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The Best of All Possible Worlds: Modal Metaphysics and Possibilia, by James Shapiro

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A brilliant and highly productive intellectual whose work spanned over many fields—mathematics, geometry, physics, etc., in addition to his philosophical contributions—Gottfried Wilhelm Leibniz remains best known for his rather unique version of “theodicy.” This term refers to an argument defending the benevolence of God and His methods, despite the worldly suffering and injustice that has and always will occur. In fact, while of course not the first to try to tackle the theodicy problem, it was Leibniz himself who originated the word in a 1710 work of the same name. Leibniz’s “Optimism” holds that the world we live in is the “best of all possible worlds.” In this essay I will discuss the principles of Leibniz’s philosophy that form the groundwork upon which this interesting, if controversial thesis is based. Additionally, I will compare this idea to what Descartes and Spinoza have to say about related topics, including necessity and possibilia, notably the fact that Spinoza denied the existence of alternative, “unactualized” possibilities for the way God could have created the world and the things in it.

Ironically (and in a sense, unfairly), the average person is introduced to Leibniz through a vicious mockery of his work. I am referring of course to Voltaire’s 1759 satirical novel Candide, ou l’Optimisme. The title makes it clear that Leibniz was no accidental target. In the first chapter, Dr. Pangloss, the instructor whom the title character studies under and is said to teach “metaphysico-theologo-cosmolonigology,” presents a caricatured form of Leibnizian Optimism:

“It is demonstrable that things cannot be otherwise than as they are; for as all things have been created for some end, they must necessarily be created for the best end. Observe, for instance, the nose is formed for spectacles, therefore we wear spectacles. The legs are visibly designed for stockings, accordingly we wear stockings. Stones were made to be hewn and to construct castles, therefore My Lord has a magnificent castle; for the greatest baron in the province ought to be the best lodged. Swine were intended to be eaten, therefore we eat pork all the year round: and they, who assert that everything is right, do not express themselves correctly; they should say that everything is best.” (Voltaire, Candide, 2).

The novel asks again and again the question of how a supposedly perfectly benevolent God could have brought about a world that contains so much pain, injustice and evil. How can we never question Him even as men are torturing each other and tens of thousands are dying in an earthquake in Lisbon? Though clearly a lampooning of Leibniz, the above passage does hit on some important points of his philosophy. That “all things have been created for some end” is a reference to the ‘Principle of Sufficient Reason,’ which, along with the ‘Principle of Non-Contradiction,’ forms a great part of the basis for Leibniz’s metaphysics. The former principle asserts that for every fact about the universe, and for everything that exists within it, there is a reason and/or explanation for why it is as it is.

The aforementioned ‘Principle of Non-Contradiction’ goes hand-in-hand with the ‘PSR.’ The ‘Principle of Non-Contradiction’ is an ontological notion which states that an object cannot be at once both itself and something which contradicts it, or that a proposition cannot be both true and false at the same time. Facts which embody this principle Leibniz calls “primary truths,” in the essay of the same name (1689).

The primary truths are those which assert the same thing of itself or deny the opposite of its opposite. For example, “A is A,” “A is not not-A,” or “if it is true that A is B, then it is false that A is not B or that A is not-B.” also “every thing is as it is,” “every is similar or equal to itself,” “nothing is greater or less than itself,” and others of this sort. Although they themselves may have their degrees of priority, nonetheless they can all be included under the name ‘identities.’ (“Primary Truths” in Philosophical Essays, 30-1).

Also implied here is the ‘Predicate-in-Notion’ principle, which states that for simple analytic truths, predicates are included in the subject through their definition. Leibniz’s example is the concept of a “part” of a “whole.” It is not necessary to assert that the part is less than the whole, because this fact is deducible merely from the definition of “part” as one of two or more components which, when combined or arranged together, form a “whole.” For Leibniz, this is the foundation that allows us to say that all simple analytic truths are undeniable. And by extension, Leibniz also proclaims that “this is true for every affirmative truth, universal or particular, necessary or contingent and in both an intrinsic and extrinsic denomination” (ibid., 31).

