Modal Ontological Arguments and Their Parodies

Almost every argument in this subject is disputed at the point where the premises are supposed to support the conclusion. The modal ontological argument is the exception. Its validity is not seriously contested by anyone, including its sharpest critics, and this makes it a strange object to study, because a valid argument that nobody accepts has to be failing somewhere unusual.

The intermediate tier set out the argument and noted that everything depends on its first premise. This article is about what that dependence actually amounts to, and about a family of arguments constructed to show that the dependence is fatal.

The argument and why it is valid

The version that set the terms of the modern discussion is Alvin Plantinga's, in The Nature of Necessity, Oxford University Press (1974), chapter 10. Plantinga is careful about a technical point that matters: he does not want to speak of merely possible individuals, so the argument is framed in terms of a property being instantiated in some possible world rather than in terms of a being existing there. The same chapter examines the earlier modal versions developed by Charles Hartshorne and Norman Malcolm and finds them wanting before offering its own.

It is worth understanding why the modal form was developed at all, since it was not an idle exercise in reformulation. Anselm's original argument, and Descartes's later version, proceed by treating existence as something a being can have or lack, and by ranking a being that has it above an otherwise identical one that lacks it. That is the move Kant attacked, and the intermediate tier's article on the ontological argument covered the attack. Whatever its ultimate merits, the attack has real force against any argument that treats existing as one more property in a list. The modal version was built to be immune to it. Nowhere does it say that an existing being is greater than a non-existing one. It says that a being whose greatness holds in every world is greater than one whose greatness holds only in some, which is a comparison between two ways of being great rather than between existing and not. Whether that fully escapes Kant is arguable, but it is not obviously vulnerable in the same way, and it is why the modal version is the one still discussed.

The step from the premises to the conclusion uses a principle of the modal system S5, whose characteristic effect is that modal status does not vary between worlds. If something is possible, it is necessarily possible; and what follows from that, and what the argument uses, is that if something is possibly necessary then it is actually necessary. Suppose maximal greatness is instantiated in some world. By the second premise, whatever instantiates it does so necessarily, which is to say it is instantiated in every world. Every world includes this one. So it is instantiated here.

Whether S5 is the right modal logic for metaphysical possibility is a genuine question and not a settled one, but it is not where the argument is usually attacked. S5 is the standard choice for metaphysical modality, and a critic who rejected it to escape this argument would be paying a very large bill to avoid a small purchase. The second premise is likewise not much disputed, since it is close to a stipulation about what maximal greatness means: a being whose greatness depended on how things happened to turn out would be surpassable by one whose greatness did not.

Everything, then, is in the first premise.

The premise looks modest. It says only that there is no incoherence in the idea, that a maximally great being is not ruled out the way a round square is ruled out. Presented that way it invites assent, and the argument's rhetorical force comes almost entirely from how small the request appears.

The appearance does not survive inspection, and seeing why requires a distinction the premise quietly relies on.

Two senses of possible

There is an epistemic sense of "possible" on which a claim is possible when we do not know it to be false. In this sense it is possible that Goldbach's conjecture is true and also possible that it is false, because nobody knows which. And there is the metaphysical sense the argument requires, on which a claim is possible when there is a world where it holds.

The two come apart precisely where the argument needs them not to. Goldbach's conjecture, whichever way it goes, goes that way in every world, since mathematical truths are not contingent. So one of the two epistemic possibilities is a metaphysical impossibility, and no amount of failing to see a contradiction in it changes that. Our inability to detect a contradiction is a fact about us.

Now notice the shape of the theistic claim. A maximally great being exists necessarily or not at all. So "possibly, maximal greatness is instantiated" is not a modest claim of the kind it resembles. Given the second premise, it is equivalent to the claim that a maximally great being actually exists. The premise is not easier to accept than the conclusion. It is the conclusion, in modal dress, and the argument's whole appearance of drawing a great deal from very little rests on the reader not noticing this.

This is not a refutation, and it should not be presented as one. It shows that the argument is not going to convert anyone, which is compatible with the argument being sound. But it does mean that anyone assessing the premise is assessing the conclusion, and it removes any right to say that the premise is the obvious part.

The general lesson here is not confined to philosophy of religion, and the wider literature on it is worth knowing about, because the proponent sometimes writes as though the objection were an ad hoc device invented to block this one argument. It is not. That conceivability is a poor guide to metaphysical possibility has been a settled position since Kripke's work on necessary truths knowable only by investigation. Someone ignorant of chemistry can conceive, in the sense of finding no incoherence in, water turning out not to be H2O. It could not have turned out that way, since water is that substance in every world where it exists at all. Likewise for the morning star and the evening star being distinct objects: perfectly conceivable in the relevant sense, and impossible. In each case the conceiving is real and the possibility is not, because the conceiver lacked information that fixes the modal facts.

Whether a maximally great being is possible is precisely a case of that kind. If theism is true, the impossibility of its denial is not something inspection of the concept would reveal to someone who did not already know; and if theism is false, the incoherence in the concept of maximal greatness is likewise not something inspection has managed to reveal to anyone. Either way, our finding no contradiction is weak evidence, and it is the only evidence the premise was given.

The symmetry is immediate once the point above is in view.

