Rethinking Perfection: Crusius’ Critique of the Idea of the Best of All Possible Worlds

2.1 Special Features of Leibniz’ World-Concept

As is clear from the above definition and in contrast with most modern treatments, Leibniz thinks of worlds objectually rather than propositionally: they are maximal and highly integrated groups of possible or actual entities. The integration is provided by a twofold nexus: first, the totality of any given world is informationally packed into every entity in that world by monadic mirroring; second, every substance is (albeit indirectly, through corporeal entities) causally connected with every other substance in that world.^[15] In such a model, there can be no such thing as merely local change and no merely accidental difference. If anything in such a world (possible or actual) were changed, ever so slightly, the change would instantly propagate outwards “to any arbitrary distance” though its effects would diminish with distance^[16]; if anything were imagined as different, that difference would be reflected throughout the whole world, though with greater or lesser clarity depending on the degree of the monad doing the reflecting. Thus any change, and any difference, would result in the world in question no longer being that world, but another one.^[17]

Another feature of Leibnizian worlds that is important for our purposes is what we would now call the cardinality of the set of entities within them.^[18] For at least some possible worlds, including our own, this is infinite. As Filippo Costantini has recently shown, the infinity of the world must be construed in a twofold sense:^[19]

(1) The first sense is given by the infinite divisibility of world-internal objects. Objects in our world are not only infinitely divisible but in a sense actually infinitely divided: each object is composed of proper parts, which are in turn composed of proper parts, ad infinitum.^[20] We cannot, of course, traverse this infinite process of division; nevertheless it has already taken place and can be referred to indirectly. In the Preliminary Dissertation to the Theodicy, Leibniz has this to say about the nature of the infinite. It is not a discrete quantity; rather,

the infinite or infinitely small signify only magnitudes that one may take as great or as small as one wishes, to show that an error is smaller than that which has been specified, that is to say, that there is no error; or else by the infinitely small is meant the state of a magnitude at its vanishing point or its beginning, conceived after the pattern of magnitudes already actualized. (Theodicy, Preliminary Dissertation § 70; trans. Huggard in Leibniz 1978, VI:90).

A simple way of thinking about Leibniz’s infinitely dense universe is that it consists of entities that can be analyzed or measured as far down as one likes, in a cognitive or mathematical process resembling an asymptotic approach toward a limit. The dimensions of a finitely large object as measured by some other, smaller object may well be expressible only by an irrational number.^[21] In such a case, the limit is of course finite; the infinitely large value is provided by the degree of accuracy required to ‘reach’ that strictly unreachable limit. Leibniz’ strictures against treating the infinitely large or small as an accomplished process make him sound as though he were invoking the Aristotelian ‘potential’ infinite, but Leibniz is indeed an actualist about the infinite: we should take him seriously when he talks about a state of a magnitude at its vanishing point or its beginning, conceived after the pattern of the magnitudes already actualized.^[22] We can grasp, refer to, and believe in the reality of the infinite without making the mistake of really treating it as a quantity (as the unnamed ‘friend’ in Preliminary Dissertation § 70 has done); it is something real in the world, but it is not a number, since all numbers are finite.

(2) The second sense in which the world is infinite has to do with its magnitude. Unlike world-internal objects, which due to their finite magnitude can be treated as, and indeed are, wholes despite their infinite divisibility, the world is a whole merely by grammatical courtesy. The concept of whole presupposes a finite terminus or limit, corresponding to the magnitude of the object in question, which can be expressed through a number. It follows that nothing with infinite magnitude can be a whole, since in such a case there is no such finite terminus or limit. The magnitude of any given whole is expressible as a number only by an iterative measuring process that either comes to an end at some point or continues recursively while cutting the pie into ever finer slices. A world, as it contains infinitely many disjoint entities, cannot be such a pie; hence it is strictly speaking not a whole, although it may be useful in many contexts to treat it as such.^[23] Although worlds are of course real in some sense, they are, also in some sense, degenerate objects, somewhat akin to Carnap’s quasi-objects or Russell’s conception of certain classes as “fiction[s]” or “false totalit[ies]” (Carnap 1967, 48–50; Russell 1908, 261). This is what Thomas Feeney has called Leibniz’s “tendency toward acosmism” (Feeney 2016, 145): worlds (on Feeney’s reading, the actual world, but I would argue most possible worlds) fall into the category of “real phenomena,” to be compared with bodies, rainbows, and piles of wood: mere aggregates.^[24] Indeed, unlike world-internal aggregates, which can be considered as wholes by measurement in accordance with the iterative process mentioned above, the universe is infinite not merely by division but by magnitude; it cannot be measured, and hence cannot be associated with a finite quantity as can such everyday aggregates as bodies, piles of wood, and so on.^[25]

