ontooppy

 

Ontological Arguments

Typically, when Australasian philosophers get together to sing, one of their first choices—to the tune of the unofficial Australian national anthem, Waltzing Matilda—is The Ballad of St. Anselm:

Once a jolly friar got himself an argument
And couldn't get it out of his mind.
He thought he could prove the existence of the Deity
Because of the way that the words are defined.

Thus spake St. Anselm, thus spake St. Anselm,
Thus spake St. Anselm, who now is long dead,
And we're awed as we read his proof so ontological;
Who can deny a word that he said?

If that than which nothing greater can be conceived
Can be conceived not to exist,
Then 'tis not that than which nothing greater can be conceived:
This is unquestionable, I insist.

For in that case a being greater can be conceived,
Whose major traits we can easily list:
Namely, that than which nothing greater can be conceived
And which cannot be conceived not to exist.

For if that than which nothing greater can be conceived
Has no existence outside of man's mind,
Then 'tis not that than which nothing greater can be conceived,
Due to the way that the words are defined.

For in that case a greater can be conceived
(This is of course analytically true);
Namely, that than which nothing greater can be conceived
And which exists in reality too!

Thus spake St. Anselm, thus spake St. Anselm,
Thus spake St. Anselm with weighty intent,
And we're awed as we read his proof so ontological
Would that we could understand just what it meant.

It is unlikely that any performance of this song—let alone any performance of it by Australasian philosophers—will top the charts. This is only in part because the lyrics are not entirely faithful to the ontological argument that St. Anselm devised.

0. Introduction and Outline

There are many different kinds of ontological arguments for the existence of God. All ontological arguments have a conclusion that is taken to evidently and immediately entail that God exists. In many cases, the conclusion of an ontological argument just is the claim that God exists. The logical rules that are supposed to justify the derivational steps in ontological arguments—and the logical systems to which those logical rules belong—are many and varied. While the logical rules required for some ontological arguments are relatively uncontroversial, there is serious dispute about the justification of the derivational steps in other ontological arguments. The premises of ontological arguments—and the key concepts or vocabulary employed in the framing of these premises—are also many and varied. In almost all ontological arguments, at least one of the premises is highly controversial.

A traditional characterisation of ontological arguments says that what these arguments have in common is that they purport to be a priori demonstrations of the existence of God. They are said to be a priori arguments because it is said that all of their premises can be known to be true independently of experience and empirical evidence; they are said to be demonstrations because it is said that their conclusions are logical consequences of their premises. Some say that ontological arguments appeal only to definitions of God; others say that ontological arguments appeal only to the concept or idea of God. While it is doubtful that much of the traditional characterisation of ontological arguments is exactly right, it will do to be going on with.

Significant defenders of ontological arguments include: Anselm [1033-1109], Descartes [1596-1650], Leibniz [1646-1716], Hegel [1770-1831], Gödel [1906-1978], Hartshorne [1897-2000], and Plantinga [b.1932]. Important critics of ontological arguments include: Gaunilo [fl. 11th century], Aquinas [1225-1274], Kant [1724-1804], Frege [1848-1925], Meinong [1853-1920], Findlay [1903-1987], Mackie [1917-1981], and Sobel [1929-2010].

In the coming discussion, we shall examine: (1) Anselm’s ontological argument and its criticism by Gaunilo; (2) Plantinga’s ontological argument and its criticism by Mackie and Sobel; and (3) a simplified version of Gödel’s ontological argument. We shall also look carefully at (4) Kant’s attempt to show that it is impossible for there to be a successful ontological argument. For more extensive survey and discussion of ontological arguments, readers may like to consult Oppy (1996) (2006).

1. Anselm and Gaunilo

Anselm’s ontological argument is set out in Proslogion II. Here is one well-regarded translation of the text from the original medieval Latin:

Even the Fool, then, is forced to agree that something than which nothing greater can be thought exists in the mind, since he understands this when he hears it, and whatever is understood is in the mind. And surely that than which a greater cannot be thought cannot exists in the mind alone. For if it exists solely in the mind even, it can be thought to exist in reality also, which is greater. If then that than which a greater cannot be thought exists in the mind alone, this same that than which a greater cannot be thought is that than which a greater can be thought. But this is obviously impossible. Therefore there is absolutely no doubt that something than which a greater cannot be thought exists both in the mind and in reality.

