Category Archives: Leibniz

Leibniz, Hangnails & the Best Possible World

In a brief Twitter conversation it was suggested to me that a world with one less hangnail would be a better world than the world we live in, and thus the world we live in cannot be the best possible world (BPW). Take that, Leibniz!

Let’s call our world up to 2014 W1. Now let’s go back in time to Billy Bob in 1956 when he suffered a hangnail and intervene ever so slightly so he avoids suffering a hangnail. Let’s call this new world W2. Now, fast-forward again to 2014. Are W1 and W2 identical except that in W1 in 1956 Billy Bob suffered a hangnail? I don’t see how we can make such a claim, and in fact we can easily imagine how by 2014 W1 and W2 could very well be radically different worlds. How so? Well, in W1 after suffering a hangnail, Billy Bob went to get medical treatment. He met a nurse at the hospital; they hit it off, eventually got married, and had 4 children. When we consider the enormous number of different events that take place in W1 as a result of Billy Bob’s hangnail it should be fairly obvious that by 2014 W1 is very different from W2.

But is it different for the better? Maybe, maybe not. Maybe for a time it gets better, after which it gets horrendously worse. Or maybe it’s horrendously worse for a time but ultimately gets far better. Maybe Billy Bob’s kids turn out to be wonderful philanthropists, and humanity reaps all manner of boons. Or perhaps they end up a family of serial killers and bring misery to hundreds. But regardless of how they turn out we still can’t tell if W1 is ultimately better or worse than W2, since there are further multiple consequences of both scenarios which we, as creatures of limited intelligence and insight, simply cannot trace.

But isn’t a world with one less hangnail – W2 – better than a world – W1 – which is identical in all respects except there is one additional hangnail? Again, this isn’t obvious. It relies on a certain understanding of “better” which we needn’t agree with. If we understand the chief purposes of God for the world to lie in the maximisation of pleasure and the minimisation of pain then perhaps W2 is “better.” But of course in Christian theism this is not God’s sole or ultimate purpose. In any event, for the sake of argument let’s grant that W2 would indeed be better than W1. But, now we must ask: is W2 a feasible world? It’s not clear that it is. Take Billy Bob again. Perhaps every world in which he suffers the hangnail turns out differently from all the worlds in which he doesn’t, such that there simply are no two worlds which are identical in all respects except that Billy Bob suffers a hangnail in one of them. And this should not surprise us as such cases – even relatively minor ones like a stubbed toe – are always part of the matrix of events. Such pains have a number of uses in the grand scheme of things. Firstly, that such pains are of biological value is well documented. Secondly, as Swinburne argues, the experience of pain is an intrinsic part of any world where creatures are to have significant moral responsibility and freedom to do good or evil. Thirdly, such experiences form part of our “epistemic environment,” contributing to the background against which we reflect on the world and form opinions about good, evil, value, and about God and the nature of ultimate reality. Fourthly, they play a role in our development as moral creatures, as we respond daily to the aches and hurts that accompany daily living.

Thus, even relatively minor hurts like stubbed toes and hangnails play a role in life, even a significant one such that a world with one less hangnail – W2 – might have over-ridding deficiencies that make W1 preferable.

The principle behind this has been named “the butterfly effect.” The basic idea is that something seemingly unimportant – a butterfly fluttering around some flower – can potentially set in motion a chain of events (or play a small but crucial role in the “events matrix”) that leads to something massive – a hurricane off the coast of Florida; and we have no way to predict or trace it.

The same idea appears in the movie Sliding Doors. In this movie the lead character is hurrying to catch a train. The film then branches off into 2 strands or “mini-movies.” In one of these worlds she catches the train, while in the other events conspire to cause her to miss it. The movie then plots how her life goes in two completely different directions as the result of this one seemingly benign and insignificant event (which of course was itself dependent on millions of prior contingent events either occurring or not).

The upshot of all this is that we really can’t tell which is better – W1 or W2 – by engaging in observation and imaginative thought experiments. In fact, whilst Leibniz believed that this world is the BPW, he didn’t believe it on the basis of observation. He understood that drawing such a conclusion was impossible. His belief that this world is the BPW was a deduction from his prior belief that the world is the creation of an omnipotent and perfectly good God. If the universe is the creation of such a being then, reckoned Leibniz, there is some reason to think it is the BPW. But Leibniz would have had no time for modern atheistic arguments that run like so:

(1) If God exists our world would be the best possible world.
(2) Our world is not the best possible world.
(3) Therefore God does not exist.

