The label ‘ontological argument’ was introduced by Kant for arguments for the existence of God that proceed ‘completely a priori, from mere concepts’. Here is an example:

1. 1. A property is a perfection if and only if it is necessarily better for there to be at least one thing that has that property than it is for there to be nothing that has that property. (Definition)

2. 2. It is necessarily better for there to be at least one thing that exists than it is for there to be nothing that exists. (Premise)

3. 3. (Therefore) Existence is a perfection. (From 1, 2)

4. 4. God is a being that has every perfection. (Definition)

5. 5. (Therefore) God has existence, i.e. God exists. (From 3, 4)

It is common for theists to claim that the concept of God just is the concept of a perfect being. And, at least roughly speaking, this argument may seem to be nothing more than an unpacking of that idea, or concept, or definition, of God.

There are many different ontological arguments. Most ontological arguments are very difficult arguments to assess. Entire libraries have been filled with discussions of ontological arguments in the works of, for example, St Anselm, Descartes, Leibniz, Spinoza, Hegel, Collingwood, Hartshorne, Plantinga, and Gödel. Here are some sample arguments. (Do not worry if they make your head spin. The point here is just to illustrate the diversity of ontological arguments. I am not proposing to discuss any of the following arguments in this article.)

1. A. An argument inspired by Anselm's Proslogion 2:

   1. 1. Whatever is understood exists in the understanding. (Premise)

   2. 2. That-than-which-no-greater-can-be-conceived is understood. (Premise)

   3. 3. If that-than-which-no-greater-can-be-conceived exists only in the understanding, then that-than-which-no-greater-can-be-conceived-that-exists-in-reality is greater than that-than-which-no-greater-can-be-conceived. (Premise)

   4. 4. It is impossible for anything to be greater than that-than-which-no-greater-can-be-conceived. (Premise)

   5. 5. (Therefore) That-than-which-no-greater-can-be-conceived exists in reality. (From 1–4)

2. B. An argument inspired by Descartes's Meditation V:

   1. 1. The idea of a supremely perfect being includes the idea of existence. (Premise)

   2. 2. The idea of a supremely perfect being is the idea of a being with a true and immutable nature. (Premise)

   3. 3. Whatever belongs to the true and immutable nature of a being may truly be affirmed of it. (Premise)

   4. 4. (Therefore) A supremely perfect being exists. (From 1–3)

3. C. An argument inspired by Plantinga's Nature of Necessity:

   1. 1. A being is maximally excellent if and only if it is omnipotent, omniscient and perfectly good. (Definition)

   2. 2. A being is maximally great if and only if it is necessarily maximally excellent. (Definition)

   3. 3. It is possible that something is maximally great. (Premise)

   4. 4. (Therefore) Something is maximally excellent. (From 1–3)

4. D. An argument inspired by Gödel's Notebook:

   1. 1. A is an essence of x if and only if, for every property B, x has B necessarily if and only if A entails B. (Definition)

   2. 2. x necessarily exists if and only if every essence of x is necessarily exemplified. (Definition)

   3. 3. x is God-like if and only if x has as essential properties those and only those properties that are positive. (Definition)

   4. 4. If a property is positive, then its negation is not positive. (Premise)

   5. 5. Any property entailed by a positive property is positive. (Premise)

   6. 6. The property of being God-like is positive. (Premise)

   7. 7. If a property is positive, then it is necessarily positive. (Premise)

   8. 8. Necessary existence is positive. (Premise)

   9. 9. Necessarily, there is something that is God-like. (From 1–8)

Many of the critical points that come out in discussion of ontological arguments can be brought out in discussion of very simple ontological arguments. These simple arguments are not arguments that anyone seriously defends. However, appreciating the reasons why these simple arguments are unsuccessful is a useful starting point for those interested in making a deeper and more careful investigation of the kinds of ontological arguments given in the preceding paragraphs.

