in exactly one world. God might exist in every absolutely possible world, even if every world is metaphysically isolated from all others.
The principle of the best entails that God actualizes only the best possible world, since the biconditional in (2) entails (4). But the thesis in (4) is false unless we assume a logic as strong as S5.
◻︎((God actualizes w) ⟶ (∀y(w ≠ y ⟶ w >G y))
We can still derive the conclusion in (3) without (4). That is, we can prove that God necessarily actualizes the best world w. But in the absence of (4) the fact that God necessarily actualizes the best world w is consistent with the fact that God could also have actualized a less-than-best world w’.23 And that is not consistent with classical theism.
Assuming S5, possible worlds might be related in the following way. w0 is metaphysically isolated from the cluster of worlds w1 – w3. And the cluster of worlds is metaphysically isolated from w0. So, w0 is impossible relative to the cluster of worlds and the cluster of worlds is impossible relative to w0. All of the theorems of S5 hold throughout the pluriverse. So, modal reasoning does not vary from world to world.
none
Worlds can be related in this way, even granting that there is a classical God and the classical God necessarily actualizes the best world. But it must be true that the classical God exists in w0 only and that there is no best world in the cluster of worlds. So, it might be the case that both the classical God necessarily exists and necessarily actualizes a world - in this case, the world w0 - and there are large regions of worlds in metaphysical space in which the classical God does not exist.
Spatiotemporally isolated worlds can overlap, so individuals might exist in more than one world in the cluster above. Metaphysically isolated worlds can also overlap, so individuals might exist in both w0 and in w1 - w3.24 Individuals might exist in worlds in which God necessarily exists - namely, w0 - and also in worlds in which God necessarily does not exist – w1, w2, and w3. And every world - w0 – w3 - satisfies all of the S5 theorems.
(2) entails that no member of the cluster of worlds - no member in any cluster of worlds - is a metaphysically isolated world. So, every world in any cluster of worlds is necessarily less-than-best. Otherwise, the classical God would have necessarily actualized that world and it would be metaphysically isolated. Since the classical God necessarily creates only the best world, the classical God exists in none of these less-than-best worlds. All of the worlds in the cluster are relatively impossible from God’s point of view, since God exists in w0 alone. And God is an impossible being from the point of view of every world in the cluster.25
Everything in metaphysically isolated worlds exists, occurs, or obtains as a matter of metaphysical necessity. So, it follows from the classical theist argument above that every person in w0 performs every action as a matter of metaphysical necessity and every object in w0 exemplifies all of its properties essentially and every event in w0 occurs necessarily.
It is an open question - one that classical theists have not addressed - whether the classical God might necessarily actualize the best cluster of worlds rather than necessarily actualize a uniquely best world. If the classical God necessarily actualizes the cluster of worlds below, for instance, then the region of worlds in that cluster is metaphysically isolated and so it is the uniquely best cluster of worlds. The cluster is metaphysically isolated in the sense that no world outside the cluster sees any world inside the cluster and vice versa. The advantage of necessarily actualizing a cluster of worlds is that w1, w2, and w3 are not themselves metaphysically isolated - though the cluster of worlds is metaphysically isolated - and at least some contingency is preserved in divine creation. There is contingency in creation despite the fact that the cluster itself is metaphysically necessitated and satisfies the strongest principle of sufficient reason.26 The cluster of worlds could not be any different from the way it in fact is - there are no alternative clusters. But it is true in each world w in the cluster of worlds that events in w could have been different from the way they are - there are alternative worlds for each world.
noneThe Paradox of Best Worlds
It is a consequence of the classical theist argument that God necessarily actualizes the best possible world. The best possible world w is metaphysically isolated - and not merely causally or spatiotemporally isolated - from every other world in the pluriverse. Since w is metaphysically isolated, there exist no other worlds possible relative to w and so, from the point of view of w, there exist no other possible worlds that are as good as w. The proposition that God necessarily actualizes w entails that w satisfies the principle of the best. It is true in w that it is the best possible world since it is true in w that it is the only possible world.
◻︎(God actualizes w) ⟶ ◻︎∀y(w ≠ y ⟶ w >G y)
But metaphysically isolated worlds also satisfy the principle of plenitude. Since w is the only possible world, there are no possibilia that are not included in world w. So, the variety of possibilia in w is unequalled by any other possible world. And so (3) above - the fact that God necessarily actualizes w - also entails that w satisfies the principle of plenitude.