The reasoning is exactly as valid as the original. If in some world nothing is maximally great, then it is not the case that maximal greatness is instantiated in every world; but a maximally great being would be instantiated in every world if in any; so it is instantiated in none, this one included. The second premise is the same premise the theist supplied, and the modal principle is the same one the theist invoked.

Set the two arguments side by side and the position is this. Both are valid. Their premises cannot both be true. Each premise is exactly as intuitively appealing as the other to someone who has not already taken a side. And nothing internal to either argument breaks the tie.

The theist's usual response is that the two premises are not in fact equally appealing, because there are independent reasons to think maximal greatness coherent and no comparable reasons on the other side. That response may be right. Notice what it costs: it concedes that the modal argument cannot stand on its own and must be propped up by considerations drawn from outside it, which is exactly what an argument of this genre was supposed to make unnecessary. An ontological argument that needs a cosmological argument behind it is not doing the job ontological arguments were invented to do.

What the pair jointly establishes is worth stating precisely, because it is a real result rather than a stalemate. Maximal greatness is either necessarily instantiated or necessarily uninstantiated. There is no third option, no world in which the matter comes out one way and another world in which it comes out the other. That is a substantive piece of modal metaphysics, and it is all the arguments deliver. Which of the two disjuncts holds is left open, and settling it requires reasons of an entirely different kind, which is to say the reasons canvassed everywhere else in this subject.

Parodies

Parody is an old method in this area and it is worth being clear about what a successful one accomplishes. It does not show which premise of the target is false. It shows that the target's credentials, whatever they are, are shared by an argument whose conclusion nobody will accept, so that those credentials cannot be sufficient. The proponent's only reply is to find a relevant difference, and the parody has succeeded in shifting the work onto them.

Two conditions have to be met for a parody to do that work, and most of the arguing takes place over the second. The parody must have the same form as the target, which is usually easy to check and rarely disputed. And its premise must have the same claim on us as the target's premise, which is neither easy to check nor ever conceded. A parody whose premise is merely stated has achieved nothing, since the proponent will say the premise is false and the parody's author has given no reason to think otherwise. A parody whose premise is supported in exactly the way the target's premise is supported, by the absence of any detectable incoherence in the concept, is a different matter, because the proponent must then either give up that mode of support or explain why it works in one case and fails in the other.

Gaunilo, a monk and a contemporary of Anselm, wrote his reply under the title "On Behalf of the Fool", taking up the position of the fool of the Psalm whom Anselm's Proslogion had addressed. His island is the ancestor of every parody since.

Anselm's reply is the one every proponent still makes in some form: the parallel fails because the concept of a greatest possible island is incoherent. Greatness for an island is a matter of features that admit of no intrinsic maximum. However many palm trees an island has, one more is better, and there is no number of palm trees at which an island cannot be improved. God's great-making properties are held to be different, since power, knowledge, and goodness are supposed to have intrinsic maxima that a being can possess completely.

Before assessing that reply it is worth noticing that it makes a commitment the theist has to honour elsewhere. The reply says that God's great-making properties have intrinsic maxima while an island's do not. Knowledge cooperates: knowing every truth is a determinate condition and there is no knowing more than all of them. Power is already contested, since the intermediate tier's paradox of the stone was an argument that unlimited power has no coherent maximum, and any resolution of that paradox constrains what the reply can say here. Goodness is worse, and the difficulty surfaces again later in this tier: if for every world God might create there is a better one, then creating well admits of no maximum, and a being's goodness may be as unboundable as an island's size. The Gaunilo reply is therefore not a free move. It is a promissory note drawn on doctrines defended in other articles, and it is worth as much as they are.

The reply is a good deal better than it is often credited with being, and it is not sufficient. Its trouble is that it defends the argument only against parodies built out of unbounded quantities, which invites the construction of parodies that are not. A being maximally great in every respect except that it permits exactly the quantity of suffering the world contains is not obviously incoherent, has no unbounded parameter to be increased without limit, and would by the same reasoning exist necessarily. So would a being maximally great in knowledge and power but indifferent rather than good, if indifference is a determinate condition rather than a deficiency of degree. Graham Oppy's Ontological Arguments and Belief in God, Cambridge University Press (1995), is the standard survey of these constructions and of the replies to them.

The proponent's answer at this point is that the concepts in the parodies are only apparently coherent, and that a maximally great being is the unique case where the concept genuinely holds together. That answer is not empty. It is a substantive claim in the metaphysics of value and modality, and defending it means defending the coherence of maximal greatness directly. Which returns the argument to where the previous section left it, since defending that coherence is defending the possibility premise, and defending the possibility premise is defending the conclusion.

It is worth recording that the parody strategy is not the only line of attack on this family. Peter Millican's "The One Fatal Flaw in Anselm's Argument", Mind 113(451): 437-476 (2004), argues that the Proslogion argument fails for a reason internal to it rather than by parity with any parody, and the paper is a model of how to take an argument of this kind seriously enough to locate its defect precisely.

Next

The last three articles have treated God as the terminus of an argument. The next four treat God as a subject of doctrine, starting with the classical claim that God has no parts of any kind, no location in time, and no states brought about from outside. Each of those doctrines is older and stranger than the arguments just examined, and each generates objections that the arguments never had to face.