2.2 Special Features of Wolff’s World-Concept

Wolff takes over from Leibniz both the idea of possible worlds as giving us an adequate idea of possibility in general and the idea that God selects the best one in accordance with the PSR. His definition of a world has at least one important feature that distinguishes it from that of Leibniz: For Wolff, the world is not actually infinitely divided, or indeed even infinitely divisible. There are, for Wolff, no actual infinities outside of God; hence the world, like everything in it, is composed of a finite number of elements. The apparent continuum breaks down at a certain point; one reaches a stage, in mentally dividing such an apparent continuum, at which a new element cannot be inserted (a new division cannot be made) between two others.^[26] More generally, the world is, in many respects, simply another object, albeit one with certain special properties. Wolff defines the concept ‘world’ at least three times in his works. Here is the last of these three definitions:

The series of finite beings, whether simultaneous or successive, interconnected with one another, is called the World, or also the Universe.^[27] (Cosmologia § 48)

The world, then, is a collection of entities of a broadly contingent character (whether that contingency is cashed out in terms of finitude, possibility, or transitoriness) which is bound together spatially and temporally. The further special features of this world are best illustrated by reference to the Deutsche Metaphysik (they are not materially changed in the Cosmologia). Apart from being all-encompassing (DM § 543), the world is connected both spatially and temporally according to the PSR, with each element determined by some other element (DM §§ 546–547); it is thus unitary, a single object (DM §§ 548–549); the world is a whole, which therefore consists of parts (DM § 550); it is therefore a composite thing (DM § 551); and its essence (taking essence in a special Wolffian sense, which amounts to the set of its internal predicates) is thus determined by its composition, which means that worlds are distinguished from each other solely by their composition, that is, structurally (DM § 552). As in Leibniz, the identity of a world is maximally sensitive to the slightest alteration; since such an alteration would interrupt the pattern established by the PSR, thus establishing a new principle of composition for that world, the alteration would make the world into a different one (DM § 553). Furthermore, since it conforms to the definition of ‘machine’ — an interconnected system whose movements are grounded in its composition — the world is a machine (DM § 557).^[28] As a machine, it is comparable to a Euclidean proof, and like a proof, it produces truth rather as a proof yields a conclusion (DM § 558).^[29] Moreover, and crucially, the world is a contingent thing (ein zufälliges Ding) since it could have been other than it is (DM § 576). Here Wolff makes an important distinction. There are two senses in which the world can be called zufällig: (1) with respect to its actuality; in this sense, it is indeed zufällig, since some other world could have been promoted by God to actuality; (2) with respect to its essence; in this sense, strictly speaking, the world is not zufällig but necessary, since essences have an unchangeable position in the array of possibilities available to God for actualization.

To sum up: the world, ultimately, is a complex object not ontologically different from the objects that make it up. It is a systematic whole, like a clockwork (DM § 557). The cardinality of objects within it, as noted above, is finite, like that of all its proper parts. It could have been otherwise in the modest sense that worlds differing from it in this or that aspect (or in many aspects) could have been actualized in preference to it; but any change to it would render it a different world altogether.

