The Ontological Argument Essay

Anselm: Ontological Argument for God's Existence

One of the most fascinating arguments for the existence of an all-perfect God is the ontological argument. While there are several different versions of the argument, all purport to show that it is self-contradictory to deny that there exists a greatest possible being. Thus, on this general line of argument, it is a necessary truth that such a being exists; and this being is the God of traditional Western theism. This article explains and evaluates classic and contemporary versions of the ontological argument.

Most of the arguments for God's existence rely on at least one empirical premise. For example, the "fine-tuning" version of the design argument depends on empirical evidence of intelligent design; in particular, it turns on the empirical claim that, as a nomological matter, that is, as a matter of law, life could not have developed if certain fundamental properties of the universe were to have differed even slightly from what they are. Likewise, cosmological arguments depend on certain empirical claims about the explanation for the occurrence of empirical events.

In contrast, the ontological arguments are conceptual in roughly the following sense: just as the propositions constituting the concept of a bachelor imply that every bachelor is male, the propositions constituting the concept of God, according to the ontological argument, imply that God exists. There is, of course, this difference: whereas the concept of a bachelor explicitly contains the proposition that bachelors are unmarried, the concept of God does not explicitly contain any proposition asserting the existence of such a being. Even so, the basic idea is the same: ontological arguments attempt to show that we can deduce God's existence from, so to speak, the very definition of God.

Table of Contents

  1. Introduction: The Non-Empirical Nature of the Ontological Arguments
  2. The Classic Version of the Ontological Argument
    1. The Argument Described
    2. Gaunilo's Criticism
    3. Aquinas's Criticisms
    4. Kant's Criticism: Is Existence a Perfection?
  3. Anselm's Second Version of the Ontological Argument
  4. Modal Versions of the Argument
  5. References and Further Reading

1. Introduction: The Non-Empirical Nature of the Ontological Arguments

It is worth reflecting for a moment on what a remarkable (and beautiful!) undertaking it is to deduce God's existence from the very definition of God. Normally, existential claims don't follow from conceptual claims. If I want to prove that bachelors, unicorns, or viruses exist, it is not enough just to reflect on the concepts. I need to go out into the world and conduct some sort of empirical investigation using my senses. Likewise, if I want to prove that bachelors, unicorns, or viruses don't exist, I must do the same. In general, positive and negative existential claimscan be established only by empirical methods.

There is, however, one class of exceptions. We can prove certain negative existential claims merely by reflecting on the content of the concept. Thus, for example, we can determine that there are no square circles in the world without going out and looking under every rock to see whether there is a square circle there. We can do so merely by consulting the definition and seeing that it is self-contradictory. Thus, the very concepts imply that there exist no entities that are both square and circular.

The ontological argument, then, is unique among such arguments in that it purports to establish the real (as opposed to abstract) existence of some entity. Indeed, if the ontological arguments succeed, it is as much a contradiction to suppose that God doesn't exist as it is to suppose that there are square circles or female bachelors. In the following sections, we will evaluate a number of different attempts to develop this astonishing strategy.

2. The Classic Version of the Ontological Argument

a. The Argument Described

St. Anselm, Archbishop of Cantebury (1033-1109), is the originator of the ontological argument, which he describes in the Proslogium as follows:

[Even a] fool, when he hears of … a being than which nothing greater can be conceived … understands what he hears, and what he understands is in his understanding.… And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. For suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater.… Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.

The argument in this difficult passage can accurately be summarized in standard form:

  1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined).
  2. God exists as an idea in the mind.
  3. A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.
  4. Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).
  5. But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)
  6. Therefore, God exists.

Intuitively, one can think of the argument as being powered by two ideas. The first, expressed by Premise 2, is that we have a coherent idea of a being that instantiates all of the perfections. Otherwise put, Premise 2 asserts that we have a coherent idea of a being that instantiates every property that makes a being greater, other things being equal, than it would have been without that property (such properties are also known as "great-making" properties). Premise 3 asserts that existence is a perfection or great-making property.

Accordingly, the very concept of a being that instantiates all the perfections implies that it exists. Suppose B is a being that instantiates all the perfections and suppose B doesn't exist (in reality). Since Premise 3 asserts that existence is a perfection, it follows that B lacks a perfection. But this contradicts the assumption that B is a being that instantiates all the perfections. Thus, according to this reasoning, it follows that B exists.

b. Gaunilo's Criticism

Gaunilo of Marmoutier, a monk and contemporary of Anselm's, is responsible for one of the most important criticisms of Anselm's argument. It is quite reasonable to worry that Anselm's argument illegitimately moves from the existence of an idea to the existence of a thing that corresponds to the idea. As the objection is sometimes put, Anselm simply defines things into existence-and this cannot be done.