Likely the principle for which Leibniz is most well-known, and certainly the principle upon which the Optimism is most dependent is the ‘Principle of the Best.’ I have related the previous three principles first because this fourth is built upon each of them. Just as Descartes uses the definition of God in order to prove His existence, Leibniz uses it in order to establish the notion that this world is the “best of all possible worlds.” Leibniz begins the Discourse on Metaphysics by saying that “The most widely accepted and meaningful notion we have of God is expressed well enough in these words, that God is an absolutely perfect being; yet the consequences of these words are not sufficiently considered” (Discourse on Metaphysics, I). As Leibniz goes on to say, for both he and Descartes, and as generally accepted at the time, the definition of God is essentially that which is supremely perfect, and embodies the unification of all perfections, and all to the highest degree. “Whence it follows,” says Leibniz, “that God, possessing supreme and infinite wisdom, acts in the most perfect manner, not only metaphysically, but also morally speaking…” (Discourse on Metaphysics, I). In defending this idea throughout the Discourse, Leibniz relies almost exclusively on this definition of God (and on evidence from the “Sacred Sciptures”). Just as I criticized Descartes for assuming that existence is a necessary and essential property of God’s identity, I must also criticize Leibniz for assuming that perfect benevolence holds this same status.

In Meditation IV of Meditations on First Philosophy, Descartes tries his hand at the theodicy problem, and in fact comes up with a conclusion which is very similar to Leibniz’s. “I cannot adduce an argument,” he says, “to prove that God ought to have given me a greater faculty of knowing than he did. No matter how expert a craftsman I understand him to be, still I do not for that reason believe he ought to have bestowed on each one of his works all the perfections that he can put into some.” (Descartes, Med. IV, 42). This point implies a distinction between the perfection of individual things within the world and a holistic sense of the perfection of God’s act of Creation as a whole, in that although Descartes (or of course any individual) could have been made more perfect on an individual level, we cannot say that this would have the world as a whole more perfect. What this idea amounts to is something essentially akin to the old adage that “God works in mysterious ways”—or, as Leibniz says, that there are “the hidden reasons for God’s conduct” (Discourse on Metaphysics, III).

In asserting that this is the “best of all possible worlds,” Leibniz’s Optimism posits that God, through his infinite will, actually chose this world from an infinity of possibilia, and likewise that all creatures and objects that inhabit this world were also chosen from an infinite selection of other versions of themselves, as “best.” In one of Leibniz’s letters to Antoine Arnauld (with whom Descartes was also quite close), he writes that “…we are led to conceive that there is an infinity of possible first men, each connected to a long sequence of persons and events, and that God has chosen from them the one who, together with his sequence, pleased him” (From the letters to Arnauld; Philosophical Essays, 74-5). An interesting consequence of this idea is that the “pure possibles,” i.e. those that God did not choose to actualize, have a unique type of existence in that they have “no other reality… than the reality that they have in the divine understanding…” (ibid, 74-5), thus suggesting that there are an infinite number of worlds, objects and entities which exist in the divine intellect. This idea was also present in Descartes’ Meditations in the discussion of the “representation thesis.” It is built on the distinction between the objective reality of an idea—the being of an idea based on what it represents or stands for—and the formal reality of an idea—the being of an idea in itself, independent of its representative power.

Now indeed it is evident by the light of nature that there must be at least as much [reality] in the efficient and total cause as there is in the effect of that same cause. For whence, I ask could an effect get its reality, if not from its cause? And how could the cause give that reality to the effect, unless it also possessed that reality? Hence it follows that something cannot come into being out of nothing, and also that what is more perfect (that is, what contains in itself more reality) cannot come into being from what is less perfect… it is also true that there can be in me no idea of heat, or of a stone, unless it is placed in me by some cause that has at least as much reality as I conceive to be in the heat or in the stone… that a particular idea contains this as opposed to that objective reality is surely owing to some cause in which there is at least as much formal reality as there is objective reality contained in the idea (Descartes, Med. III, 36).

A common objection to this idea is the fact that we have clear (relatively speaking) ideas of many things which do not necessarily exist, such as unicorns and “chimeras,” of which Descartes likes to speak. Just because these ideas have formal reality does not mean that they have objective reality. Descartes can attempt to get out of this problem by saying that these objects exist in the divine intellect, and also that the “representation thesis” need not apply to them since they are combinations of different ideas which do have formal reality. He includes these amalgamations of different ideas in the category of “invented” ideas, which he distinguishes from the “adventitious” and “innate.”

Among my ideas, some appear to be innate, some to be adventitious, and others to have been invented by me. My understanding of what a thing is, what truth is, and what thought is, seems to derive simply from my own nature. But my hearing a noise, as I do now, or seeing the sun, or feeling the fire, comes from things which are located outside me, or so I have hitherto judged. Lastly, sirens, hippogriffs and the like are my own invention (Descartes, Med. III, 40).