While there are many challenges to the interpretation of the argument contained in this text—and, indeed, while there are many different arguments that have been read into this text—it is plausible to reconstruct the argument along the following lines:

1. When the words ‘that than which no greater can be conceived’ are heard, they are understood. (Premise)

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

3. (Therefore) That than which no greater can be conceived exists in the understanding. (From 1, 2)

4. If that than which no greater can be conceived exists in the understanding alone, it can be conceived to exist in reality. (Premise)

5. That than which no greater can be conceived is greater if it exists in reality than if it exists in the understanding alone. (Premise)

6. (Therefore) If that than which no greater can be conceived exists in the understanding alone, it is something than which a greater can be conceived. (From 4, 5)

7. It is impossible to conceive of something greater than that than which no greater can be conceived. (Premise)

8. (Therefore) That than which no greater can be conceived does not exist in the understanding alone. (From 6, 7)

9. (Therefore) That than which no greater can be conceived exists in reality. (From 3, 8)

The key vocabulary that is used in framing this argument raises many questions. What is it for one thing to be ‘greater’ than another? What is required for it to be true that something ‘can be conceived’? What is meant by ‘the understanding’? What is it for something to ‘exist in the understanding’? How is ‘existence in the understanding’ related to being something that ‘can be conceived’? Can the very same thing ‘exist in the understanding’ and ‘exist in reality’? If so, does it have the very same properties ‘in the understanding’ and ‘in reality’? Since we certainly appear to understand the expression ‘the really existent tallest inhabitant of the planet Mars’, does Anselm think that the really existent tallest inhabitant of the planet Mars exists in the understanding? If so, does he think that, in the understanding, the really existent tallest inhabitant of the planet Mars has the property of really existing? If so, does he think that it follows that the really existent tallest inhabitant of the planet Mars has the property of really existing? Would Anselm be uncomfortable with a priori commitment to the existence of Martians? Would he deny that we understand the expression ‘the really existent tallest inhabitant of the planet Mars’? Would he say that, even though, in the understanding, the really existent tallest inhabitant of the planet Mars has the property of really existing, nonetheless it does not follow that that the really existent tallest inhabitant of the planet Mars has the property of really existing?

Some philosophers have thought that we do not need to answer all of these questions before we come to the conclusion that Anselm’s ontological argument is unsuccessful. In particular, some philosophers have thought that Anselm’s contemporary, Gaunilo of Marmoutiers, provided a method for showing that there must be something wrong with Anselm’s argument. Gaunilo’s strategy is to provide a parallel argument with an absurd conclusion and premises that are no less acceptable to the Fool than the premises of Anselm’s original argument:

1. When the words ‘that island than which no greater island can be conceived’ are heard, they are understood. (Premise)

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

3. (Therefore) That island than which no greater island can be conceived exists in the understanding. (From 1,2 )

4. If that island than which no greater island can be conceived exists in the understanding alone, it can be conceived to exist in reality. (Premise)

5. That island than which no greater island can be conceived is greater if it exists in reality than if it exists in the understanding alone. (Premise)

6. (Therefore) If than island than which no greater island can be conceived exists in the understanding alone, it is an island than which a greater island can be conceived. (From 4, 5)

7. It is impossible to conceive of an island greater than that island than which no greater island can be conceived. (Premise)

8. (Therefore) That island than which no greater island can be conceived does not exist in the understanding alone. (From 6, 7)

9. (Therefore) That island than which no greater island can be conceived exists in reality. (From 3, 8)

Since everyone agrees that the conclusion of Gaunilo’s argument is absurd, and since it is obvious that the derivational moves in the two arguments are exactly the same, it is clear that we can only defend Anselm’s original argument by defending the claim that, while one of the premises in Anselm’s original argument is acceptable, the corresponding premise in Gaunilo’s argument is not acceptable. Which premise might that be?

It seems obvious that the expressions ‘being than which no greater being can be conceived’ and ‘island than which no greater island can be conceived’ are on a par: we can be credited with understanding the one if and only if we can be credited with understanding the other.

It seems obvious that the claim that if that being than which no greater being can be conceived exists in the understanding alone it can be conceived to exist in reality stands or falls with the claim that if that island than which no greater island can be conceived exists in the understanding alone it can be conceived to exist in reality.

It seems no less obvious that that being than which no greater being can be conceived is greater if it exists in reality than if it exists in the understanding alone if and only if that island than which no greater island can be conceived is greater if it exists in reality than if it exists in the understanding alone.

It seems equally obvious that it is impossible to conceive of a being greater than a being than which no greater being can be conceived if and only if it is impossible to conceive of an island greater than an island than which no greater island can be conceived.

The only remaining premise—that whatever is understood exists in the understanding—is shared in common between the two arguments. In this case, we can be absolutely certain that the premise in Anselm’s argument is acceptable if and only if the corresponding premise in Gaunilo’s argument is acceptable.

Given that there is no premise in Anselm’s original argument that is more acceptable than the corresponding premise in Gaunilo’s argument, it seems that we are drawn to the conclusion that there is something wrong with Anselm’s argument.