Gaunilo shared this worry, believing that one could use Anselm's argument to show the existence of all kinds of non-existent things:

Now if some one should tell me that there is … an island [than which none greater can be conceived], I should easily understand his words, in which there is no difficulty. But suppose that he went on to say, as if by a logical inference: "You can no longer doubt that this island which is more excellent than all lands exists somewhere, since you have no doubt that it is in your understanding. And since it is more excellent not to be in the understanding alone, but to exist both in the understanding and in reality, for this reason it must exist. For if it does not exist, any land which really exists will be more excellent than it; and so the island understood by you to be more excellent will not be more excellent."

Gaunilo's argument, thus, proceeds by attempting to use Anselm's strategy to deduce the existence of a perfect island, which Gaunilo rightly views as a counterexample to the argument form. The counterexample can be expressed as follows:

  1. It is a conceptual truth that a piland is an island than which none greater can be imagined (that is, the greatest possible island that can be imagined).
  2. A piland exists as an idea in the mind.
  3. A piland that exists as an idea in the mind and in reality is greater than a piland that exists only as an idea in the mind.
  4. Thus, if a piland exists only as an idea in the mind, then we can imagine an island that is greater than a piland (that is, a greatest possible island that does exist).
  5. But we cannot imagine an island that is greater than a piland.
  6. Therefore, a piland exists.

Notice, however, that premise 1 of Gaunilo's argument is incoherent. The problem here is that the qualities that make an island great are not the sort of qualities that admit of conceptually maximal qualities. No matter how great any island is in some respect, it is always possible to imagine an island greater than that island in that very respect. For example, if one thinks that abundant fruit is a great-making property for an island, then, no matter how great a particular island might be, it will always be possible to imagine a greater island because there is no intrinsic maximum for fruit-abundance. For this reason, the very concept of a piland is incoherent.

But this is not true of the concept of God as Anselm conceives it. Properties like knowledge, power, and moral goodness, which comprise the concept of a maximally great being, do have intrinsic maximums. For example, perfect knowledge requires knowing all and only true propositions; it is conceptually impossible to know more than this. Likewise, perfect power means being able to do everything that it is possible to do; it is conceptually impossible for a being to be able to do more than this.

The general point here, then, is this: Anselm's argument works, if at all, only for concepts that are entirely defined in terms of properties that admit of some sort of intrinsic maximum. As C.D. Broad puts this important point:

[The notion of a greatest possible being imaginable assumes that] each positive property is to be present in the highest possible degree. Now this will be meaningless verbiage unless there is some intrinsic maximum or upper limit to the possible intensity of every positive property which is capable of degrees. With some magnitudes this condition is fulfilled. It is, e.g., logically impossible that any proper fraction should exceed the ratio 1/1; and again, on a certain definition of "angle," it is logically impossible for any angle to exceed four right angles. But it seems quite clear that there are other properties, such as length or temperature or pain, to which there is no intrinsic maximum or upper limit of degree.

If any of the properties that are conceptually essential to the notion of God do not admit of an intrinsic maximum, then Anselm's argument strategy will not work because, like Guanilo's concept of a piland, the relevant concept of God is incoherent. But insofar as the relevant great-making properties are limited to omnipotence, omniscience, and moral perfection (which do admit of intrinsic maximums), Anselm's notion of a greatest possible being seems to avoid the worry expressed by Broad and Guanilo.

c. Aquinas's Criticisms

While St. Thomas Aquinas (1224-1274) believed that God's existence is self-evident, he rejected the idea that it can be deduced from claims about the concept of God. Aquinas argued, plausibly enough, that "not everyone who hears this word 'God' understands it to signify something than which nothing greater can be thought, seeing that some have believed God to be a body." The idea here is that, since different people have different concepts of God, this argument works, if at all, only to convince those who define the notion of God in the same way.

The problem with this criticism is that the ontological argument can be restated without defining God. To see this, simply delete premise 1 and replace each instance of "God" with "A being than which none greater can be conceived." The conclusion, then, will be that a being than which none greater can be conceived exists - and it is, of course, quite natural to name this being God.