2.3 Special Features of Crusius’ World-Concept

Here is Crusius’ definition of a world:

The concept of a world in general must, therefore, be as follows: a world is a real connection of finite things which itself is not, in turn, a part of another to which it would belong through a real connection. Or: a world is a system of finite and really connected things that is not itself contained as a part within another system. The concept must be understood in a reduplicative manner:^[30] Insofar as and as long as a system of creatures is not connected as a part to another [system], it constitutes a distinct world.^[31] (Entwurf § 350)

The essential properties in this definition are apparently two: (1) a really interconnected set of entities; (2) a maximally interconnected set (hence not a proper part of a larger interconnected set).^[32] Criterion (1) rules out constituting a world by simple mereological sum; there must be real, extramental connections between all elements in any given world. Criterion (2) is introduced as a response to Joachim Lange’s objection that Wolff’s world-definition, since it lacks this codicil, makes any interconnected complex object (e. g., a beehive) into a world.^[33] However, there is much more to say about Crusian worlds.

To start with, the world cannot be constituted as a partition into isolated and fully connected subsets or isolated clusters of substances: a complete interconnection is part of the definition of a single world. However, in striking contrast to the world-concepts of Leibniz and Wolff (and, as far as I can tell, those of everyone else), there is a strong tendency towards a kind of modal pluralism in Crusius’ writings on the subjects of possible worlds. Although he never claims to be able to prove that other possible worlds exist, he repeatedly stresses that we cannot rule this out (Entwurf § 349, § 373). It might be that two or more such isolated clusters, constituting independent really existing worlds, can remain separate; Crusius declares himself agnostic on the question of whether God, on supposed grounds of the greater perfection of unity, would find it morally necessary to join such worlds together, and even moots the possibility of a single entity moving from one really existing world to another (Entwurf §§ 349, 356). Indeed, for Crusius, the concept ‘possible world’ seems to contain a sort of default assumption of existence; unlike Leibniz and Wolff, he has no strong conception of a nonexistent, merely possible entity that would count as a real world if God were to grant it reality. This, at any rate, is what I gather from his insistence that “things belong to a world […] insofar as they were previously in a real connection with it.”^[34] Note that the stress is on real connection; the idea of a merely ideal connection, or a connection to a nonexistent possible world (as in the modern idea of transworld identity), seems alien to Crusius. Further on, Crusius writes that “every world [n.b. not every really existing world, just every world] has been created by God and once did not exist”^[35]; once again, modal pluralism seems to be his default assumption. This makes sense if we assume that Crusius is responding here to two pressures: (1) the pressure to downplay the reality of merely possible entities; for him, the possible is subsequent to, and in some sense parasitical upon, the actual, and this is true “both naturally and in terms of our cognition” (Entwurf § 57)^[36]; (2) the pressure to engage in possible-world talk nonetheless, on the grounds that it is useful for cashing out modal claims. The idea, in any case, is that for him to use possible-world talk at all, he finds it intuitive (though not obligatory, and in fact unprovable) to talk about entities — worlds — that really exist. In any case, he likes the idea; and this preferred feature of his model stands in stark contrast with the entire tradition stemming from Leibniz and Wolff, in which the PSR guarantees a uniquely best world — the only world worth actualizing — chosen from an infinite array of merely possible worlds.^[37]

Crusius’ world-conception is teleological: worlds have a purpose, namely the creation of rational and free creatures. Every other goal in creation in any given world must be subordinate to that main goal (Entwurf § 354). This purposive character of Crusian worlds is tied to another quite fundamental difference between the respective world-conceptions of Leibniz and Wolff and that of Crusius: the ontological flexibility of the Crusian world. While the fundamental purpose of a world cannot change without the world becoming a different one, much else can change: there is a rich array of merely contingent features in any given world, and these features can be replaced with others while leaving the identity of that world intact. Crucially, among these features are the free actions of created beings. Let us turn to Crusius’ own words in Entwurf § 358:

[I]t is clear that actions and changeable states, insofar as they depend directly or indirectly on free acts, do not contribute to altering the essence and thus the identity of the world. For it is precisely for this reason that a world is created, so that free acts and the changes dependent on them can occur within it. (Entwurf § 358, p. 692)

A world remains the same, and does not become another [world], so long as its main purposes persist and no change occurs in the kinds of things, the laws of their connection, the individuals, and essential actions within it, which would alter the established main purposes of the world and the nature of the means that are necessarily linked to them. (Entwurf § 358, p. 693)