It is sometimes said that Gaunilo’s objection fails because there is—and can be—no such thing as an island than which no greater island can be conceived. For example, Plantinga (1974: 91ff) says:

The idea of an island than which it is not possible that there be a greater is like the idea of a natural number than which it is not possible that there be a greater, or the idea of a line than which none more crooked is possible. There neither is nor could be a greatest possible number, indeed, there isn’t a greatest actual number. And the same goes for islands. No matter how great an island is, no matter how many Nubian maidens and dancing girls adorn it, there could always be a greater—one with twice as many, for example. The qualities that make for greatness in islands—number of palm trees, amount and quality of coconuts, for example—have no intrinsic maximum. That is, there is no degree of productivity or number of palm trees (or of dancing girls) such that it is impossible that an island display more of that quality. So the idea of a greatest possible island an inconsistent or incoherent idea; it’s not possible that there is such a being.

But how is this any criticism of Gaunilo’s objection? Gaunilo agrees that the Fool maintains that there is—and can be—no such thing as an island than which no greater island can be conceived. However, Gaunilo realises that the Fool also maintains that there is—and can be—no such thing as that than which no greater can be conceived.

It is worth noting that, in order to understand Anselm’s argument, we need to understand the words ‘something greater than that than which no greater can be conceived’. (You can check for yourself that these words occur in our reconstruction of the argument.) But, if whatever is understood is in the understanding, then there is, in the understanding, something greater than a being than which no greater can be conceived. And, in that case, it seems that premise 7 is simply false.

For the Fool, the expressions ‘that than which no greater can be conceived’, ‘that island than which no greater island can be conceived’, and ‘something greater than that than which no greater can be conceived’ are on a par: none of them refers to something that could possibly exist (in reality). Since there is nothing in Anselm’s argument that gives the Fool a reason to think that just one of these expressions—‘that than which no greater can be conceived’—refers to something that could possibly exist (in reality), there is nothing in Anselm’s argument that gives a neutral person—one who is initially undecided between the points of view of Anselm and the Fool—a reason to move towards Anselm’s position.

As we have already observed, even if you are persuaded by Gaunilo’s objection, you may well be uncertain exactly why Anselm’s argument fails. It is because the argument is invalid? Is it because the argument is question-begging? Is it because at least one of the premises is plainly unacceptable (at least to neutral parties and friends of the Fool)? It is part of the lasting fascination of Anselm’s argument that there is no agreed answer to these questions even among those who think that the argument is plainly unsuccessful.

2. Plantinga

Plantinga’s (modal) ontological argument may be set out as follows:

1. It is possible that there is an unsurpassably great being. (Premise)

2. (Therefore) There is an unsurpassably great being (From 1.)

A being is unsurpassably great if and only if it is both necessarily existent and necessarily maximally excellent (hence, in particular, necessarily omnipotent, necessarily omniscient, and necessarily perfectly good). It follows from this definition of unsurpassable greatness that a being is unsurpassably great if and only if it is necessarily unsurpassably great.

The vast majority of philosophers accept that this argument is valid. In order to deny the validity of this argument, you need to reject one or both of the following two claims: first, that, if it is possible that it is necessary that p, then it is necessary that p; and, second, that if it is necessary that p, then it is the case that p. I do not propose to contest—or examine—these claims here.

Perhaps the most obvious objection to Plantinga’s argument is motivated by consideration of the following argument:

3. It is possible that there is no unsurpassably great being. (Premise)

4. (Therefore) There is no unsurpassably great being. (From 1)

If you agree with Plantinga that there is an unsurpassably great being, then you will think that the first argument is sound; if you agree with those who deny that there is an unsurpassably great being, then you will think that the second argument is sound. Once we have both arguments before us, it is obvious that neither of these arguments provides anyone with any reason to change their views about whether there is an unsurpassably great being.

Perhaps you might think that, if you were initially confused—accepting the premise of one argument and the conclusion of the other—then the argument for which you accept the premise gives you a reason to reject the conclusion of the other argument. But that thought is evidently forlorn. There are two arguments here, and you ought to take that fact into account when you try to resolve the contradiction in your thought. Whichever way you go, you will end up thinking that one of these arguments is sound: but there is nothing in the arguments themselves to tell you which way you should revise your beliefs.

Plantinga agrees with this verdict. He acknowledges that judgments about the soundness of these two arguments simply tracks prior judgments about the truth of the conclusions of these two arguments. Nonetheless, Plantinga claims that the first argument is ‘victorious’. In his view, the first argument establishes that it is reasonable to believe the claim that there is an unsurpassably great being.