A similar distinction of types of ideas is made by Leibniz when he says, in the same letter to Arnauld, that “even if there were no perfect square in the world, we would still see that it does imply a contradiction” (Letters to Arnauld; in Philosophical Essays, 75). Though the idea of a perfect square may only have reality in a formal capacity, it is no less true or existent (due to the ‘Principle of Non-Contradiction’) than something which possesses objective reality; in fact, in the Cartesian picture, this is in a way a positive thing, since the idea would depend only on existence in the mind, which Descartes argues is the only realm of which we can be certain epistemologically.

Leibniz goes on from there to say that “…if we wished absolutely to reject pure possibles, contingency would be destroyed; for, if nothing were possible except that which God actually created, then what God created would be necessary, in the case he resolved to create anything” (ibid., 75). This is an interesting, and somewhat puzzling, claim. To understand it we must, of course, investigate Leibniz’s definitions of contingency and necessity. Like Descartes and Spinoza, Leibniz held that God and only God exists essentially—that existence is a part of God’s essence (“…it is essential for God to exist. Whence God is a necessary being…” [“On Contingency”; Philosophical Essays, 28];  “For if there is a reality in essences or possibilities, or rather in eternal truths, this reality must needs be founded in something existing and actual, and consequently in the existence of the necessary Being, in whom essence involves existence, or in whom to be possible is to be actual” [Monadology, 44]). Accordingly, every other entity and object, since its existence depends on God or God’s Creation, is contingent. So what Leibniz seems to be saying in that letter to Arnauld is that if we were to deny the existence of “un-actualized” possibilia (or “pure possibles”), we would be making their existence a part of their essence, since every entity in this scenario must have been actualized by God in order for us to be able to conceive of it, since nothing but what had been actually created would exist in this picture. This argument makes sense but seem to hinge on a false dichotomy: Leibniz says we can either think of possiblia as floating in some sort of limbo within the realm of the “divine intellect” or we can imagine that there were never any other possible alternatives for God to choose from in the Creation. But it seems that even if we were to deny the existence of “pure possibles” we could think of entities and objects as contingent in the sense that they would not exist if it were not for God having created them. It seems to me that “pure possibles” don’t have to continue to exist in the divine intellect in order for them to have been a factor. The element of God’s “choice” to create seems to still be present in this picture—if His will is infinite, there is still no limit to what He could have brought into existence at the moment of Creation. Leibniz’s concept of “pure possibles” carries the implication that God sat and created Judas One through Judas Thirty-Six, or an infinite amount of Judases one by one, then sat back and surveyed them all and decided that Judas Twelve was the best, and actualized him.

This way of thinking about God strikes a far too anthropomorphic chord. It seems contradictory to imagine God creating the world step-by-step (although it is, of course, presented this way in the Book of Genesis). In imagining this being which is the unification of all perfections, it seems more right to consider the act of Creation in a way that is along the lines of Leibniz’s own idea of the ‘complete individual concept.’ This is the idea that the identity of any individual substance contains all information on the possibilities of that substance’s past, present and future. Leibniz holds that God can always picture the totality of all outcomes for each object within the world. Accordingly the picture of God creating different possible versions of each and every object before deciding on the best one seems not to make sense, and would violate the “efficiency” criterion for God’s perfect Creation, which I will be discussing shortly. Spinoza argues against the existence of any “pure,” or “unactualized,” possibilia on a similar footing to our present discussion, in I Proposition 33 of the Ethics. Interestingly Spinoza makes the same point that is the underlying premise for Leibniz’s “best of all possible worlds” theory to deny the existence of any possible worlds besides the one in which we find ourselves: “…things have been brought into being by God with supreme perfection, since they have necessarily followed from a most perfect nature” (Spinoza, Ethics, I P33). But Spinoza takes this to have the consequence of eliminating other possibilia, for the most perfect nature of God as infinite substance involves the infinite expression of infinite attributes in infinite ways; thus all things that can be called ‘possible’ exist as modes of the unified substance which is God and nature. Here we see the fundamental difference in the two thinkers’ metaphysics playing an important role in the discussion of possibilia: Spinoza’s theory of one unified substance (which rests on the fact that God is infinite and therefore must be everything) as opposed to Leibniz’s ‘monadism’ (a belief that substance is made up of single units of unextended mental points) Spinoza also points out a loophole in Leibniz’s argument which is, again, connected to the “existence in essence” status of the nature of God:

All things have necessarily followed from the nature of God (Pr. 16) and have been determined to exist and to act in a definite way from the necessity of God’s nature (Pr. 29). Therefore, if things could have been of a different nature or been determined to act in a different way so that the order of nature would have been different, then God’s nature, too, could have been other than it now is, and therefore (Pr. 11) this different nature, too, would have had to exist, and consequently there would have been two or more Gods… therefore things could not have been produced by God in other way than is the case (ibid.).