Consider, then, the following argument:

1. 1. God has every perfection. (Definition)

2. 2. Existence is a perfection. (Premise)

3. 3. (Therefore) God has existence, i.e. God exists. (From 1, 2)

I have never met anyone who, when presented with this argument, thinks: OK, that settles it! But, when I ask people why we should not think that this is a proof that God exists, I get a vast range of different responses. The same is true – with bells on – when we move to more complicated ontological arguments. What I shall now go on to say in criticism of this argument is not necessarily what other philosophers would say when they turn to criticize it.

In this argument, I have not explained what it is for a property to be a perfection. You might understand it like this: a property is a perfection of beings just in case it is better for beings that at least one being has that property than it is that no beings have the property. Or like this: a property is a perfection of beings just in case, for any being, it is better that that being has the property than it is that that being lacks the property. Or perhaps you might understand it in some other way. However you understand it, when you come to specify the property, you make some reference to beings, or to all beings, or the like. Properties are properties of beings: beings are the bearers of properties. If a property is a property of something, then there is some being that has that property.

Just as the class of perfections is defined over the entire class of beings, there are restricted classes of perfections that are defined over sub-classes of the class of beings. So, for example, there are the Martian perfections: the properties that are perfections for Martians, i.e. of intelligent native inhabitants of the planet Mars. You might understand it like this: a property is a Martian perfection just in case it is better for Martians that at least one Martian has that property than it is that no Martians have that property. Or like this: a property is a Martian perfection just in case, for any Martian, it is better that that Martian has the property than it is that that Martian lacks the property. Or perhaps you might understand it in some other way.

Consider the following argument:

1. 1. Rod has every Martian perfection. (Definition)

2. 2. Existence is a Martian perfection. (Premise)

3. 3. (Therefore) Rod has existence, i.e. Rod exists.

Just as the first argument purports to establish the existence of a being – God – that has every perfection for beings, this argument purports to establish the existence of a Martian – Rod – that has every perfection for Martians.

Of course, nobody thinks that this argument is successful. Nobody thinks that we should take seriously supposes that there are any intelligent native inhabitants of the planet Mars. But this argument is on all fours with the previous argument.

First, if we are prepared to grant that existence is a perfection, then we ought to be prepared to grant that existence is a Martian perfection. If we are to accept that it is better for beings that at least one being exists than it is that no beings exist, then we should also accept that it is better for Martians that at least one Martian exists than it is that no Martians exist. If we are to accept that, for any being, it is better that that being exists than it is that that being does not exist, then we should also accept that, for any Martian, it is better that that Martian exists than it is that that Martian does not exist. And so on. It would be intolerably ad hoc to suppose that existence is a perfection for beings in general, and yet not a perfection for particular kinds of beings, e.g. Martians.

Second, if we are prepared to accept the definition of God as the being that has every perfection for beings, then we should also be prepared to accept the definition of Rod as the Martian that has every perfection for Martians. If we can frame the concept of a being that has every perfection, then we can certainly frame the concept of a Martian that has every Martian perfection. And, if we can frame both of these concepts, then we can certainly construct definitions that make use of them. Note, by the way, that it does not matter if we cannot say exactly which properties are perfections for beings and which properties are perfections for Martians. It is standard for religious believers to insist that we do not know exactly what the perfections for being are; it would be intolerably ad hoc to insist that we cannot also allow that we do not know exactly what the perfections for Martians are.

If what I have just said is right, then these two arguments stand or fall together. But, obviously, the second argument falls. So we can conclude that the first argument falls: the first argument is not a successful argument for the existence of God. If you want to insist that only the first argument is successful, then, at the very least, you need to point to some relevant difference between the first argument and the second argument. But what could that difference be?

I anticipate that some might say: there is something wrong with the definition in the second case, but not in the first case. After all, while there is no such thing as Rod, there is such a thing as God. The definition that was being offered in each case was not a merely ‘nominal’ definition: the attachment of a meaning to an arbitrarily selected word. Rather, the definition in each case was meant to be a ‘real’ definition of an existing thing. And a definition of that kind does not succeed if there is nothing that answers to the definition.