Suppose that you think that it is not reasonable to believe that there is an unsurpassably great being. Given minimal rationality, when you consider the claim that it is possible that there is an unsurpassably great being, you will recognise that, if it is not reasonable to believe that there is an unsurpassably great being, then it is also not reasonable to believe that it is possible that there is an unsurpassably great being. So, if you think that it is not reasonable to believe that there is an unsurpassably great being, then, given minimal rationality on your part, Plantinga’s ‘victorious’ argument will give you no reason to revise you belief that it is not reasonable to believe that there is an unsurpassably great being.

Suppose, instead, that you are undecided about whether it is reasonable to believe that there is an unsurpassably great being. Given minimal rationality, when you consider the claim that it is possible that there is an unsurpassably great being, you will recognise that, so long as you are undecided about whether it is reasonable to believe that there is an unsurpassably great being, you ought also be undecided about whether it is reasonable to believe that it is possible that there is an unsurpassably great being. So, if you are undecided about whether it is reasonable to believe that there is an unsurpassably great being, then, given minimal rationality on your part, Plantinga’s ‘victorious’ argument gives you no reason to move away from your indecision about whether it is reasonable to believe that there is an unsurpassably great being.

Perhaps you might think that, if you are initially confused—holding inconsistent beliefs about the reasonableness of believing that there is an unsurpassably great being—then Plantinga’s ‘victorious’ argument gives you a reason to accept the claim that there is an unsurpassably great being. But how could that be? Consider the following set of arguments:

5. It is reasonable to believe that it is possible that there is an unsurpassably great being. (Premise)

6. (Therefore) It is reasonable to believe that there is an unsurpassably great being. (From 5.)

7. It is reasonable to believe that it is possible that there is no unsurpassably great being. (Premise)

8. (Therefore) It is reasonable to believe that there is no unsurpassably great being. (From 7.)

9. It is not reasonable to believe that it is possible that there is an unsurpassably great being. (Premise)

10. (Therefore) It is not reasonable to believe that there is an unsurpassably great being. (From 9.)

11. It is not reasonable to believe that it is possible that there is no unsurpassably great being. (Premise)

12. (Therefore) It is not reasonable to believe that there is no unsurpassably great being. (From 11.)

There is nothing in the six arguments that we now have before us that tells us how to resolve inconsistency in our beliefs about whether it is reasonable to believe that there is an unsurpassably great being. In particular, Plantinga’s ‘victorious’ argument gives you no guidance at all about how you should resolve the inconsistency in your beliefs about whether it is reasonable to believe that there is an unsurpassably great being. Whichever way you revise your beliefs, some of these arguments will come out sound, and others will come out unsound. In themselves, these arguments simply give you no guidance at all about how to revise your beliefs.

3. A Simple Higher-Order Argument

Gödel’s ontological argument develops some ideas originally due to Leibniz. In what follows, I present a simplified version of Gödel’s argument. Although it is a simplified version of Gödel’s argument, it is still quite challenging. I begin with some definitions.

An object has a property essentially if and only if it is impossible for that object to exist and yet to lack that property. (I could lose all of my hair. So the property of being hairy is not one of my essential properties. On the other hand, I could not exist and yet be something other than human. So the property of being human is one of my essential properties.)

A collection of properties entails a further property if and only if, necessarily, anything that has all of the properties in the collection also has the further property. (Necessarily, anything that has the following four properties—being a plane figure, being closed, having three rectilinear sides, and having equal internal angles—has the further property of being an equilateral triangle. So the collection of properties—being a plane figure, being closed, having three rectilinear sides, having equal internal angles—entails the property of being an equilateral triangle.)

A collection of properties is closed under entailment if and only if any property that is entailed by a sub-collection of the properties in the collection of properties also belongs to the collection of properties. (For any existing object, the collection of its essential properties is closed under entailment. Suppose that a property P is entailed by an object’s essential properties. Since the property P is entailed by the object’s essential properties, it is impossible for the object to exist without having the property P. But that’s just to say that the property P is one of the object’s essential properties.)

A property is a God-property if and only if it is one of the properties that God has essentially if God exists.

The core of our simple higher-order ontological argument is the following:

1. There are properties that are not God-properties. (Premise)

2. The God-properties are closed under entailment. (Premise)

3. (Therefore) It is possible that there is something that has all of the God-properties. (From 1, 2)

In order to argue that 3 follows from 1 and 2, we rely on the principle that, for any p and q, the claim necessarily, if p then q is true if it is impossible that p. This principle is one of the ‘paradoxes’ of classical logic. The vast majority of philosophers are happy to accept this principle.