Nevertheless, Aquinas had a second problem with the ontological argument. On Aquinas's view, even if we assume that everyone shares the same concept of God as a being than which none greater can be imagined, "it does not therefore follow that he understands what the word signifies exists actually, but only that it exists mentally."

One natural interpretation of this somewhat ambiguous passage is that Aquinas is rejecting premise 2 of Anselm's argument on the ground that, while we can rehearse the words "a being than which none greater can be imagined" in our minds, we have no idea of what this sequence of words really means. On this view, God is unlike any other reality known to us; while we can easily understand concepts of finite things, the concept of an infinitely great being dwarfs finite human understanding. We can, of course, try to associate the phrase "a being than which none greater can be imagined" with more familiar finite concepts, but these finite concepts are so far from being an adequate description of God, that it is fair to say they don't help us to get a detailed idea of God.

Nevertheless, the success of the argument doesn't depend on our having a complete understanding of the concept of a being than which none greater can be conceived. Consider, for example, that, while we don't have a complete understanding (whatever this means) of the concept of a natural number than which none larger can be imagined, we understand it well enough to see that there does not exist such a number. No more complete understanding of the concept of a maximally great being than this is required, on Anselm's view, to successfully make the argument. If the concept is coherent, then even a minimal understanding of the concept is sufficient to make the argument.

d. Kant's Criticism: Is Existence a Perfection?

Immanuel Kant (1724-1804) directs his famous objection at premise 3's claim that a being that exists as an idea in the mind and in reality is greater than a being that exists only as an idea in the mind. According to premise 3, existence is what's known as a great-making property or, as the matter is sometimes put, a perfection. Premise 3 thus entails that (1) existence is a property; and (2) instantiating existence makes a thing better, other things being equal, than it would have been otherwise.

Kant rejects premise 3 on the ground that, as a purely formal matter, existence does not function as a predicate. As Kant puts the point:

Being is evidently not a real predicate, that is, a conception of something which is added to the conception of some other thing. It is merely the positing of a thing, or of certain determinations in it. Logically, it is merely the copula of a judgement. The proposition, God is omnipotent, contains two conceptions, which have a certain object or content; the word is, is no additional predicate-it merely indicates the relation of the predicate to the subject. Now if I take the subject (God) with all its predicates (omnipotence being one), and say, God is, or There is a God, I add no new predicate to the conception of God, I merely posit or affirm the existence of the subject with all its predicates - I posit the object in relation to my conception.

Accordingly, what goes wrong with the first version of the ontological argument is that the notion of existence is being treated as the wrong logical type. Concepts, as a logical matter, are defined entirely in terms of logical predicates. Since existence isn't a logical predicate, it doesn't belong to the concept of God; it rather affirms that the existence of something that satisfies the predicates defining the concept of God.

While Kant's criticism is phrased (somewhat obscurely) in terms of the logic of predicates and copulas, it also makes a plausible metaphysical point. Existence is not a property (in, say, the way that being red is a property of an apple). Rather it is a precondition for the instantiation of properties in the following sense: it is not possible for a non-existent thing to instantiate any properties because there is nothing to which, so to speak, a property can stick. Nothing has no qualities whatsoever. To say that x instantiates a property P is hence to presuppose that x exists. Thus, on this line of reasoning, existence isn't a great-making property because it is not a property at all; it is rather a metaphysically necessary condition for the instantiation of any properties.

But even if we concede that existence is a property, it does not seem to be the sort of property that makes something better for having it. Norman Malcolm expresses the argument as follows:

The doctrine that existence is a perfection is remarkably queer. It makes sense and is true to say that my future house will be a better one if it is insulated than if it is not insulated; but what could it mean to say that it will be a better house if it exists than if it does not? My future child will be a better man if he is honest than if he is not; but who would understand the saying that he will be a better man if he exists than if he does not? Or who understands the saying that if God exists He is more perfect than if he does not exist? One might say, with some intelligibility, that it would be better (for oneself or for mankind) if God exists than if He does not-but that is a different matter.

The idea here is that existence is very different from, say, the property of lovingness. A being that is loving is, other things being equal, better or greater than a being that is not. But it seems very strange to think that a loving being that exists is, other things being equal, better or greater than a loving being that doesn't exist. But to the extent that existence doesn't add to the greatness of a thing, the classic version of the ontological argument fails.