◻︎(God actualizes w) ⟶ ◻︎∀x(x ∈ S ⟶ Ixw))
And (5) and (6) are exactly what the classical theist was aiming to show. God necessarily actualizes a world w that satisfies both the principle of the best and the principle of plenitude. The classical God does this just if he creates a metaphysically isolated world.
According to classical theism, God necessarily creates a world that satisfies the principle of the best and the principle of plenitude. But we should expect that the classical God also necessarily creates a world that includes significantly free and rational agents among their possibilia. Significantly free and rational agents are the source of most of the moral value in a world.
… [A]s theodicists have argued since the time of Augustine, freedom of the will, if not itself a great intrinsic good, appears to be indispensable for some of the very important goods we know of - freely given love, freely sacrificing for the well-being of others, freely chosen acts of charity, etc. Indeed, from the point of view of the creator it might well be uninteresting to create beings who are programmed from the start to worship God, to honor him, to do good to others. From the perspective of the creator it may well be better to have beings who can freely choose to love and worship or not to love and worship, for love and worship that is freely given is of much greater value than love and worship that is compelled. (Rowe, 2004, pp. 77-78)
So, we expect that the best possible world includes at least some moral agents in some universes that are significantly free. Indeed, we should expect that the best possible world includes at least some universes that are morally perfect. Morally perfect universes include significantly free moral agents who always freely go morally right. Moral agents that freely go right with respect to morally significant actions produce moral good or moral value. And moral agents that freely go wrong with respect to morally significant action produce moral evil or moral disvalue.
Since w is the best possible world, it is true in at least some universes in w that moral agents always freely go right with respect to morally significant actions. Moral agents in some universes in w observe duties of justice, for instance, by always freely refraining from harming others. And moral agents in some universes observe duties of beneficence by always freely benefitting others.
According to the argument from classical theism, God necessarily actualizes w, since w is the best possible world. But God necessarily actualizes w only if w is a metaphysically isolated world. But metaphysically isolated worlds - whether or not they are multiverses - include no significantly free moral agents at all. The actions of all moral agents in metaphysically isolated worlds are metaphysically necessitated. So moral agents in metaphysically isolated worlds are neither libertarian free nor compatibilist free. 27 No moral agent in any metaphysically isolated world does anything freely.
Since w is the best possible world we know that at least some universes in w include some moral agents who always freely go right with respect to morally significant actions. Classical theists insist that God necessarily actualizes the best world w. But God necessarily actualizes w only if the resulting world w’ includes no significantly free moral agents at all. So, the necessitated world w’ is exactly like the best world w except that moral agents in w are significantly free and moral agents in w’ are not significantly free. The fact is the best possible world w loses a significant amount of value when God necessitates w. The necessitation of w costs w all of the value arising from the actions of significantly free moral agents.
Since the necessitated world w’ is exactly like w except that w’ excludes all significantly free moral agents, the world w’ is worse than the world w. The paradox of best worlds is that God necessarily actualizes the best world w only if the resulting world w’ is worse than w despite the fact that (i) w’ satisfies the principle of the best and (ii) w’ satisfies the principle of plenitude. That is, it is true in w’ that w’ is the best possible world and that w’ satisfies the principle of plenitude, nevertheless w is overall better than w’. So, It is better overall if God does not necessarily actualize the best possible world..
Concluding Remarks
We found that the result of God necessarily actualizing w is a possible world w’ that satisfies both the principle of the best and the principle of plenitude. Nevertheless, the world contingently actualizing world w is better than necessarily .since w an w. The contingently actualized w includes significantly free moral agents and the necessarily actualized w includes no significantly free moral agents.
The paradox of the best states that the result of God necessarily actualizing the best possible world w results in the actualization of a world w’ that is worse than w. So, it is better if God contingently actualizes w rather than necessarily actualizing w.
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I do not dispute the classical theist’s view that divine creation must satisfy some version of the principle of plenitude and some version of the principle of the best. The main aim in this paper is to investigate the consequences of necessary creation or necessary actualization.