We then argue that 3 follows from 1 and 2 as follows. Suppose (for reductio) that it is not possible that there is something that has all of the God-properties. By our first premise, there are properties that are not God-properties. Arbitrarily select one of them: the property P. Since it is not possible that there is something that has all of the God-properties, it follows by the principle noted above that, necessarily, anything that has all of the God-properties has property P. But that’s just to say that the God-properties entail property P. So, by our second premise, property P is one of the God-properties. But that means that property P both is, and is not, one of the God-properties. Contradiction! We conclude (by reductio) that our initial supposition is false: it is possible that there is something that has all of the God-properties.

It seems plausible to suppose that there are properties that are not God-properties. Consider the property of being ignorant about almost everything. Surely, if God exists, that is not one of God’s properties.

It seems plausible that the God-properties are closed under entailment. After all, as we noted earlier, for any existing object, the collection of its essential properties is closed under entailment. Clearly, if God exists, the God-properties are closed under entailment.

So, it seems, we have very good reason to accept that it is possible that there is something that has all of the God-properties. But, now, let’s ask: what properties number among the God-properties, i.e. among the properties that God has essentially if God exists. Many theists say that the properties that God has essentially if God exists include: omnipotence, omniscience, perfect goodness and necessary existence. Suppose that those theists are right. Then we can argue as follows:

1. It is possible that there is something that has all of the God-properties.

2. The God-properties include: necessary omnipotence, necessary omniscience, necessary perfect goodness and necessary existence.

3. (Therefore) There is something that has all of the God-properties. (From 1, 2)

4. (Therefore) God exists. (From 3)

To justify the move from 1 and 2 to 3, we observe that, given 2, 1 says that it is possible that there is something that is necessarily omnipotent, necessarily omniscient, necessarily perfectly good and necessarily existent. Since it is possible that there is this necessarily existent thing, it follows that this thing actually exists. Moreover, since it is possible that this thing is necessarily omnipotent, necessarily omniscient, and necessarily perfectly good, it follows that this thing is necessarily omnipotent, necessarily omniscient, and necessarily perfectly good. The justification of the move from 3 to 4 is straightforward: the thing that we have just been discussing has every one of the properties that God has essentially if God exists; so, of course, it is God.

How might one object to this simplified higher-order ontological argument?

Well, let’s start with this: if we are supposing that, were God to exist, God would be necessarily existent, necessarily omnipotent, necessarily omniscient, and necessarily perfectly good, then, of course, those who deny that God exists also deny that it is possible that God exists. So, by the lights of those who deny that it is possible that God exists, the properties that God has essentially if God exists cannot be had by anything. But that’s just to say that, necessarily, anything that has all of the properties that God has essentially if God exists has every property. In other words, by the lights of those who deny that it is possible that God exists, every property is a God-property. If we suppose that, were God to exist, God would be necessarily existent, necessarily omnipotent, necessarily omniscient, and necessarily perfectly good, then—on the assumption that the God-properties are closed under entailment—there are properties that are not God-properties if and only if God exists.

Recall our earlier justification for the claim that there are properties that are not God properties. It is true that, if God exists, the property of being ignorant about almost everything is not one of God’s properties. But, for those who deny that God exists, the claim if God exists, the property of being ignorant about almost everything is not one of God’s properties is only trivially true, because the claim that God exists is necessarily false. For those who deny that God exists, the claim if God exists, then the property of being ignorant about almost everything is one of God’s properties is also trivially true, for the same reason. Since, for those who deny that God exists, every sentence of the form if God exists, then God has property p essentially is trivially true, it follows that, by their lights, every property is a God-property.

Perhaps proponents of the argument might think to reply that we ought to understand the conditional that occurs in the definition of God-property in a way that means that it is not trivialised if the antecedent of that conditional is impossible. After all, there are ways of understanding conditionals on which claims of the form if God exists, God has property P essentially do not come out trivially true if it is impossible that God exists. So why not adopt one of those ways of understanding conditionals?

Short answer: because, as we noted way back, the derivation at the core of our simple higher-order ontological argument depends upon the claim that conditionals with impossible antecedents are trivially true. In order to derive the claim that it is possible that there is something that has all of the God-properties from the claim that there are properties that are not God-properties and the claim that the God-properties are closed under entailment, we need to suppose that conditionals with impossible antecedents are trivially true. Given that we make this supposition, we are obliged to accept that conditionals of the form if God exists, God has property P essentially are trivially true if it is impossible that God exists.

