Ontological Arguments

Every other argument in this subject begins by looking at something. There is a universe, and it has a character, and the arguments proceed from there.

This one begins by looking at nothing at all. It claims that understanding what the word God means is by itself sufficient to establish that God exists, and that anyone who grasps the concept and denies the conclusion has contradicted themselves.

Almost everybody's first reaction is that this cannot possibly work. The difficulty, and the reason the argument has been buried and exhumed for nine hundred years, is that saying exactly where it fails has proved much harder than being sure that it does. Russell made the observation that being convinced these arguments are no good is considerably easier than identifying what is wrong with them, and the observation has held up.

Arguing without evidence

The previous two articles were not like this. Both took as a premise something about the world that could have been otherwise: that there is a universe, that it began, that its constants fall where they do. Both were probabilistic, and neither could deliver more than support.

An argument of the present kind would deliver something else entirely. If the conclusion follows from concepts alone, then it holds necessarily, and God's existence turns out to be a necessary truth of the same standing as a truth of mathematics. That is a demonstrative argument in the sense set out in the beginner tier, and it is the only place in this subject where anyone still claims one.

The oddity that should be registered immediately is that arguments of this form do not usually establish that anything exists. Reasoning from concepts tells you what would be true of a thing if there were one. Getting from there to there being one is precisely the step in dispute, and the whole history of this argument is a history of attempts to make that step and attempts to say why it cannot be made.

Anselm

Anselm set it out in the Proslogion, written around 1077 and 1078, in the second, third, and fourth chapters. The setting is worth knowing because it changes how the text reads: the Proslogion is a prayer, addressed throughout to God, and the argument arrives inside an act of devotion rather than a debate.

The argument in chapter two runs as follows. God is that than which nothing greater can be conceived. Even someone who denies that God exists understands that phrase, and what is understood is in that person's understanding. Now suppose that this being existed only in the understanding and not in reality. Then a greater being could be conceived, namely one that existed in reality as well. But then something greater than that than which nothing greater can be conceived could be conceived, which is impossible. So the being exists in reality.

Chapter three then argues something further, and many readers think it is the better argument. A being that cannot be conceived not to exist is greater than one that can. So that than which nothing greater can be conceived cannot be conceived not to exist, which is to say that it exists necessarily. This second argument is the ancestor of the modal versions at the end of this article, and it is not vulnerable to the same objections as the first.

The argument needs existence to be such a property, and it needs greatness to work in a specific way. Two assumptions are buried here, and both were flagged in the beginner tier when the divine attributes were assembled.

Greatness has to admit of a single ordering, so that of any two conceivable beings one is greater or they are equal. If greatness has several dimensions that trade off against one another, there may be no maximum, in the way that there is no greatest number that is both large and easily written.

And the great-making properties have to be jointly satisfiable. If maximal power and perfect goodness cannot be held together, then there is no being that has all of them and the concept picks out nothing. A later article in this tier takes that question up directly.

The lost island

Gaunilo, a monk who wrote a reply titled on behalf of the fool, produced the objection that everyone now reaches for. Consider the most excellent island that can be conceived, an island than which no greater island can be conceived. If it existed only in the understanding, a greater could be conceived, namely one that also existed. So the most excellent conceivable island exists. Since it evidently does not, something is wrong with the form of the reasoning.

Anselm's reply is better than it is usually given credit for. He says that the argument does not transfer, because an island has no intrinsic maximum. Whatever island you conceive, a better one is conceivable with one more palm tree, one more sheltered bay, one more freshwater spring. There is no greatest conceivable island, so the phrase does not pick anything out and the parody has no subject.

That answer is a genuine one, and it does not come free. It commits Anselm to the claim that the divine perfections do have intrinsic maxima: that there is a greatest possible degree of power, of knowledge, of goodness, and that these are not open-ended in the way that island quality is. That claim is defensible and it is not obvious, and any modern defender of the argument has to make it. It also means that the argument's fate is tied to a substantive metaphysics rather than to logic alone.

Descartes

Descartes gives a version in the fifth of the Meditations on First Philosophy, published in 1641, and returns to it in the Principles and in his replies to objectors.

His formulation goes through essence rather than through conceivable greatness. When we examine the idea of a supremely perfect being, we find that existence belongs to it in the way that having angles summing to two right angles belongs to the idea of a triangle. We cannot separate existence from a supremely perfect being any more than we can separate that property from a triangle, and so we cannot coherently conceive of a supremely perfect being that does not exist.