This view is also notably advanced in (Forrest, 1981, pp. 49-54), (Forrest, 1996, chp. 8), (Hudson, 2006), (O’Connor, 2008), (Turner, 2003), and (Draper, 2004) all of whom take seriously the idea that classical theism requires the multiverse. Compare Johnson, D. K. (2014). For additional defense of the many universe hypothesis, see (McHarry, 1978; Coughlan, 1987; Turner, 2014; Kraay, 2014). The multiverse hypothesis has been in the literature for some time and I do not contest the hypothesis here.
The world w0 is a metaphysically isolated world, iff (i) w0 sees itself, (ii) w0 sees no other worlds and (iii) no other worlds see w0. But and in, for instance, w1 ⟵ w2 are not metaphysically isolated.
Cf. (Lewis, 1986. pp. 75-77.). For reasons of demarcation, Lewis reluctantly rejects the thesis that multiverses are possible worlds. But the argument the classical theist’s advance is valid even under the assumption that there are no multiverses.
The logic of counterpart theory plus the thesis of world-bound individuals also licenses quantification over all possible worlds for genuine modal realists. All possible worlds are compossible. See (Lewis, 1968). These assumptions would also allow him to quantify over all universes in a multiverse, if Lewisian metaphysics permitted multiverses. But compare (McDaniel, 2004, p. 144)). McDaniel argues that we should take the parthood relation for material objects to be indexed to universes and times.
Accordingly, if the advocate of modal realism with overlap must believe in compositional pluralism, then she is in good company. There is still a difference between taking the parthood relation defined on material objects to be indexed to a time and taking it to be indexed to a spacetime region, as the advocate of MRO should. However, I believe that there is a powerful reason for the three dimensionalist to take the fundamental parthood relation defined on material objects to be spatiotemporally indexed as well. That is, instead of taking the fundamental parthood relation defined on material objects to be x is a part of y at t, the three dimensionalist should take it to be x is a part of y at R, where R is a region of spacetime.
For arguments against modal realism with overlap see (Lewis, 1986, pp. 198-209) and (Teller, 2001, pp. 105-21). Our worlds and universes are concrete objects that permit individuals to exist in more than one world or universe. Quantification over all universes and all possible worlds is licensed, though may be restricted. Indexing the copula ensures the compossibility of worlds and universes. The fact of Jones’ being tall, for instance, is regimented as the fact of Jones’ exemplifying-at-u the property of being tall and that is compossible with Jones’ exemplifying-at-u’ the property of being short. Since we can avoid postulating counterparts simpliciter, we have the advantage of not postulating counterparts of God. It is an additional advantage that we can avoid postulating that God exists independently of all possible worlds. See (Ross, 2015)
For more on indexing and endurantism, see (Johnston, 1987; Johnston, 1987b; Haslanger, 1989; Lewis, 2002). For criticism of this view see (Garcia, 2024).
Lewis resists the use of ‘actual’ as a blanket term for just everything there is. I allow both the indexical use of ‘actual’ in some contexts and the blanket use in others. Compare (Lewis, 1986, pp. 97–99)
Lewis provides translation rules according to which formulas of quantified modal logic are true relative to a world and an assignment function. Quantifiers are given a standard (actualist) interpretation, ranging over just the individuals in the relevant world. The interpretation of the modal operators (taking □ as primitive) is as follows: N. □B is true relative to a world w and assignment g iff B is true relative to every world w′ accessible from w and every assignment g′ such that g′(x) is a counterpart of g(x) for each variable x that is free in B. Since we reject counterpart theory, the assignment in g’(x) is irrelevant. Our worlds are concrete objects and our truth-conditions are standard.
N. □B is true relative to a world w and assignment g iff B is true relative to every world w′ accessible from w. See (Hall et al., 2024) and (Lewis, 1968; 1986)
The argument of classical theism entails that there are metaphysically isolated worlds. What is possible from the point of view of metaphysically isolated worlds is different from what is possible from the point of view of other worlds.
Compare Alvin Plantinga (1974). For Plantinga, creation is just the instantiation of individual essences and their properties. The creation of Jones running in the park, for instance, requires the instantiation of Jones’ essence and the instantiation of the predicate ‘running in the park’.