Whilst Leibniz would agree with (1), he would regard (2) – quite rightly in my view – as utterly speculative. William King put it like so: “You’ll say that some particular things might have been better. But, since you do not thoroughly understand the whole, you have no right to affirm this much.”

Thus, though Leibnizian arguments might rationally conclude that this is the BPW because it has been created by an omnipotent and perfectly good God, atheist arguments to the opposite conclusion will always rely on a premise that is fundamentally unknowable.

Stephen J Graham.

See also:

My main essay on Leibniz here:

and another shorter article here:

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Improving the Best Possible World

Leibniz’s main contribution to the problem of evil and theodicy is the notion that the world we live in is the best possible world. Leibniz doesn’t derive the notion that the world we live in is the best possible from observation and reflection on the nature of the world; for him such an endeavour would be impossible for mere mortals limited in space, time, intelligence and insight. Rather, Leibniz’s belief that this is the best possible world flows from his belief that the creator is omnipotent and perfectly good.

One common criticism of Leibniz is that his theodicy leaves us without hope. If this is the best possible world then there is, so the argument goes, no hope of improvement. Arthur Lovejoy puts it: “It was possible to hope that in the fullness of time the Devil might be put under foot, and believers in revealed religion were assured that he would be; but logical necessities are eternal, and the evils which arise from them must therefore be perpetual.” Since we live in the best possible world, and this world unavoidably contains evils, then there is no hope of those evils being defeated. If they are defeated then that would be a better world.

Critics such as Lovejoy assume that if this is the best possible world then it cannot be improved. This assumption certainly appears, at least prima facie, to be reasonable. However, on closer examination it’s false and represents an unduly wooden interpretation of Leibniz.

Let W1 stand for our world. Further, let W1a stand for our world in 2014 and W1b stand for our world at some later time, say, 2064. For the sake of argument let’s suppose that by 2064 we have solved world hunger, ended wars, and drastically reduced criminality. Now, undoubtedly W1b represents a better state of affairs, all other things being equal, than W1a. Does not this refute Leibniz? Hardly! All it shows is failure to understand Leibniz. According to Leibniz, when God entertained all possible worlds as ideas in His mind, with a view to bringing the best into existence, he knew each world completely: past, present and, crucially, future. So, whilst W1b represents an improvement on W1a it is still the same world we are thinking about: W1.

By way of illustration imagine going to the theatre to see the best possible play. Perhaps scene one is incredibly boring, even confusing; maybe it’s horrendously sad, maddening, and altogether unpleasant. Should I despair? Should I lose hope that because this is the best possible play that it cannot get any better? Of course not! These early scenes might be laying an important foundation which contributes to the play’s being the best possible. Later scenes may well cast these earlier ones in a drastically different light. When we judge a play we judge it as a whole – beginning to end.

Those who argue a’ la Lovejoy treat the world statically – like a picture rather than a drama. In contrast to a drama a picture exists all at once, such that there can never be any improvement. The picture is as good as it’s ever going to be. However, this view totally ignores the time dimension to existence. Lovejoy mistakenly equates “best possible world” with some state of affairs at some particular time within that world.

There is therefore no reason whatsoever why, on Leibniz’s view, the world today can’t be a better place than it was yesterday. When we say “best possible world” we are referring to the entire state of affairs: past, present and future. Moreover, some evils might be necessary in the early stages of this world but that does not mean, contra Lovejoy, that they will be perpetual. It’s perfectly plausible and consistent with Leibniz’s theodicy to suggest that perhaps part of the reason why this world is the BPW is precisely because evil is not going to last forever; and of course Christianity does indeed envisage a future in which this becomes a reality.

And thus the criticism of Lovejoy fails. Once we allow for this the dynamic view of the world there is no reason at all why the best possible world could not be such that the state of affairs at time t2could indeed be better than it was at t1.

Stephen J Graham

For further details on Leibniz’s theodicy see my much longer essay:


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Leibniz’s Best Possible World


Karth Barth accused Leibniz of having no serious interest in the problem of evil. Barth was wrong about many things, and such is the case here also. The problem of evil was of concern to Leibniz from his youth, and his thinking on the problem culminated in his influential work, “Theodicy.”