Finally, there is a third sense in which Spinoza’s anti-“pure possibles” argument can be understood—a sense which invokes the aforementioned ‘Principle of Non-Contradiction.’ Spinoza argues that in any sense in which we imagine “unactualized” possibilia, we have an unclear and incomplete picture of the alternate universe we are discussing. Therefore we do not know if there lies in that universe some contradiction that will make it invalid and impossible.

We have discussed at length Leibniz’s ‘Principle of the Best’—that God, by His nature of being the supreme unification of all perfections, must have created the best of all possible worlds—at length, yet we have not brought up the question of what exactly the criteria is that could make one world, or object, more perfect than another. In a sense this is an irrelevant question for Leibnizian Optimism, because it is an ontological argument—since God is perfect, whatever he created is perfect, and therefore the world he created (this one) is the best possible world. But this is an unflatteringly simplistic version of Leibniz’s argument. In an essay entitled “Perfection and Happiness in the best possible world,” David Blumenfeld states that “…it is important to note that Leibniz thinks these canons [of divine choice] are objective. Issues of good and evil rest on God’s intellect rather than His will, and it is with reference to fixed and eternal standards that God makes his infallible choice of the best possible world.” Blumenfeld defines Leibniz’s measurement of perfection as the “variety/simplicity criterion” (Blumenfeld, in Cambridge Companion to Leibniz, 383). This criterion is rather puzzling. For one, (a) the ideas of variety and simplicity seem to be contradictory, and, (b) the assignment of a desirable value to this criterion demands explanation. Nicholas Rescher explains critique (a) in his work Leibniz’s Metaphyiscs of Nature:

The immediately striking feature of the [variety/simplicity] criterion is that the two factors are opposed to one another and pull in opposite directions. On the one hand, a world whose metal is (say) copper, or whose only form of animal life in the amoeba, will obviously have a simpler structure of laws because of this impoverishment. On the other hand, a world whose laws are more complex than the rules of the astrologers demands a wider variety of occurrences for their exemplification. Clearly, the less variety a world contains—the more monotonous and homogeneous it is—the simpler its laws will be; and the more complex its laws, the greater the variety of its phenomena must be to realize them. Too simple laws produce monotony; too varied phenomena produce chaos. (Rescher, 12)

Blumenfeld suggests that a possible solution to this apparent paradox is to adopt the view that “the actual world has the greatest varierty of phenomena governed by the simplest laws that are compativle with maximum variety. Although more complex laws would accommodate as much diversity, by choosing the simplest ones that do so, God maximizes harmony without trading-off any variety at all” (Blumenfeld, 383).

As for critique (b), Leibniz seems to offer an account of how the greatest variety—seemingly of objects and phenomena—and, the greatest order or “harmony” of these diverse things in the world (as Blumenfeld suggests we should understand “simplicity”), produce a feeling of pleasure in the mind of the perceiver. This pleasure or “delight” seems to be a major justification offered for why the variety/simplicity criterion is a measure of perfection. Leibniz writes that

…the most perfect of all beings, those that occupy the least volume, that is, those that least interfere with one another, are minds, whose perfections consist in their virtues. That is why we mustn’t doubt that the happiness of minds is the principal aim of God and that he puts this into practice to the extent that general harmony permits it. (Discourse on Metaphysics, V)

This is fine as an aesthetic theory, but it is unclear how it could explain the benevolence of God in the face of the presence of so much evil within the world.  Additionally, in a curious move, Leibniz seems to make the efficiency of with which God created the world a major criterion for its goodness.

…one who acts perfectly is similar to an excellent geometer who can find the best constructions for a problem; or to a good architect who makes use of his location and the funds set aside for a building in the most advantageous manner, allowing nothing improper or lacking in the beauty of which it is capable; or to a good householder, who makes use of his holdings in such a way that there remains nothing uncultivated and sterile… (ibid.)