On this account, God creates w if and only if God actualizes w. Actualization just is creation. God and abstract objects exist in possible worlds as well, but they are necessarily existing, uncreated objects.
We make the assumption that there is a best possible world for the sake of the forthcoming argument. The issue concerns the consequences of necessarily actualizing the best possible world, granting that there is one. Compare (Climenhaga, N. (2018)).
The most inclusive compossible set of universes might be a single universe. In metaphysically isolated regions of the pluriverse, for instance, there might be a single world with a single universe.
We are focused on issues arising from the necessary creation of a possible world. So, for the sake of discussion, we grant classical theism its basic position that there is a best possible world. It is observed below that the paradox of best worlds can be generated without this concession. A strict ordering >G on worlds is irreflexive, asymmetric, and transitive. We assume the ordering is total, so for any worlds w, w’, w >G w’ or w’ >G w or w = w’. There is a similar argument for the paradox on the assumption of a partial ordering of worlds. The assumption of a unique ordering of worlds >G holding in all worlds is not critical to the argument. It is more complicated, but we might have assumed that there are several orderings, >G0, >G1, >G2, >Gn based on various possible sets of values. If there is no privileged ordering, we can arrive at the conclusion that God necessarily actualizes every world w that is best according to some ordering of worlds. There would then be many metaphysically isolated worlds. But the main conclusion in the paradox of best worlds would remain unchanged.
If the rankings varied from world to world, and w0 was best according to >G0 and w1 was best according to >G1 and so on, then we would have a series of premises in the argument, for instance, ◻︎∀y(w0 ≠ y) ⟶ (w0 >G0 y) and ◻︎∀y(w1 ≠ y) ⟶ (w1 >G1 y) and so on. And a series of conclusions ◻︎(God actualizes w0) and ◻︎(God actualizes w1) and so on. On these assumptions, it might happen that the entire pluriverse is composed of metaphysically isolated worlds.
The small model provides the semantic picture of the argument from (i) God necessarily actualizes w0 to (ii) w0 is metaphysically isolated.
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We assume S5 and let w0 be the best possible world. We assume that P is the complete description of the non-modal facts in w0 and finally assume that necessarily P is true in w0 or that God necessarily actualizes w0. Since ◻︎P ⟶ ◻︎◻︎P and ◻︎P are true in w0, ◻︎P is true in every world. And since ◊P ⟶ ◻︎◊P and ◊P are true in w0, ◊P is true in every world. So, the worlds do not differ in modal facts. The worlds also do not differ with respect to any non-modal facts - that is, all of the propositions in P are true in every world. Since each of these worlds includes numerically identical universes, objects, events, and states of affairs, each of the worlds is the uniquely best world and w0 = w1 = w2. That is the conclusion the classical theist is after. It is true in w0 that there exists exactly one world, since no other world is relatively possible. But that is consistent with the absolute possibility of many other worlds. A world is absolutely possible if it exists somewhere in metaphysical space, whether or not it is accessible to other worlds or itself. So, the argument does not rule out the existence of other worlds that are absolutely possible, though relatively impossible. But compare the forthcoming argument that this inference fails without S5.
It should also be noted that the argument does not depend on the existence of multiverses or the assumption of non-world-bound individuals. Let w be the best possible world ranked according to >G. Assume there are no multiverses and no individuals that are not world-bound (universe-bound). If God necessarily actualizes w, then there are no possible worlds w’ such that w ≠ w’. This is because it is true in w that ◻︎P, where P is the conjunction of non-modal propositions in w. That is, it is true in w that God necessarily actualizes w. But ◻︎P is true in w only if, in every possible world w’, it is true that P and ◻︎P. But then every possible world w’ is identical to w. So, there is just one world and that world is w. It does not follow from this argument that there are no absolutely possible worlds diverse from w existing somewhere in the pluriverse and inaccessible to w. So, the most we can conclude is that w is a metaphysically isolated world.
To illustrate, the world w0 is metaphysically isolated, but world w0 is not metaphysically isolated. W1 sees only itself, but w2 also sees w1. w0 sees only itself and no other worlds sees w0.
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I do not discuss the possibility here, but we might want to expand the notion of metaphysical isolation so that at least some ‘dead end’ worlds count as metaphysically isolated as well. A dead-end world sees no world, not even itself. It is reasonable to suggest that dead end worlds that are not seen by any other world are also metaphysically isolated. The name and notion of dead-end worlds is due to (Segerberg, 1971).