[T]he state of the world can be altered through the free actions of creatures in such a way that it could be different without the world thereby having to be another. For the fundamental nature of spirits and the physical connection of things are not altered by the free actions having this or that nature, since it is not the actuality and direction but only the possibility of free actions which belongs to their fundamental nature. (Entwurf § 358, p. 694)

Two further points are worth stressing. First, as in Wolff’s approach, the world and its components are finite (a word that appears in both disjuncts of Crusius’ world-definition).^[38] Second, Crusius strongly challenges Wolff’s idea that the world is, in its entirety, a machine. A machine is a “body composed of material parts intentionally shaped so that, through the figure and position of its parts, determined movements can be facilitated when a driving force is applied” (§ 382).^[39] The mere fact that minds are entities within the world, and are thus part of it, proves that the world cannot be a machine. Rather, it is “something incomparably nobler and better […] an extensive kingdom of God, equipped with laws, filled with diverse goods for its subjects, and governed by the rules of holiness and justice” (§ 382).

3.1 C1: Crusius’ First Critique of BPW

Within his own system, Crusius defines ‘perfect’ in terms of specific purposes and functions^[42]; nevertheless, for the sake of the argument, the first interpretation of BPW is one that takes an entirely general, not to say generic, notion of ‘perfect’ by abstracting from any specific purpose. The result of this operation is a derivative but nevertheless robust concept: It includes “all possible final purposes and all possible means, which do not conflict with the concept of perfection in the abstract […] or with the divine attributes” (Entwurf § 385). Given this general concept, the idea of a best possible world falls prey to a simple objection:

First, I claim that such a best world, in which all possible perfections would exist, is impossible. For every world is necessarily finite (§ 353); therefore, its perfection is also finite, and God can continually add more through a progressively infinite process (Infinitatem progressivam) (§ 135). Thus, he must arbitrarily set the limits of its perfection somewhere (§ 291). The number of creatures that divine omnipotence can create is infinite. The number of purposes he can set for himself is infinite. The number of degrees in which he can will the attainment of his purposes, as well as the number of degrees of finite perfection he can bestow upon a metaphysical subject, are infinite. Nevertheless, what is actually created is always, necessarily, finite (§§ 138, 148, 149). Thus we are driven to the conclusion that God must arbitrarily determine the number of purposes, creatures, and degrees of perfection, both of individual creatures and of the world as a whole. This, however, implies that he could always have added more, and therefore no world is possible that is absolutely the best. (Entwurf § 386)

The idea is straightforward: if we take perfection as an attribute that comes in countable degrees, like the set of natural numbers, there is simply no limit to the perfection that can characterize any creature or entity within any world. Furthermore, if the various perfections of the entities, and types of entity, can be simply summed together, and if that sum is equivalent to the perfection of the world in question, then the same objection pertains to that world as a whole. Hence, for any world you like, a better one is imaginable. The notion of a ‘best of all possible worlds,’ on the abstract interpretation of ‘perfection,’ is chimerical. This state of affairs — the existence of an endless hierarchy of perfection, with no summit available to fix God’s choice of which world to create — would constitute a refutation by example of the PSR: given a world with finite cardinality — which, as we have seen, Crusius affirms — then at some point, God must make a decision, and that decision must be, in a sense, arbitrary.^[43]

The appeal to endless improvability is an old objection; as Scribano (2003) has shown, it dates back at least to Thomas Aquinas, and was picked up later by Francisco Suárez, followed by Leibniz himself.^[44] Leibniz’ discussion occurs in Theodicy § 195 (briefly referred to in 2.1 above) and will be discussed in the next section.

I now turn to the evaluation of C1’s force against the world-pictures that one might consider its targets, namely those of Leibniz, Wolff, and Crusius himself. The results differ. Leibniz manages to escape the force of the argument, but Crusius manages to throw some doubt on Leibniz’ appeal to infinity cardinality. Wolff, however, is a fit target for C1; and since Crusius takes over crucial portions of Wolff’s world-picture, the argument is effective within his system as well. The details are reviewed in 3.1.1 and 3.1.2. below.

