Aren’t worlds comparably better or worse?

Si c’est ici le meilleur des mondes possibles, que sont donc les autres?
~Voltaire

I here mean to explore a paradox about comparing worlds with each other insofar as they are supposedly comparably better or worse. On the one hand I will maintain the alethic truism that there is no such thing as a best of all possible worlds, and conversely that there is no such thing as a worst of all possible worlds. To see why, consider that a best of all possible worlds is a world than which no better world could be conceived. However, the concept of a world than which no better could be conceived seems to be incoherent. Stephen T. Davis explains:

Take the notion of the tallest conceivable human. This notion is incoherent because, no matter how tall we conceive a tall human to be, we can always conceptually add another inch and thus prove that this person was not, after all, the tallest conceivable human. Just so, it may be argued, the notion of the best of all possible worlds is incoherent. For any possible world, no matter how much pleasure and happiness it contains, we can always think of a better one, i.e., a world with slightly more pleasure and happiness.[1]

Alvin Plantinga offers a more amusing illustration:

Just as there is no greatest prime number, so perhaps there is no best of all possible worlds. Perhaps for any world you mention, replete with dancing girls and deliriously happy sentient creatures, there is an even better world, containing even more dancing girls and deliriously happy sentient creatures. If so, it seems reasonable to think that the second possible world is better than the first. But then it follows that for any possible world W there is a better world W’, in which case there just isn’t any such thing as the best of all possible worlds.[2]

This truth seems indubitable once it has made its first impression on the mind, but it also leads to a conspicuous problem. To obviate the problem, we should turn first to St. Thomas Aquinas:

“The terms ‘more’ or ‘less’ only make sense if something is the maximum in a genus.”[3]

If there is neither a best nor a worst of all possible worlds, and if Thomas is right, then what sense can we make of calling some worlds better than others? Solutions do not abound. What I intend to do in this article is to survey some candidate solutions, and then share what has become my preferred solution to this problem inspired by St. Thomas Aquinas’ Quinque viæ (five ways), in particular from the fourth argument for God’s existence.

Gottfried Leibniz was the philosopher who introduced logically possible world semantics in the first place, and though he was clearly exceptionally brilliant, contemporary philosophers like Alvin Plantinga have raised their eyebrows high at Leibniz’ suggestion not only that there is a best of all logically possible worlds, but that this is it! Plantinga has, in fact, taken to calling this ‘Leibniz’ lapse.’[4] Although amusing, this charge has been criticized by those attempting to protect Leibniz’ good name. Thus, for example, Dr. George Gale, one of my philosophy professors at Concordia, has attempted an answer to the following effect: he has argued that, at least for Gottfried Leibniz, “this most perfect, best of all possible worlds is so only in accordance with a mathematical formula [relating simplicity of laws to abundance and variety of phenomena], and not in accord with our normal, everyday, Candidate-like notions of perfection, i.e., moral ones.”[5]

Thus, Plantinga’s criticism is guilty of an equivocation, since Plantinga must have something other than Leibniz’ notion of better-making properties in mind. As an aside, it seems to me that Leibniz’ solution is open to a deeper objection from William Lane Craig and possibly also from Alexander Pruss,[6] who have both concluded that it is absurd to posit an actually infinite number of contingent beings. Leibniz needs for the aggregate of all contingent beings, his ‘monads,’ to be actually infinite in number. Leibniz’ eclectic notion of better-making properties notwithstanding, however, unless one is inclined to think that Leibniz is right about better-making properties, it seems that Plantinga, Davis and others like them have posed an indissoluble difficulty. One, at least, for which a plausible and satisfying answer will not be found in Leibniz’ work.

One could, of course, simply bite the bullet and admit that what makes one world better than another is merely a matter of taste, and that the ascriptions ‘better’ or ‘worse’ express nothing more profound than preference. This solution is likely to be only as satisfying as moral nihilism is, and for the same reasons. A world in which a thousand more pregnant women get kicked in the stomach than another world seems, ceteris paribus, a much worse world relative to the other, and its being so isn’t simply a matter of taste or convention, like the way a world with a thousand fewer key-lime pies than ours seems worse than ours to me.

One could object to Plantinga that, though Leibniz does not have the right conception of what properties make worlds better, neither does Plantinga (at least, not as reflected in his thought experiment). Thus one can argue that Utilitarian standards of better-making properties are simply the wrong standards in the same way as Leibniz’ mathematical standards are; a world with more deliriously happy sentient creatures may be no better for it. Perhaps there are some other standards (known or unknown, discernible or indiscernible) which, like Leibniz’ standards, admit of a maximally good (or bad) world. This solution also strains credulity, however, as one need not be a Utilitarian to concede that, all things being equal, a world with more deliriously happy creatures really is better. Moreover, some Utilitarians could argue that two worlds in which the same average happiness obtains are really just as good as each other, so that the addition of more deliriously happy sentient creatures makes no calculable difference to how good a world is. So, Plantinga’s suggestion is about as far from being Utilitarian as he is. Moreover, for just about any standards it seems that one can simply run a parody of the kinds of arguments presented by Plantinga and Davis – perhaps even Leibniz’, if there really are different sizes of infinity and no greatest size of infinity. I am familiar enough with set-theory to know that there are different sizes of infinity, since some infinite sets cannot be bijected into others, but I am not familiar enough with set-theory to know if there is a species among these different ‘sizes’ of infinity than which no greater size exists. Either way, perhaps somebody opting for this Leibnizian avenue could argue, in a fashion similar to our hypothetical Utilitarian above, that once a world has the quality of instantiating an actually infinite number of desideratum it can no longer be meaningfully called ‘worse’ than any other world, even if that other world has ‘more’ desiderata.