Suppose that we accept these somewhat fanciful uses of the words ‘nominal’ and ‘real’; suppose, in particular, that a definition is only ‘real’ if there is some existing thing that answers to it. Go back to the definition in the first argument: God has every perfection. There are two cases. If God exists, then this is, we may suppose, a real definition of God. But, if God does not exist, then this is not a real definition of God. So, we have an argument, with the conclusion that God exists, that has a definitional premise whose acceptability turns directly on whether or not God exists. Since we cannot determine whether the premise is acceptable without first determining whether God exists, we can hardly use this argument to settle the question whether God exists.

There is a wider perspective on arguments that delivers the same conclusion. Suppose that a theist and an atheist are arguing about whether God exists. Suppose, further, that the theist gives the first argument to the atheist. ‘Look. You should accept that God exists, because it is true by definition that God has every perfection, and existence is a perfection.’ What would you expect the atheist to say? ‘Oh, dear, I might as well just pack it in …’ Hardly! The atheist thinks that God does not exist. So the atheist thinks that the proposed definition of God is not a ‘real’ definition. So the atheist thinks that the premises of the first argument are in no better standing than the premises of the second argument. So the atheist is on very solid ground in maintaining that the first argument is unsuccessful.

Still, you might think, there is something unsatisfactory here. Even if we agree that there is something wrong with both arguments, we have not identified exactly what it is that is wrong with those arguments. For all we have said so far, it could be that both of the premises in each of the arguments are true. How, then, could it be that the arguments both fail? To answer this question, it will help us to do some preliminary thinking about non-existent objects.

There are things that we suppose do not exist. Consider Santa Claus. Santa Claus has a white beard. Santa Claus wears a red suit. Santa Claus lives at the North Pole. Santa Claus has a flying sleigh. Santa Claus brings presents to children at Christmas. Santa Claus does not exist.

Hang on! How can something that does not exist have a white beard, wear a red suit, live at the North Pole, have a flying sleigh and deliver presents to children at Christmas? If Santa Claus lives at the North Pole, then someone lives at the North Pole. And if someone lives at the North Pole, then the North Pole is inhabited. If Santa Claus has a flying sleigh, then someone has a flying sleigh. And if someone has a flying sleigh, then there are flying sleighs. But the North Pole is uninhabited and there are no flying sleighs. So it is not true that Santa lives at the North Pole; it is not true that Santa has a flying sleigh. For similarly obvious reasons, it is not true that Santa has a white beard and a red suit; and it is not true that Santa delivers presents to children at Christmas.

It is tempting to say: if Santa Claus does not exist, he has no properties. But, when we say that Santa Claus does not exist, we seem to be saying that there is some particular thing that fails to exist. And if there is some particular thing that fails to exist, then that thing must have properties that distinguish it from other particular things that fail to exist. Consider Superman. Superman is not Santa Claus. Superman does not exist. But, if Superman has no properties, and Santa Claus has no properties, then what makes it the case that Superman is not Santa Claus?

It might occur to you that we could say that certain claims about Santa Claus and Superman are simply true by definition. By definition, Santa Claus is the red-suited, white-bearded, North-Pole-dwelling, flying-sleigh-piloting deliverer of presents to children at Christmas; by definition, Superman is the blue-suited, red-caped, crime-fighting inhabitant of Metropolis. The claims that we are ordinarily prepared to accept about Santa Claus and Superman are not made true by the properties possessed by Santa Claus and Superman; rather, they are made true by the definitions that we make of ‘Santa Claus’ and ‘Superman’. Nonetheless, there is nothing that answers to the definitions of ‘Santa Claus’ and ‘Superman’: Santa Claus and Superman do not exist.

Can we rest content with this? I do not think so. If it is true by definition that Santa Claus lives at the North Pole, then it is true that Santa Claus lives at the North Pole. If it is true that Santa Claus lives at the North Pole, it is true that someone lives at the North Pole. If it is true that someone lives at the North Pole, it is true that the North Pole is inhabited. But it is not true that the North Pole is inhabited. We cannot save the ways that we ordinarily speak about Santa Claus and Superman by supposing that the claims that we ordinarily make about them are simply true by definition.