The upshot of our examination of our simple higher-order ontological argument is clear. Those who suppose that God necessarily exists will suppose that the argument is sound; but those who deny that it is possible that God exists will suppose that the argument is unsound. Moreover, holding fixed commitment to the claim that the God-properties are closed under entailment, those who suppose that God necessarily exists will suppose that there are properties that are not God-properties while those who deny that it is possible that God exists will suppose that all properties are God-properties. Since the argument contains as a premise the claim that there are properties that are not God-properties, the argument is powerless to decide between that claim and its denial. Consequently, the argument provides no assistance in deciding between worldviews according to which God necessarily exists and worldviews according to which it is not possible that God exists.

4. Kant

In the Critique of Pure Reason (in the Transcendental Doctrine of Elements, Second Division, Book II, Chapter III, Section IV), Kant argues for the impossibility of an ontological proof of the existence of God. The only ontological argument that Kant actually mentions is that of Descartes, but there is no textual citation. So it is not entirely clear which version of Descartes’ argument—Discourse, Meditations, or Replies—Kant has in mind. Since the discussion in the Discourse is a good fit, we will run with that.

In the Discourse, Descartes writes as follows:

[E]xistence is comprised in the idea [of a perfect being] in the same way that the equality of the three angles of a triangle to two right angles is comprised in the idea of a triangle. … [C]onsequently, it is at least as certain that God … exists as any geometric demonstration can be. (57)

In what looks like a direct response to this passage, Kant writes:

To posit a triangle, and yet to reject its three angles, is self-contradictory; but there is no contradiction in rejecting the triangle together with its three angles. The same holds true of the concept of an absolutely necessary being. If the existence is rejected, we reject the thing itself with all its predicates; and no question of contradiction can then arise. (502)

The relevant geometrical proposition is that, in all triangles, the internal angles sum to 180 degrees. The necessary truth of this proposition does not require the existence of even one triangle. By analogy, the relevant theological proposition is that all perfect beings exist. The necessary truth of this proposition does not require the existence of even one perfect being.

If it is said that God is a perfect being—and so exists—then the obvious question to ask is whether those who deny that there are any perfect beings should accept the claim that God is a perfect being. If we agree that the claim that God is a perfect being entails the claim that there are perfect beings, then it is clear that those who deny that there are any perfect beings should deny that God is a perfect being. By their lights, the most that is true is that, according to some theists, God is a perfect being. But there is no legitimate way to move from the premise that, according to some theists, God is a perfect being, to the conclusion that God is a perfect being (still less to the conclusion that God exists).

Consider the claim that Santa Claus lives at the North Pole. Is that true? Surely not! If Santa Claus lives at the North Pole, then there is someone who lives at the North Pole. But we all know that there isn’t anyone living at the North Pole. The most that is true is that, according to the well-known story, Santa Claus lives at the North Pole. And, plainly enough, there is no legitimate way to move from the premise that, according to the well-known story, Santa Claus lives at the North Pole, to the conclusion that there is someone who lives at the North Pole.

If you have a residual urge to insist that it is true that Santa Claus lives at the North Pole, consider the following case. The idea of existence is comprised in the idea of an existent Martian. I introduce the name ‘Rod’ for the oldest existent Martian. Now, consider the claim that Rod is an oldest existent Martian. Is this claim true? Surely not! If Rod is an oldest existent Martian, then there are existent Martians, i.e. there really are Martians! But it is not true that there really are Martians. Even if you do suppose that there are Martians, you should surely deny that you can prove that there are Martians by consideration of the claim that Rod is an oldest existent Martian.

In response to this kind of objection, Descartes says that the concept of an existent Martian differs from the concept of a perfect being because the former concept is artificial whereas the latter concept is natural. But this consideration is irrelevant. That all existent Martians exist is no less a necessary truth than that all perfect beings exist. If it is fine to infer that God exists from the claim that God is a perfect being, then it is fine to infer that Rod exists from the claim that Rod is an oldest existent Martian.

Kant’s ambition extends much further than criticism of Descartes’ arguments. He aims to show that it is impossible for there to be a successful ontological argument. Famously, he writes:

‘Being’ is obviously not a real predicate, that is, it is not a concept of something which could be added to the concept of a thing. It is merely the positing of a thing, or of certain determinations, as existing in themselves. Logically, it is merely the copula of a judgment. The proposition ‘God is omnipotent’ contains two concepts, each of which has its object—God and omnipotence. The small word ‘is’ adds no new predicate, but only serves to posit the predicate in its relation to the subject.

Kant think that the proposition ‘God is omnipotent’ is a necessary judgment, because omnipotence is contained in the concept of God. On his analysis, ‘God’ is the subject of the proposition, ‘omnipotent’ is the predicate, and ‘is’ is merely a copula that ‘relates the predicate to the subject’. In his view, the proposition ‘God exists’ is the same as the proposition ‘God is’, and in this proposition ‘is’ has the same function that it has in the proposition ‘God is omnipotent’.