3. Anselm's Second Version of the Ontological Argument

As it turns out, there are two different versions of the ontological argument in the Prosologium. The second version does not rely on the highly problematic claim that existence is a property and hence avoids many of the objections to the classic version. Here is the second version of the ontological argument as Anselm states it:

God is that, than which nothing greater can be conceived.… And [God] assuredly exists so truly, that it cannot be conceived not to exist. For, it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction. There is, then, so truly a being than which nothing greater can be conceived to exist, that it cannot even be conceived not to exist; and this being thou art, O Lord, our God.

This version of the argument relies on two important claims. As before, the argument includes a premise asserting that God is a being than which a greater cannot be conceived. But this version of the argument, unlike the first, does not rely on the claim that existence is a perfection; instead it relies on the claim that necessary existence is a perfection. This latter claim asserts that a being whose existence is necessary is greater than a being whose existence is not necessary. Otherwise put, then, the second key claim is that a being whose non-existence is logically impossible is greater than a being whose non-existence is logically possible.

More formally, the argument is this:

  1. By definition, God is a being than which none greater can be imagined.
  2. A being that necessarily exists in reality is greater than a being that does not necessarily exist.
  3. Thus, by definition, if God exists as an idea in the mind but does not necessarily exist in reality, then we can imagine something that is greater than God.
  4. But we cannot imagine something that is greater than God.
  5. Thus, if God exists in the mind as an idea, then God necessarily exists in reality.
  6. God exists in the mind as an idea.
  7. Therefore, God necessarily exists in reality.

This second version appears to be less vulnerable to Kantian criticisms than the first. To begin with, necessary existence, unlike mere existence, seems clearly to be a property. Notice, for example, that the claim that x necessarily exists entails a number of claims that attribute particular properties to x. For example, if x necessarily exists, then its existence does not depend on the existence of any being (unlike contingent human beings whose existence depends, at the very least, on the existence of their parents). And this seems to entail that x has the reason for its existence in its own nature. But these latter claims clearly attribute particular properties to x.

And only a claim that attributes a particular property can entail claims that attribute particular properties. While the claim that x exists clearly entails that x has at least one property, this does not help. We cannot soundly infer any claims that attribute particular properties to x from either the claim that x exists or the claim that x has at least one property; indeed, the claim that x has at least one property no more expresses a particular property than the claim that x exists. This distinguishes the claim that x exists from the claim that x necessarily exists and hence seems to imply that the latter, and only the latter, expresses a property.

Moreover, one can plausibly argue that necessary existence is a great-making property. To say that a being necessarily exists is to say that it exists eternally in every logically possible world; such a being is not just, so to speak, indestructible in this world, but indestructible in every logically possible world - and this does seem, at first blush, to be a great-making property. As Malcolm puts the point:

If a housewife has a set of extremely fragile dishes, then as dishes, they are inferior to those of another set like them in all respects except that they are not fragile. Those of the first set are dependent for their continued existence on gentle handling; those of the second set are not. There is a definite connection between the notions of dependency and inferiority, and independence and superiority. To say that something which was dependent on nothing whatever was superior to anything that was dependent on any way upon anything is quite in keeping with the everyday use of the terms superior and greater.

Nevertheless, the matter is not so clear as Malcolm believes. It might be the case that, other things being equal, a set of dishes that is indestructible in this world is greater than a set of dishes that is not indestructible in this world. But it is very hard to see how transworld indestructibility adds anything to the greatness of a set of dishes that is indestructible in this world. From our perspective, there is simply nothing to be gained by adding transworld indestructibility to a set of dishes that is actually indestructible. There is simply nothing that a set of dishes that is indestructible in every possible world can do in this world that can't be done by a set of dishes that is indestructible in this world but not in every other world.

And the same seems to be true of God. Suppose that an omniscient, omnipotent, omnibenevolent, eternal (and hence, so to speak, indestructible), personal God exists in this world but not in some other worlds. It is very hard to make sense of the claim that such a God is deficient in some relevant respect. God's indestructibility in this world means that God exists eternally in all logically possible worlds that resemble this one in certain salient respects. It is simply unclear how existence in these other worlds that bear no resemblance to this one would make God greater and hence more worthy of worship. From our perspective, necessary existence adds nothing in value to eternal existence. If this is correct, then Anselm's second version of the argument also fails.