3.2 C2: Crusius’ Second critique of BPW

I now turn to Crusius’ second interpretation of BPW, which he lays out in § 387 and the sections following. According to C2, the existence of a best world cannot quite be ruled out, but nor can it be proven. Crusius explains himself as follows:

[T]he opinion that the world which God created is the best — at least in the sense that one assumes certain main purposes of it in advance and merely supposes that God has arranged the world in such a way that, according to the prescription of these purposes, it is the best among all possible ones — is, at the very least, indemonstrable. For it cannot be refuted that many means to certain ultimate purposes of God may be, in themselves, indifferent or may be rendered indifferent through the interconnection of things, as we have already previously noted. God can create countless similar creatures of any kind (§ 383). Therefore, it will be indifferent to his purpose which among so many possible creatures he brings into existence for the promotion of that purpose. Moreover, even if two things are not entirely similar in themselves, they may still be indifferent with respect to the established purposes, so their remaining dissimilarity^[52] need not be considered, as it does not concern the intended purposes. Indeed, even if the relationship between two means to a purpose is entirely dissimilar when considered individually, that dissimilarity can be neutralized by the combination of many things with each other. And many of these combinations through which [this dissimilarity] is neutralized may be indifferent with respect to the purpose. Furthermore, God can associate various incidental purposes with his main purposes for a world. And the number of such purposes is infinite. So how can one then say that one of them is the best for the already established purposes? Therefore, it cannot be disproven that, with respect to already established purposes for a world, the divine mind could recognize several worlds as equally good, and furthermore, that it is possible that the difference in goodness between some other worlds might not have a necessary influence on the established purposes, and thus God is not compelled to prefer one over the other. From the first point, we see that a best world is unprovable; from the second, it becomes clear that God is not obliged, at creation, to prefer one world over others simply because some incidental perfections (§§ 181, 182) might make it seem better than another. (Entwurf § 387)

This argument seems new with Crusius; at any rate, aside from some very brief remarks by Adolph Friedrich Hoffmann, I am not aware of any obvious antecedents.^[53] And indeed, of the two aspects under which Crusius is prepared to consider BPW, this second interpretation seems the more Crusian. While C1 is essentially an ad hominem argument directed at those who think that it is possible to prescind from any given specific purpose, C2 starts out from the assumption that God has made up his mind and selected a main purpose of the world. In the argument, the specific purpose is of course selected arbitrarily; the point is that only one such is assumed. Recall that Crusius in fact insists on a single main purpose of the world in § 354 (see 2.3 above).

Despite this tight focus on a single world-purpose, the leitmotif of C2 and the sections following it is the looseness of Crusius’ world-concept. As is clear from the passage, Crusius insists that there might well be a plurality of equally good possible worlds, among which God’s choice to actualize the world is, in a sense, arbitrary. Not all, but many roads lead to Rome; many arrangements of means can lead equally well to one and the same end. Indeed, some of the ‘means’ involved are themselves incidental ends, and it is precisely their infinite cardinality that prevents even God from selecting a single best subordinate end out of the set of such ends. According to the terms of the thought experiment, each such arrangement constitutes a distinct but equally good world; those alternative worlds could just as easily have been selected by God for actualization.^[54] The PSR cannot decide among these equally good claimants to reality, because, for Crusius, there is no PSR in the unrestricted sense of Leibniz and Wolff.

This is, in fact, the crucial point. The cardinality of entities within individual worlds plays no role in C2; thus, in contrast with C1, the differences between the Leibnizian and the Wolffian world-conceptions also play no role here. Everything depends on the cogency of the PSR.^[55] If the PSR (as Leibniz and Wolff conceive of it) does not hold, the possibility of a plurality of equally good worlds is no longer ruled out; indeed, the plurality of equally good worlds would simply be a special case of the failure of the PSR in general. If, on the other hand, Leibniz and Wolff are right about the PSR, then there must be a best world. On the assumption that two or more worlds are of equal value, then God has no means of choosing between them. Granting existence to a plurality of worlds would seem to be God’s only way out of the difficulty, but this option is not available to him. This point is not altogether obvious, and is worth a small detour.^[56]