This leads to another solution which I find not altogether unattractive. Perhaps instead of talking about a single ‘best’ or ‘worst’ of all possible worlds, one can identify a class of worlds than which no greater world can be conceived, and then speak of this class of worlds as the standard against which the goodness of worlds is measured. Any world with an actually infinite number of desideratum would surely be a world than which no greater could be conceived (I put no stock in any distinction, here, between conceivability and ‘possibility’ simpliciter).

I see two problems with this recommendation. First, due to the looseness of the definition, the set of all possible worlds would qualify as a set of worlds than which there could be no better world. Second, however, in order to isolate a class of worlds than which no better world could be conceived, and other than which every world is worse, seems to require positing an actual infinity of some sort, and we are led straight back to the problem posed by Dr. Craig.

Given that the impossibility of an actually infinite number of beings seems to pose such a problem for talk of best/worst possible worlds, perhaps one could run the following response in the form of an argument:

  1. If there is a best/worst of all possible worlds, then it includes an actually infinite number of beings and/or (better/worse-making) properties.
  2. If there is no best/worst of all possible worlds, then no world is better or worse than any other(s).
  3. But, at least some worlds are better or worse than some other(s).
  4. Therefore, there is a best/worst of all possible worlds.
  5. Therefore, there is at least one world which includes an actually infinite number of beings and/or (better/worse-making) properties.

I don’t find that satisfying myself, but that’s because W.L. Craig has sold me on thinking that it is logically impossible (indeed clearly incoherent) to talk about any actually infinite aggregate of contingent beings (I note in passing that he has not sold me on the idea that there couldn’t be an actually infinite number of events, anymore than there couldn’t be an actually infinite number of true propositions – to reify either of these into quasi-beings is a mistake, and though I would agree that if time were tensed there could not possibly be an actually infinite number of past events, I am adamantly a B-theorist).

A philosopher named Jean David Robert brought one solution to my attention which attempts to show that the objection to there being better or worse possible worlds is based on the presumption that there are better and worse possible worlds, and thus the objection cannot go through. Scilicet, the objection only works if the objection fails. He explains:

If it’s true that “there is no such thing as the best of all possible worlds because one can always conceive of a better world,” then it’s false that “one can never conceive of a better world because there is no such thing as the best of all possible worlds.” […]
Consider the following counterexample: on my desk, I have a potentially infinite number of rulers of different lengths. In other words, I have one potentially infinite ruler. I also have two rulers of different finite lengths. I compare the length of these two rulers using the potentially infinite ruler, and determine that one of the finite rulers is 1 cm longer than the other. Now imagine that the rulers are in fact possible words and the length of the rulers correspond to the objective value of these possible worlds. We can see that it does make sense to speak of one possible world being objectively better than another.

I like this answer; it has an almost Moorean quality to it. An actually Moorean answer may also be provided; perhaps we all know that some worlds are better than others, and we are surer of this truth than we are or can be sure of all the clever arguments against it. However, the trouble with the Moorean answer, and in a subtler way the trouble with J.D. Robert’s answer, is that it doesn’t actually help us make good sense of ‘better’ or ‘worse’ possible worlds. It may help us sleep at night, but it doesn’t get us anywhere. J.D. Robert’s doesn’t precisely because his potentially infinite ruler consists of the indefinite put-together of differently sized rulers, but for any ruler to have a size relative to any other it must be in principle comprised of commensurable units of length. However, to say that there are in principle commensurable units of length is just to say, pace the metaphor, that there is some standard against which these worlds can be compared so as to make one ‘better’ than another.

All of the aforementioned solutions seem to leave me high and dry. None of them seem to me to represent a plausible answer to the question ‘how can we meaningfully say of one world that it is better or worse than any other?’ I have come to think, however, that there may be a natural theological solution to the problem. Once again, I turn to St. Thomas Aquinas:

Among beings there are some more and some less good, true, noble and the like. But “more” and “less” are predicated of different things, according as they resemble in their different ways something which is the maximum, as a thing is said to be hotter according as it more nearly resembles that which is hottest; so that there is something which is truest, something best, something noblest and, consequently, something which is uttermost being; for those things that are greatest in truth are greatest in being, as it is written in Metaph. ii. Now the maximum in any genus is the cause of all in that genus; as fire, which is the maximum heat, is the cause of all hot things. Therefore there must also be something which is to all beings the cause of their being, goodness, and every other perfection; and this we call God.[7]

This may sound appealing to Theists like me, but presumably we shouldn’t be satisfied with merely gesturing in the direction of Theism, as though saying ‘God!’ loudly enough solves every problem. How can one cash-out this solution?