Again, this is an anthropocentric idea that makes little sense when applied to God. Why would God need to worry about the efficiency with which he uses His resources, which, by definition, are infinite? But in any case, it seems that Leibniz offers no criterion for the moral quality of the best world, merely relying on the definition of God’s nature as infinitely benevolent. In the Theodicy, he argues that God permits evil essentially because it brings out “the best” in humanity. This is a reasonable argument when one considers the religious ideals of suffering bringing growth and salvation, and sacrifice for the greater good. Of course, the best example to justify this claim would be that God permitted Judas to betray Jesus because of the great example Jesus’ martyrdom set for mankind. Yet it is still unconvincing that so much suffering and so much sin could be allowed in the “best of all possible worlds.” War, slavery, genocide, disease and natural disaster have forged the landscape of our world through all time, and continue to do so to this day. Can we reconcile a perfectly benevolent God allowing (and in the rationalists’ definition wouldn’t He even be directly causing?) all of this to happen? It is not trivial to note, also, that even the scripture from which Leibniz inherits his concept of God depicts Him as quite malevolent, vengeful and deceptive at various points (i.e. the Book of Job).

I have demonstrated some important similarities and differences between Leibniz, Descartes, and Spinoza on some of the matters involved in Leibniz’s notorious “best of all possible worlds” doctrine. As I mentioned earlier, and as I wrote about previously in dealing with Descartes, the argument boils down to an ontological claim. Just as with Descartes’ argument for the existence of God, Leibniz’s Optimist claim rests on a kind of argumentative trick which involves assuming the definition of God that he has in mind is the correct one, and then arguing from the ontology of that pre-conceived notion. Even granting the rationalists’ definition of God as the unification of all perfections, I am inclined to side with Spinoza’s anti-“pure possibles” argument. The question of the “best possible world” seems to be a moot one. There simply is a world and there seems no reason to imagine that it could have been any different. Furthermore, Leibnizian Optimism seems to have undesirable consequences in practical life, namely encouraging passivity. For, if we believe that “all is for the best in the best of all possible worlds,” why attempt to change anything?



Works Cited:

Ariew, Roger and Watkins, Eric (ed). Readings in Modern Philosophy, Vol Descartes, Spinoza, Leibniz and Associated Texts. Indianapolis: Hackett Publishing, 2000. [Selections from Descartes’ Meditations on First Philosophy and Spinoza’s Ethics quoted from this source]

Jolley, Nicholas (ed.) The Cambridge Companion to Leibniz. Cambridge: Cambridge University Press, 1995.

Leibniz, G.W.; Ariew, Roger and Garber, Daniel (ed.). Philosophical Essays. Indianapolis: Hackett Publishing, 1989

Rescher, Nicholas. Leibniz’s Metaphysics of Nature. New York: Springer Press, 1981.

Comment by Alan N. Shapiro:

I think that this is a great essay by my nephew James Shapiro. He has done a lot of important work, and he is a subtle and very logical thinker. Recently I read the novel Nemesis by Philip Roth, where the main character – surrounded by the horrors of a polio outbreak in Newark, New Jersey during the Second World War – doubts the basic tenets of his Jewish upbringing and doubts the existence of God. How can God exist when there is so much suffering and injustice in the world? Similar to Voltaire’s Candide, and to what Jamie (the long-suffering Mets fan) wrote here, this doubting is really the focal point of Roth’s novel. I thought while reading Nemesis that Philip Roth has made an error. Roth’s Error. Didn’t Philip Roth ever read Dostoyevsky? Is Dostoyevsky not part of Philip Roth’s literary culture? You have to take into account the existence of the Devil, as Dostoyevsky did. God is not the only metaphysical power in the universe. The world is a permanent struggle between the forces of good and the forces of evil, between God and the Devil. This is clear in the story of Job in the Bible. God and the Devil are gambling on what is going to happen to Job. God and the Devil play dice with the universe (contra Einstein). My Dostoyevsky-inspired worldview allows me to reconcile the existence of evil in the world with my Walter-Benjamin-like Jewish belief in God and Kabbalah. God is trying awfully hard to make things better (and God sometimes desperately needs our help), but She is up against some very powerful fascist forces. This is also why I like Baudrillard – his ontology takes deeply into account the existence of Evil, the machinations of the Devil. Baudrillard wrote something brilliant about Descartes called The Evil Demon of Images. It is simultaneously an essay on cinema. This small book is hard to find. It was published only in English and only in Australia.

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