I think that he is wrong about nearly all of this. In English, there are two quite distinct uses for the word ‘is’: it is standard to distinguish between the ‘is’ of existence and the ‘is’ of predication. In the proposition ‘God is omnipotent’, while the subject is ‘God’, the predicate is ‘is omnipotent’. Since the proposition ‘God is omnipotent’ entails the proposition ‘God exists’, it is utterly controversial whether ‘God is omnipotent’ is a necessary judgment. As we saw earlier, those who deny that God exists also deny that God is omnipotent, while accepting that, according to many theists, God is omnipotent. (‘If God exists, God is omnipotent’ is a plausible candidate to be a necessary judgment. But, of course, it does not entail that God exists.) In order to mark the salient ontological difference between Santa Claus and Barack Obama, we need to be able to affirm that only Barack Obama exists: so there is a way in which only our concept of Barack Obama ‘contains existence’. But the story of Santa Claus does not say that Santa Claus is a non-existent object that lives at the North Pole: there is also a way in which our concept of Santa Claus ‘contains existence’ (just as it ‘contains living at the North Pole’). What Kant needs—but lacks—is the distinction between the part or aspect of our Santa Claus concept that reflects the ontological reality about Santa Claus and the part of aspect of our Santa Claus concept that reflects the content of the familiar Christmas story. While Santa Claus does not exist, the story says that Santa Claus exists. Non-theists say the same about God: the theistic story says that God exists, and, on many variants of that story, necessarily so; but, nonetheless, God does not exist.

In my view, Kant’s attempt to show that it is impossible for there to be a successful ontological argument fails. This is not merely because so many of the details of his discussion are mistaken. Setting those failures aside, it is not clear how his critique would apply to the vast majority of ontological arguments. While Kant strikes some significant blows against Descartes’ ontological arguments, it is unclear that his critique has any force against the ontological arguments of Anselm, Plantinga, and Gödel. And who is to say what other forms of ontological arguments might come to light in the future?

Concluding Remarks

Although philosophers have been discussing ontological arguments for nearly one thousand years, there is no expert agreement on the general standing of ontological arguments. Throughout that history, some of the best and smartest philosophers have supposed that particular ontological arguments successfully prove the existence of God, while others have maintained that it is obvious that no ontological arguments can be successful.

In this discussion, I have charted a middle path. On the one hand, I have urged that none of the ontological arguments considered here—Anselm’s Proslogion II argument, Plantinga’s ‘victorious’ modal argument, and our simplified version of Gödel’s argument—is successful. On the other hand, I have emphasised (a) that we have only examined some among the many extant ontological arguments; (b) that it is very likely that there will be new and challenging ontological arguments devised in the future; and (c) that extant arguments for the claim that there could not be a successful ontological argument are no more successful than the ontological arguments that we have examined here.

My discussion of the arguments of Anselm, Plantinga, and [simplified] Gödel illustrates some of the main strategies taken up by critics of ontological arguments. Against Anselm, it was suggested that there are parallel arguments with absurd conclusions whose credentials are on a par with those of the Proslogion II argument. Against Plantinga, it was observed that there are parallel arguments with exactly opposed conclusions whose credentials are on a par with those of the ‘victorious’ modal argument. Against [simplified] Gödel, it was claimed that the core of the argument depends upon a principle whose acceptance provides a defeater for the first premise of the argument. In the face of an ontological argument, it is often illuminating to think about parallel arguments with absurd conclusions, parallel arguments with exactly opposed conclusions, and possible ways in which the argument might be self-defeating. Of course, there are ontological arguments that are obviously invalid, and there are ontological arguments that are obviously unsound. But interesting ontological arguments—including those considered in this chapter—typically do not have readily pinpointed features in virtue of which they are invalid or unsound.

My discussion of Kant illustrates some of the main strategies taken up by critics of those who purport to be able to prove that there cannot be a successful ontological argument. In the face of a purported demonstration that there cannot be a successful ontological argument, it is often illuminating to consider the implications of that demonstration for what we can say about fictional objects and things that we agree do not exist. If a purported demonstration that there cannot be a successful ontological argument has the consequence that it is unproblematically and straightforwardly true that Santa Claus lives at the North Pole, then there is good reason to doubt that the purported demonstration succeeds.

Annotated Bibliography

Charlesworth, M. (1965) St. Anselm’s Proslogion Oxford: Clarendon

Annotated translation of, and commentary upon, the Proslogion, together with Gaunilo’s response, and Anselm’s reply to Gaunilo.

Mackie, J. (1982) The Miracle of Theism Oxford: Clarendon

Careful and detailed discussion of arguments for and against the existence of God. The chapter on ontological arguments includes discussion of Anselm, Descartes, Kant and Plantinga.