The central thesis of Leibniz’s work is the notion that the world in which we live is the best possible world (BPW). The concept of the BPW is a slippery one, often left ill-defined as if those who use it expect their listeners to instinctively know what it means. Unfortunately it is used differently by different thinkers, and, as we will see, criticisms of one understanding do not necessarily apply to others. According to Leibniz the BPW is that state of affairs – or combination of possibilities – which allows the maximization of being, in terms of both quantity and quality. His idea here has echoes of Neo-Platonism’s so called “principle of plenitude;”in creating God intends to manifest his goodness beyond the bounds of his own being, and such purposes are best served by creating a rich variety of finite beings, as opposed to a mere quantitative maximum of the same sort of being: “To multiply one and the same thing only would be superfluity, and poverty too. . . to eat nothing but partridges, to drink only Hungarian or Shiraz wine – would one call that reason?

In developing his notion of the BPW Leibniz also points out that while X, Y, Z might be individually possible, they may not be “compossible” – capable of existing in the same reality. For instance, it’s possible for Dodos to exist in the year 2014 and it’s possible that Dodos be extinct by 2014. But we can’t have one reality in which Dodos exist in 2014 and are extinct in 2014. One excludes the other. So, God must choose which set of coherent possibilities to actualize. Leibniz pictures an infinite number of possible universes present as ideas in God’s mind: W1…Wn. These universes exhaust all possibilities, such that any change in W1 would render it identical to, say, W2. From surveying each possible universe God applied his creative power to bring one into existence. The combination of God’s omnipotence, perfect understanding, and perfect goodness leads him to choose the best world.

It is Leibniz’s notion of compossibility – or noncompossibility – that means that whilst God chooses the BPW, this world still contains a great deal of evil. God’s creative activity is thus limited by inherent compatibility issues. There are, however, countless possibilities from which God can choose. He compares them – perfections and imperfections, weaknesses and strengths, goods and evils – and then in His wisdom chooses the best “in order to satisfy goodness completely.”

So, God surveys all the possible worlds he could make: W1 to Wn. According to Leibniz God knows these possible worlds exhaustively, including all the free decisions of any beings he could create in whatever circumstances he chooses to create them. Moreover, God sees each world as a completed whole. So, in terms of the idea of our own world in the divine mind, He knew about the Fall and its corrupting effects, about the redemption of Christ, and about the choices of each person which leads them to either salvation or damnation. God doesn’t determine these choices; He simply decrees the existence of this world and its entire history.

Here we meet the first common criticism of Leibniz: that the universe is just as rigidly determined as Spinoza’s, despite Leibniz’s protestations to the contrary. In fact, Charles Werner accuses Leibniz of presenting us with “a perfect and devastating image of necessity.” After all, in Leibniz’s scheme, God has decreed a complete sequence of events; what room then for human freedom?

This criticism is much too hasty, as Leibniz’s view needn’t exclude genuine free will. If – as many philosophers of religion think – God has so-called “middle knowledge,” then He knows what any creature He might create would do under any set of circumstances in which God might place him. These circumstances are “freedom-permitting” circumstances. For example, under the particular circumstances God knew that Peter would freely deny Christ three times. God’s knowing this does not, however, make the actions any less free – even in the libertarian sense. So, when our world was considered in its totality in the divine mind, this included all the free actions of free agents within it. God does not determine the agents to act as they do, but rather He knows how they will freely act in the circumstances in which they find themselves.

On the Leibnizian view we notice that evil is unavoidable. Evil – for Leibniz – is very real, though always a privation of something good. No matter what form evils come in – whether metaphysical evils in terms of finitude and imperfection, physical evils in terms of pain and suffering, or moral evils in terms of human sins – they are part of the BPW by virtue of being inter-connected with certain goods. Leibniz here agrees with Augustine that the universe as a whole is good despite containing elements that, when considered in isolation, are bad: “Not only does [God] derive from [evils] greater goods, but he finds them connected with the greatest goods of all those that are possible: so that it would be a fault not to permit them.”

Leibniz thus approves of the ancient hymn which translates as “O fortunate sin that merits such and so great a redeemer,” to illustrate this principle, and writes: “all the evils of the world contribute, in ways which generally we cannot now trace, to the character of the whole as the best of all possible universes.” But, what about tiny evils? Couldn’t we do away with even just one of them and so make a better world than this? Leibniz answers: “if the smallest evil that comes to pass in the world were missing in it, it would no longer be this world; which, with nothing omitted and all allowance made, was found best by the Creator who chose it.”