What we should hang onto here is the claim that it is not true, strictly speaking, that Santa Claus lives at the North Pole. After all, speaking strictly, Santa Claus does not exist. When we happily say that Santa Claus lives at the North Pole, we are speaking loosely. Perhaps our speech is elliptical: we commit ourselves only to the claim that, according to the Santa Claus story, Santa Claus lives at the North Pole. Perhaps our speech involves an element of pretence: it is only when we are playing along with the Santa Claus story that we are happy to say that Santa Claus lives at the North Pole. Or perhaps there is some other account to be given of why this is mere loose speech.

Granted a distinction between strict and loose speech, we can see that the circumstances in which we are prepared to say that Santa Claus lives at the North Pole should also be circumstances in which are are prepared to say that Santa Claus exists. According to the Santa Claus story, Santa Claus exists. If we are playing along with the Santa Claus story, we are happy to say that Santa Claus exists. The puzzles with which we began arise only because we do not always pay careful attention to the degree of strictness that attends to the claims that we are endorsing.

Return, now, to the argument about Rod. If we speak loosely, we can endorse the claim that Rod has every Martian perfection. It is true, according to the Rod story, that Rod has every Martian perfection. If we are playing along with the Rod story, we are happy to say that Rod has every Martian perfection. But, if we treat the argument about Rod by the standards of loose speech, the conclusion that we get is only that, loosely speaking, Rod exists. And that conclusion is innocuous: while it is true that, according to the Rod story, Rod exists, it is not true, strictly speaking, that Rod exists.

With this account of the argument about Rod in hand, we can explain why the initial argument about God is unsuccessful. True enough, if you believe in God, you may think that it is strictly speaking true that God has all of the perfections of beings. Consequently, if you believe in God, you may think that the argument is sound, treating it by the strictest standards of speech. But, if you do not believe in God, then you should think only that it is loosely speaking true that God has all of the perfections of beings. And, if that is what you think, then the argument can, at best, get you to the innocuous conclusion that, according to the God story, God exists. By the lights of atheists, when they speak strictly, it is simply not true that God has all of the perfections of beings – and that suffices to establish that our simple ontological argument is unsuccessful, i.e. no proof of the existence of God.

It is perhaps worth noting how minimal this criticism of our simple ontological argument is. There are many other criticisms that some might want to make of this argument. Some may say that the argument is question-begging, i.e. that it assumes what it sets out to prove. Some may say that the first premise is ill-formed: you cannot make proper definitions of beings using existence-entailing predicates. Some may say that the second premise entails, falsely, that existence is a real property of beings. Some may say that the second premise is false because, even though existence is a real property of beings, it is not a perfection of them. I think that all of these criticisms are too controversial and too complicated to do justice to the obvious failure of our simple ontological argument.

There is no agreement among philosophers about what makes an argument question-begging. There is no agreement among philosophers about whether you can use existence-entailing predicates in definitions. There is no agreement among philosophers about whether existence is a real property of beings. There is no agreement among philosophers about whether existence is a perfection of beings. Moreover, there is no agreement among atheists about any of these things. Some – but not all – atheists think that our simple ontological argument is question-begging. Some – but not all – atheists think that you cannot use existence-entailing predicates in definitions. Some – but not all – atheists think that existence is not a real property of beings. Some – but not all – atheists think that existence is not a perfection. For myself, I am inclined to deny that the simple argument is question-begging, and inclined to think that you can use existence-entailing predicates in definitions, and inclined to think that existence is a real property of beings, and perhaps even inclined to think that existence is a perfection.

Of course, I should admit that my way with the simple ontological argument is also controversial. Some philosophers think that, speaking strictly, there are non-existent objects, and, also speaking strictly, that those non-existent objects have properties. Those philosophers may well think that it is just true that Rod has all of the perfections of Martians, and that it is just true that God has all of the perfections of beings. Philosophers with these kinds of commitments are bound to insist that you cannot use existence-entailing predicates in definitions: while, for them, it may be true that the circular square is circular, it is certainly not true for them that the existent circular square is existent. While theories of non-existent objects have their attractions, you certainly do not need to buy into them in order to get a satisfying explanation of the failure of our simple ontological argument.