Within Leibniz’ system, let us assume, for reductio, that the goodness of worlds tops out in a plateau rather than at a pinnacle of quality: there are many optimally good worlds. Thus they must be qualitatively distinct, on pain of violating the Identity of Indiscernibles. Therefore they form, as a group, a disunified whole. The Leibnizian God has a strong preference for ontological economy: perfection is measured, among other things, by the distance between simplicity of means and complexity of results.^[57] This being so, a ‘plateau’ model of world-goodness would present God with a dilemma: Creating the whole plurality would yield an ontological mess, so that any individual (well-ordered, wholly unified) member of the plurality would trump the whole ensemble in this respect. On the other hand, selecting any individual member of the ensemble for actualization would be arbitrary, thus violating the PSR. Under such circumstances, the Leibnizian God would simply not create at all. Yet we see that there is at least one world; here we are, living in it. Hence, world-goodness is not a plateau but a pinnacle; there is a best world, and it is ours. Wolff, too, embraces both the PSR and the principle of simplicity of means and complexity of results^[58]; therefore his God, too, is caught in this dilemma.

Let us then look at Crusius’ attack on the PSR from the perspective of its immediate relevance to C2. In the context of Crusius’ system, the rejection of the PSR is a consequence of the premium placed on libertarian freedom. His critique comprises a negative and a positive part. The negative part consists of an attack on Wolff’s various attempts to prove the PSR as a metaphysical theorem; although cogent and incisive, this attack is not directly relevant here.^[59] The positive part consists of a reinterpretation of the PSR into two principles with different spheres of application. According to Crusius, the central mistake made by adherents of the PSR is the confusion of the Principle of Sufficient Reason, which indeed obtains quite generally, with the Principle of Determining Reason, which applies to everything except the decisions of a free will.^[60] There must be a reason for absolutely everything, including free decisions; the choice between two different courses of action cannot be, and is not, mere “blind chance” (ein blindes Ungefehr), but neither can it be determined (either morally or causally) in the sense which Leibniz and Wolff seem to endorse. Other options are always on the table. Indeed, if the choices of free agents (including divine agents) were determined in this way, the main end of any given world, namely the presence of creatures with the genuine freedom necessary to act morally, would be thwarted. Free choice may be between better and worse options, but it need not be: it can be between equally good options. Schierbaum 2020 reviews the arguments adduced by Crusius in his 1767 Anweisung against what she terms the ‘Arbitrariness Objection,’ that is, the claim that the kind of freedom Crusius insists on is nothing but an appeal to blind chance. The essential idea is that for any choice to act or not to act, as for any choice to act this way as opposed to that way, there can be a variety of rational grounds that can be adduced by a free agent. The ‘principle of the good,’ rather than the ‘principle of the best,’ is here in effect: given an array of equally good options, we have all the warrant we need for anything in the array. Hence questions of the type “Why this choice rather than that choice?” are, as it were, badly formed; they ask for reasons where none are appropriate.^[61] In the context of C2, this means that God may rationally choose to make an arbitrary choice between equally good possible worlds — after all, all of them get the job done — just as humans may rationally choose this or that equally desirable option. The upshot of all this is that C2 is highly effective against both Leibniz and Wolff, as it rests on a plausible and powerful critique of a strong and dubious metaphysical principle that they share.

Having reviewed, and confirmed, C2’s effectiveness against the Leibnizian and Wolffian world-pictures, what can we say of its effectiveness on the world-picture of Crusius himself? Unsurprisingly, it fits it to a tee. C2 emerges directly from Crusius’ own analysis of worlds, their identity conditions, and their irreducibly teleological character, an analysis that has been painstakingly developed over thirty-eight sections of closely reasoned prose. Essentially, then, it is simply a theorem of Crusius’ system: it consists of drawing a negative conclusion (the non-necessity of a single best possible world) from a feature Crusius himself has specified for worlds, namely the non-obtaining of the PSR in its unrestricted form and the general ontological flexibility which that non-obtaining permits.^[62] In C2, this flexibility manifests itself as a scenario in which there are equally good but distinct ‘best’ worlds; but, as we shall see below, there is another option, drawing on other salient features of Crusius’ world-concept, and in the final sections of Crusius’ discussion of BPW, that option is explored.