Caterus made the reply that survived. What follows from the triangle case is conditional: if anything is a triangle, its angles sum to two right angles. Nothing about the essence of a triangle establishes that there are any. By parity, what follows from Descartes' analysis is that if there is a supremely perfect being, it exists, which is not news. Descartes answered that the case of God is unlike all others precisely because existence is among the perfections rather than a further fact about an instance, and it is that answer that Kant's objection is aimed at.

Kant

Kant's objection appears in the Critique of Pure Reason, published in 1781 with a substantially revised second edition in 1787, and it is that existence is not a determining predicate. Adding existence to a concept does not add anything to the concept.

His illustration is a hundred thalers. A hundred real coins contain not one coin more than a hundred merely possible ones. If the actual coins contained something extra, then what you had conceived would not have been a hundred coins after all. The concept is identical in both cases, and what distinguishes the situations is not a difference in the concept but whether anything in the world answers to it. So a concept cannot be enriched by building existence into it, and the ontological argument's move fails at the point where it treats existing as one of the features a being might have more or less of.

Frege gave the version that does the most damage, in his work on the foundations of arithmetic in 1884. Existence, on his analysis, is a second-order property: it is a property of concepts rather than of objects, and to say that horses exist is to say that the concept horse is instantiated. On this account the statement that God exists says that the concept God has an instance, and "exists" cannot be one of the properties that constitute the concept, because it is not that kind of expression at all. The problem is not that existence is a feeble great-making property. It is that the argument uses the word in a position where it cannot function.

That is where the argument stood for most of the twentieth century, and it looked settled.

The modal revival

Charles Hartshorne and Norman Malcolm revived Anselm's third chapter in the middle of the century, and Alvin Plantinga gave the version now discussed in The Nature of Necessity, published by Clarendon Press in 1974.

The argument uses the framework of possible worlds. A being has maximal excellence in a world if it is omnipotent, omniscient, and morally perfect in that world. A being has maximal greatness if it has maximal excellence in every world. Then:

It is possible that a being with maximal greatness exists. So there is some possible world containing such a being. But maximal greatness includes maximal excellence in every world, so that being exists in every world. The actual world is one of the worlds. So a being with maximal greatness exists.

Two things about this deserve attention.

It is valid, and its validity does not depend on any disputed view about existence being a property. The step from possibility to actuality relies on a principle of the modal system called S5: what is possibly necessary is necessary. The intuition behind that principle is that what is possible does not vary between worlds, so if some world contains a necessarily existing thing, then in that world the thing exists in all worlds, including this one.

And it does not build existence into a definition. Maximal greatness is defined in modal terms, and the premise asserted is a claim about possibility, not a stipulation that something exists. Whatever is wrong with it, it is not the trick the older versions were accused of.

The symmetry problem

The objection that has stopped it is simple to state and has not been answered.

Consider the premise that it is possible that a maximally great being exists. Now consider the premise that it is possible that no maximally great being exists. Both look, to someone not already committed, like perfectly ordinary claims about what could have been the case. Both are conceivable in whatever sense conceivability is the guide here.

They cannot both be true. If a maximally great being possibly exists, it exists in every world and therefore in every world it is impossible that it fails to exist. If it possibly fails to exist, then there is a world where it does not exist, and since it would exist in every world if it existed in any, it exists in none.

So the argument's premise is not a modest concession that a reasonable person could grant while remaining undecided. Granting it is granting the conclusion, and the whole content of the dispute has been packed into it. The argument is valid and it moves nobody, because its premise is exactly as contested as what it was meant to establish.

Plantinga said as much himself, which is unusual and worth reporting accurately. His verdict was that arguments of this kind cannot be said to prove or establish their conclusion, and that what they show, given that accepting the premise is rational, is that accepting the conclusion is rational. That is a claim about the internal consistency of a believer's position rather than a piece of natural theology, and it is a considerably weaker thing than the argument is usually presented as delivering.

Conceivability and possibility

Under the symmetry problem sits a general point that applies well beyond this argument.

The premise is supported by our being able to entertain the thought without finding a contradiction. But the absence of a detected contradiction is weak evidence of possibility, especially where the subject matter is remote from anything we have experience of. Consider a mathematical conjecture that has neither been proved nor refuted. It seems conceivable that it is true and conceivable that it is false. One of those states of affairs is impossible, and no amount of entertaining it reveals which. Where a claim is necessarily true if true at all, our ability to imagine it either way tells us about our imagination rather than about the possibilities.

Since both possibility premises in the ontological argument concern something that is necessary if it obtains at all, this is exactly the situation. Conceivability was never going to settle it.

Next

The three arguments so far have proceeded from existence, from order, and from a concept. The next takes a different route, arguing not from anything about the physical world but from the existence of obligations that appear to bind whether or not anyone accepts them, and from the claim that a binding of that kind needs a source of a particular sort.