Oppy, G. (1996) Ontological Arguments and Belief in God New York: Cambridge University Press

Book length treatment of ontological arguments. Identifies six major types of ontological arguments, and provides detailed discussion of each type. Also has chapters on existence, parody, and purported global objections to ontological arguments.

Oppy, G. (2006) Arguing about Gods New York: Cambridge University Press

General discussion of arguments about the existence of God. Chapter on ontological arguments extends the discussion in Oppy (1996) by taking up two additional types of ontological arguments: mereological ontological arguments and higher-order ontological arguments (in particular, Gödel’s ontological argument).

Plantinga, A. (1974a) The Nature of Necessity Oxford: Clarendon

An extended defence of the claim that objects have both necessary and accidental properties. Contains the chapter on ontological arguments in which Plantinga first introduces his ‘victorious’ modal ontological argument.

Plantinga, A. (1974b) God, Freedom and Evil London: Allen & Unwin

Popular, and less technical, presentation of material found in Plantinga (1974a). Section on ontological arguments covers some—but not all—of the ground that is covered in the corresponding chapter in Plantinga (1974a).

Sobel, J. (2004) Logic and Theism Cambridge: Cambridge University Press

Rigorous and careful analysis of a wide range of arguments about the existence of God. One chapter on the ontological arguments of Descartes, Spinoza and Anselm; one chapter on the ontological arguments of Hartshorne and Plantinga; and one chapter on Gödel’s ontological argument.

Terms (for Glossary)

A priori: A claim is said to be knowable a priori if and only if it can be known independently of experience and the acquisition of empirical evidence. When a claim is said to be a priori, what is meant is that it can be known a priori.

A posteriori: A claim is said to be knowable only a posteriori if and only if it can only be known on the basis of experience and the acquisition of empirical evidence. When a claim is said to be a posteriori, what is meant is that it is knowable only a posteriori.

Argument: Sometimes, ‘argument’ means a set of claims, one of which is identified as the conclusion, and the rest of which are premises. Other times, ‘argument’ means a derivation of a conclusion from a set of premises, with justification for each step along the way.

Concept: The word ‘concept’ is used in different ways by different philosophers. Sometimes, it is used to refer to mental representations. Other times, it is used to refer to the contents of mental representations. ‘Your concept of a dog’ might be a mental item—an aspect of your current mental state—or it might be what you take dogs to be.

Conclusion: The terminal point of an argument: the final claim that is meant to be established or supported by the argument.

Entailment: Entailment is a relationship between propositions. A entails B if and only if it is logically necessary that if A then B. That John is tired and emotional entails that John is tired.

Logical Rule: A rule that can be appealed to in the justification of a step in a derivation where it is intended that the conclusion is a logical consequence of the premises. An example of a logical rule is modus ponens: B is a logical consequence of A and if A then B.

Modal: Modal auxiliary verbs—ought, can, may, must, could, should, etc.—indicate likelihood, ability, permission, obligation, possibility and necessity. Modal logic is the study of the logic of likelihood, ability, permission, obligation, possibility and necessity.

Necessity: A claim is necessary if it must be true. A claim is absolutely necessary if it must be true no matter what. A claim is conditionally necessary if it must be that, given a certain condition, the claim is true. Many people think that the claims of elementary arithmetic—e.g. that 2+2=4—are absolutely necessary.

Possibility: A claim is possible if it could be true. It is possible that p if and only if it is not the case that it is necessary that not p. The most fundamental principle about possibility is that whatever is the case is possible.

Premise: A premise in an argument is one among the claims from which the conclusion can be derived, or from which it is alleged that the conclusion can be derived. In the argument All Greeks are mortal; Socrates is Greek; therefore Socrates is mortal, the two premises are that all Greeks are mortal and that Socrates is Greek.

Property: According to standard philosophical usage, a property is what is expressed by a predicate. In the sentence John is happy, the predicate ‘is happy’ expresses the property of happiness, and the sentence attributes this property to John.

Soundness: An argument is sound iff (a) it is valid, and (b) all of its premises are true. An argument can be valid but unsound: in that case, while its conclusion is a logical consequence of its premises, one or more of the premises is false. Consider, for example: All American presidents are aliens; Barack Obama is an American president; therefore Barack Obama is an alien.

Validity: An argument is valid iff its conclusion really is a logical consequence of its premises. In classical logic, an argument is valid just in case it is impossible both for all of the premises of the argument to be true and for the conclusion to be false. The argument All cricketers are immoral; W. G. Grace is a cricketer; therefore W. G. Grace is immoral is a valid argument.