In non-normal logics, there are non-normal worlds in which everything is possible - including contradictions - and nothing is necessary. Relatively impossible worlds are not impossible in the sense of being non-normal.
Premise (2) rules out structures such as w0 ⟵ w1. Contrary to the structure, it is impossible that God necessarily actualizes w1, since w1 is not isolated.
Clusters of worlds are metaphysical regions in a broader logical space. In logical space there are many isolated metaphysical regions in which every logically possible metaphysical truth obtains. For instance, in some regions water is not H2O and in other regions the necessity of origins is false and in still others Aristotle is mistaken, we are not rational animals. All of these metaphysical views are logically possible.
Saul Kripke offers a proof in footnote 56, Naming and Necessity, that nothing originally composed from one hunk of matter could have been originally composed of another hunk of matter. For the sake of this particular proof, Kripke assumes hunks of matter that are non-overlapping. The principle states the following:
◻︎∀x∀y((◊MCx & ◊MC’y) ⟶ x ≠ y)
Necessarily, for all x and y, if there is some world in which x is originally composed of C and some world in which y is originally composed of C’, then x is diverse from y. See (Kripke, 1972, pp. 114-117.)
Of course, the classical theist might want to modify premise (2) to require that God necessarily actualizes a world that is best according to all possible orderings or according to most orderings and so on.
Let P be the conjunction of non-modal propositions fully describing the world w0. Suppose God necessarily actualizes w0 or, equivalently, that God necessitates P. If our logic is no stronger than Kρσ, then possible worlds that verify P might have diverse modal profiles. Kρσ is equivalent to Brouwer system B that is validated by all reflexive and symmetric frames. Compare w0 and w1 where P is the conjunction of every non-modal proposition describing w0.
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God necessarily actualizes w0- that is, ◻︎P is true in w0 - so the proposition P fully describing w0 is true in every world accessible to w0. The universes, objects, events, and state of affairs in w1 are numerically identical to the universes, objects, events, and state of affairs in w0. But since it is not a theorem in Kρσ that ◻︎P ⟶ ◻︎◻︎P, it is possible that God necessitates P in w0 and God does not necessitate P in w1. And since w0 >G w1 - that is, since w0 is the best possible world - the fact that the classical God necessarily actualizes the best possible world w0 is consistent with the fact that God might have actualized the comparatively worse world w1, instead. The argument that the classical God actualizes only the best possible world is unsound in logics weaker than S5.
Compare (Strickland, 2005). Strickland argues for the thesis that God necessarily actualizes the best possible world only if there exists exactly one world. That thesis requires a logic as strong as S5 and even then it is not quite right. There may be other absolutely possible worlds. We can arrive at Strickland’s conclusion if we assume in addition to S5 that there are no other absolutely possible worlds. Here’s an example. If God necessarily creates w1 and P is the full, non-modal description of w1, then P & ◻︎P is true in every world w1 – w3. The worlds include numerically the same objects, events, and states of affairs. And the worlds do not differ modally. So, w1 = w2 = w3, just as Strickland claims. If the classical theist’s argument is sound, and there is a best possible world, then there is a unique, best possible world, w1 that is the only absolutely possible world.
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As we found above, the same composite object x might differ in original composition - and so differ in essential properties - in different, metaphysically isolated worlds w0, w1, and w2.
The argument from classical theism does not consider the possibility that God necessarily creates the best cluster of worlds. If each world w in the cluster of worlds S is spatiotemporally isolated world, then it is possible that the classical God necessarily creates the best cluster of worlds. I consider this possibility briefly below.
See (Almeida, 2018, pp. 75-79) for further discussion of this proposal.
Compatibilists maintain that there are free actions A that are necessitated by the laws of nature L and historical facts H. So, A might be free despite the fact that H & L and ◻︎ ((H & L) ⟶ A). The paradox of best worlds does not entail that compatibilism is false. The paradox of best worlds maintains that every action A - where ‘A’ is some proposition describing the action - in a metaphysically isolated world is such that ◻︎A where ‘◻︎’ is a metaphysical necessity operator. And if it is true that ◻︎A, then A is not free.