It’s crucial to understand that Leibniz does not think we can derive the conclusion that this is the BPW simply by reflecting on how it appears to us. This, reckons Leibniz, would be impossible: “For can I know and can I present infinities to you and compare them together?” We have no way to know what the BPW is, except in so far as we might arrive at this conclusion by reflection on the existence of a perfectly good creator. Being perfectly good (and omnipotent) means that – having freely chosen to create (as an expression of over-flowing goodness creatively expressing itself to creatures) – God will create the best possible world: “supreme wisdom, united to a goodness that is no less infinite, cannot but have chosen the best.” Leibniz, then, would be utterly unimpressed by recent atheistic arguments which attempt to show that God does not exist because this is not the best possible world. Leibniz was all too aware that he wasn’t nearly omniscient enough to draw such a conclusion!

This brings us to another criticism of Leibniz’s position: the coherence, or lack thereof, of the concept of “best possible world.”

Certain theologians, following Aquinas, have argued that the “best possible world” is by definition unrealizable – like the fastest possible speed. Charles Journet argued that regardless of what world God makes he could always make a better one, and thus: “To demand that God, to be above reproach, must make the best of all possible worlds is to demand him to make what is not feasible, and to give existence to something absurd.”

It seems to me that Journet has failed to grasp the sense in which Leibniz uses the term. Following the Thomist tradition Journet holds that there is a scale of possible universes from non-being to God, but that this scale contains an infinity of steps, and that between any two universes there is always the possibility of another. This means that no matter what universe God creates there is always the possibility of there being one that is better but still less than God. If the Thomist tradition is correct then the concept of the best possible world is indeed incoherent, since there cannot be a best possible world in the sense of a closest approximation to perfection within an infinite series of such approximations.

However, this is not how Leibniz uses the term. Leibniz agreed that there could well be an unlimited range of possible worlds; however there is one which – though not particularly close to the level of God – is such as to be the most superior compossible system, in so far as it best satisfies some given criterion of excellence. Thus, Journet’s criticism misfires.

Journet then levels a second criticism at Leibniz, one with which many other commentators concur. Journet accuses Leibniz of effectively denying God’s omnipotence, and setting up a form of dualism. According to Leibniz, once God has freely chosen to create he is limited by fixed possibilities and compossibilities, and therefore even in the BPW there may well be a lot of evil. And since He is limited in these ways, God is not omnipotent.

To my mind accusing Leibniz of denying God’s omnipotence or advocating a dualist solution to the problem of evil is quite unfair. Philosophers of religion have typically argued that there are certain things which God logically cannot do. God cannot create a world in which it always rains everywhere and in which it never rains anywhere. Moreover, there are logically possible worlds that even an omnipotent God cannot create. For example, it’s possible under the conditions he finds himself in that Judas not betray Christ. But God can’t create a world with exactly those conditions in which Judas does not betray Christ, because Judas will freely choose to betray Christ under those circumstances. Such a world is not feasible for God to create despite its being a possible world.

Some critics go further and accuse Leibniz’s system of being one that leaves us without hope. Why? Well, if this is the best possible world then there is no hope of improvement. Arthur Lovejoy writes, “It was possible to hope that in the fullness of time the Devil might be put under foot, and believers in revealed religion were assured that he would be; but logical necessities are eternal, and the evils which arise from them must therefore be perpetual.” Or, as Voltaire’s Candide asks in a spirit of hopelessness: “Si c’est ici le meilleur des mondes possible, que sont donc les autres?” (“If this is the best of all possible worlds, what are the others?”)

This, however, represents an unduly wooden interpretation of Leibniz. This is best illustrated by differentiating between two other concepts: a static view of the world and a dynamic view of the world. The static view treats the world like a picture – existing all at once, such that if this is the BPW then there can never be any improvement. The picture is as good as it’s ever going to be. However, this view totally ignores the time dimension to existence. By contrast, the dynamic view treats the world more like a drama, moving across time. In fact, the best possible drama might start off incredibly boring, but such boredom may well be setting the foundation for later scenes of the play. After scene one should I despair that because this is the “best possible play” that it therefore can’t get any better? Not at all! The same holds for Leibniz’s concept of the BPW. With this dynamic view we can see that the BPW can improve as time goes on. The world today can be a better place than it was yesterday and yet it would still be true that the world is the BPW. When we say “best possible world” we are referring to the entire state of affairs: past, present and future. Moreover, some evils might be necessary in the early stages of this world but that does not mean they will be perpetual. It’s perfectly plausible and consistent with Leibniz’s theodicy to suggest that perhaps part of the reason why this world is the BPW is precisely because evil is not going to last forever; and of course Christianity does indeed envisage a future in which this becomes a reality.