First, it is clear that if God exists, then his nature is identical to ‘the Good.’ In fact, if God exists then it seems like the only way to intelligibly predicate anything of him will have to avoid univocal predication just as much as equivocal (indeed, in God’s case, univocal predication is equivocal). Thus, we can predicate things of God in two ways: either by analogy, or metaphorically. We can say that God is our king metaphorically, while we can say that God exists or is good analogously. I will spare myself the trouble of having, here, to explain St. Thomas’ whole philosophy of language. I will, instead, take the liberty of presuming that the reader is at least relatively familiar with Thomistic philosophy of language.[8] God, ex hypothesi, is clearly the bearer of superlative attributes which serve as the paradigms of those attributes insofar as they are identified as instantiated in the world. In other words, for any predicate P, if P is an intrinsic superlative attribute of God, then God’s nature serves as the paradigm according to which P is predicated of contingent beings. Thus, if a being is good, it is good to the extent that it imitates (or intimates) the nature of God. If a thing is beautiful, it is beautiful to the extent that it intimates the pleasure of ‘seeing God’ (note that beauty is defined by Aquinas as that which, upon being seen, pleases).

I suspect, therefore, that when we say one logically possible world is better or worse than another, we mean that it is better or worse in the very same (or, at least, similar enough) sense as one person may be better or worse than another. Clearly, though, the Theist (at least of the Thomistic variety) will say that one person is good to the extent that they intimate God.[9] They are virtuous to the extent that their character intimates the character of God. A possible world, therefore, is good to the extent that it intimates the nature of God (i.e., to the extent that God’s nature is intimated in that world). This may mean that it reflects God’s moral goodness as well as his justice, his wrath as well as his mercy. Thus, the suggestion is that one possible world W is better than some other world W’ just in case it better intimates the nature of God.

I am convinced that this answer is not only appealing, but exactly right. In fact, I am tempted to make an argument of it for Theism. I will end this article with a brief sketch of how this argument is likely to go:

  1. If some possible worlds are better/worse than others, then either (i) there is a best/worst of all possible worlds which acts as the standard against which the goodness of worlds is measured, or (ii) there is a class of best/worst of all possible worlds which acts as the standard against which the goodness of worlds is measured, or (iii) God’s nature serves as the paradigmatic standard against which the goodness of worlds is measured.
  2. Some possible worlds are better/worse than others.
  3. There is no best/worst of all possible worlds which acts as the standard against which the goodness of worlds is measured.
  4. There is no class of best/worst of all possible worlds to act as the standard against which the goodness of worlds is measured.
  5. Therefore, God’s nature serves as the paradigmatic standard against which the goodness of worlds is measured.
  6. If God’s nature serves as the paradigmatic standard against which the goodness of worlds is measured then God’s nature exists.
  7. Therefore, God’s nature exists.
  8. If God’s nature exists, then God exists.
  9. Therefore, God exists.

Somebody may wish to wiggle out of this argument by splitting the horns of the trilemma in the Major premise, for instance by suggesting that moral Platonism may be a fourth alternative. However, the argument could be appropriately amended by changing the first premise to include the supposed alternative, and then we could insert a ‘premise 4.1’ which denied that moral Platonism is a solution.


[1] Stephen T Davis, ed. Encountering Evil [New Ed]: Live Options in Theodicy. (Cokesbury.com, 2001): 75.

[2] Alvin Plantinga, God, Freedom, and Evil. (Wm. B. Eerdmans Publishing, 1974): 61.

[3] Apologies to the reader: I can’t seem to find this quote in St. Thomas’ works, and I’m not sure where it came from either – it may not have come from the Summa Theologiae. It’s in one of his writings, somewhere.

[4] Plantinga, Alvin C. “Which worlds could God have created?.” The Journal of Philosophy 70, no. 17 (1973): 548.

[5] Roger Stuart Woolhouse, ed. Gottfried Wilhelm Leibniz: critical assessments. Philosophy of mind, freewill, political philosophy, influences. Vol. 4. (Taylor & Francis, 1994): 453.

[6] Alexander Pruss, “Probability on Infinite Sets and the Kalaam Argument” http://alexanderpruss.blogspot.ca/2010/03/probability-on-infinite-sets-and-kalaam.html

[9] Interesting thought: if God had not incarnated setting the paradigmatic standard of a best of all possible persons, could people still be (have been) meaningfully said to be better than others? The answer is, obviously, bound up with the suggestion I am here in the business of elaborating. It could, I think, make sense, even without a best of all possible men, just in case the measure of a man’s goodness is the degree to which he intimates the divine nature.

[10] Alexander Pruss, “One Thing I have Learnt from Hume” http://alexanderpruss.blogspot.ca/2007/12/one-thing-i-have-learned-from-hume.html

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