And thus the criticisms of Lovejoy and Voltaire fail. Once we adopt the dynamic view there is no reason at all why the best possible world could not be such that it is better at time t2 than it was at t1.

Admittedly this notion of a dynamic view of the universe is not explicit in Leibniz. When he speaks of the universe as the BPW he is referring to its adequacy – as a complex whole – as an expression of the overflowing creativity of God. As such the criticism of Leibniz above is understandable, since arguably he may have thought that the universe at t2 could not in any way be better than it was at t1. At both times, for Leibniz, the world perfectly reflects God’s goodness. However, as I have argued, his view can be easily interpreted, or at least modified, in precisely the way I have outlined.

Such criticisms further expose the need to carefully define what “best possible world” means. The BPW, as I have said, is certainly a slippery concept and often different thinkers mean different things when they use the term. Some, with Leibniz, understand the term along the lines of the universe’s being the best expression of the overflowing goodness and creativity of God. Others – particularly modern atheist critics – use the term in an ontological sense to mean a world containing only “perfect” types of being. However, on the back of the dynamic view outlined above we can find another understanding of the term, one which fits neatly within an orthodox Christian view. This understanding we might call “instrumental,” and recognizes that it’s impossible to make any claims about what would be the best possible world aside from dealing with the prior question of what God is trying to achieve through creation. What are God’s purposes?

This then brings us to the question of why God created the world. We need not disagree with Leibniz that the world is the expression of the overflowing creativity of God who desires to communicate his being beyond Himself. However, on the Christian understanding of God there is more to creation than that. In fact it seems that whether or not this is the BPW ultimately depends on a prior question: why did God create us and place us in the sort of world in which we find ourselves? The BPW, then, is that state of affairs which best serves the purposes that God wishes to fulfill through it. The early church father Irenaeus seemed to think along such lines (though not in any kind of systematic way). Put simply, Irenaeus thought that man is an unfinished creature – not created in perfection, as Augustinian theologians often suggest. Human beings – as autonomous moral agents – must be developed. The world then is the “vale of soul-making,” a place built for this process, a place in which human beings can exercise and grow in virtues, but by necessity also a place where vices and real evils exist.

I will expand on this Irenaean idea in a later essay, but for now we notice what this exposes about the nature of the real divide between theists and atheists when it comes to the notion of “best possible world.” Atheists and agnostics – represented philosophically by the likes of Hume, Mill and Russell – tend to assume that if an omnipotent and perfectly good being exists then its purpose is to maximize pleasure and minimize pain for the creatures it creates. The BPW will therefore be that which works best to this end. Since this world is almost certainly not that kind of world, then God almost certainly does not exist. By contrast the Christian view is not at all like this. The highest good in Christianity is the knowledge of God – not the maximization of earthly pleasure. In other words the world is designed as an environment for the development of finite persons, and in this world they have real and significant freedom to engage in real and significant acts of good or evil.

This brings us back to Leibniz: how do we know that this is the BPW? For Leibniz, as we have seen, there is a reasonable answer: because it is the creation of an omnipotent, perfectly good God. For the atheist, how do we know that if an omnipotent, perfectly good God exists that He would create a better world than this one? I don’t see how the atheist can answer that question. It requires knowing that there is a world which is better than this one. But how can we know a thing like that? To paraphrase Leibniz: Can the atheist know and can he present infinities to us and compare them together? Most atheist arguments here take the form “If God existed he would/would not do this or that.” Unfortunately this amounts to little more than crass presumption, as if such a being might have the same values, goals and purposes as a modern day atheist, and no higher level of insight into reality. Such arguments would have been regarded as sheer folly by Leibniz, and rightly so.

It seems to me that Leibniz was certainly on to something in his central notion that we live in the best possible world. Even Christian philosophers who claim to reject Leibniz end up affirming his core thesis in some shape or form. For instance, in Evil and the God of Love, John Hick rejects Leibniz’s position, and yet his own position strikes me as inherently Leibnizian, with the exception that he defines “best” in more explicitly instrumental terms. Others make a similar move, implicitly accepting that if God exists with the attributes Christianity claims He possesses, then in some sense this must be the best possible world. And so they should, since if an omnipotent and perfectly good God exists and has a purpose for his creation it would be inexplicable why He didn’t create the world that would be best suited for achieving it.


Filed under Atheism, God, Leibniz, Problem of Evil, Theism