4. Modal Versions of the Argument

Even if, however, we assume that Anselm's second version of the argument can be defended against such objections, there is a further problem: it isn't very convincing because it is so difficult to tell whether the argument is sound. Thus, the most important contemporary defender of the argument, Alvin Plantinga, complains "[a]t first sight, Anselm's argument is remarkably unconvincing if not downright irritating; it looks too much like a parlor puzzle or word magic." As a result, despite its enduring importance, the ontological argument has brought few people to theism.

There have been several attempts to render the persuasive force of the ontological argument more transparent by recasting it using the logical structures of contemporary modal logic. One influential attempts to ground the ontological argument in the notion of God as an unlimited being. As Malcolm describes this idea:

God is usually conceived of as an unlimited being. He is conceived of as a being who could not be limited, that is, as an absolutely unlimited being.… If God is conceived to be an absolutely unlimited being He must be conceived to be unlimited in regard to His existence as well as His operation. In this conception it will not make sense to say that He depends on anything for coming into or continuing in existence. Nor, as Spinoza observed, will it make sense to say that something could prevent Him from existing. Lack of moisture can prevent trees from existing in a certain region of the earth. But it would be contrary to the concept of God as an unlimited being to suppose that anything … could prevent Him from existing.

The unlimited character of God, then, entails that his existence is different from ours in this respect: while our existence depends causally on the existence of other beings (e.g., our parents), God's existence does not depend causally on the existence of any other being.

Further, on Malcolm's view, the existence of an unlimited being is either logically necessary or logically impossible. Here is his argument for this important claim. Either an unlimited being exists at world W or it doesn't exist at world W; there are no other possibilities. If an unlimited being does not exist in W, then its nonexistence cannot be explained by reference to any causally contingent feature of W; accordingly, there is no contingent feature of W that explains why that being doesn't exist. Now suppose, per reductio, an unlimited being exists in some other world W'. If so, then it must be some contingent feature f of W' that explains why that being exists in that world. But this entails that the nonexistence of an unlimited being in W can be explained by the absence of f in W; and this contradicts the claim that its nonexistence in W can't be explained by reference to any causally contingent feature. Thus, if God doesn't exist at W, then God doesn't exist in any logically possible world.

A very similar argument can be given for the claim that an unlimited being exists in every logically possible world if it exists in some possible world W; the details are left for the interested reader. Since there are only two possibilities with respect to W and one entails the impossibility of an unlimited being and the other entails the necessity of an unlimited being, it follows that the existence of an unlimited being is either logically necessary or logically impossible.

All that is left, then, to complete Malcolm's elegant version of the proof is the premise that the existence of an unlimited being is not logically impossible - and this seems plausible enough. The existence of an unlimited being is logically impossible only if the concept of an unlimited being is self-contradictory. Since we have no reason, on Malcolm's view to think the existence of an unlimited being is self-contradictory, it follows that an unlimited being, i.e., God, exists. Here's the argument reduced to its basic elements:

  1. God is, as a conceptual matter (that is, as a matter of definition) an unlimited being.
  2. The existence of an unlimited being is either logically necessary or logically impossible.
  3. The existence of an unlimited being is not logically impossible.
  4. Therefore, the existence of God is logically necessary.

Notice that Malcolm's version of the argument does not turn on the claim that necessary existence is a great-making property. Rather, as we saw above, Malcolm attempts to argue that there are only two possibilities with respect to the existence of an unlimited being: either it is necessary or it is impossible. And notice that his argument does not turn in any way on characterizing the property necessary existence as making something that instantiates that property better than it would be without it. Thus, Malcolm's version of the argument is not vulnerable to the criticisms of Anselm's claim that necessary existence is a perfection.

But while Malcolm's version of the argument is, moreover, considerably easier to understand than Anselm's versions, it is also vulnerable to objection. In particular, Premise 2 is not obviously correct. The claim that an unlimited being B exists at some world W clearly entails that B always exists at W (that is, that B's existence is eternal or everlasting in W), but this doesn't clearly entail that B necessarily exists (that is, that B exists at every logically possible world). To defend this further claim, one needs to give an argument that the notion of a contingent eternal being is self-contradictory.

Similarly, the claim that an unlimited being B does not exist at W clearly entails that B never exists at W (that is, that it is always true in W that B doesn't exist), but it doesn't clearly entail that B necessarily doesn't exist (that is, B exists at no logically possible world or B's existence is logically impossible. Indeed, there are plenty of beings that will probably never exist in this world that exist in other logically possible worlds, like unicorns. For this reason, Premise 2 of Malcolm's version is questionable.

Perhaps the most influential of contemporary modal arguments is Plantinga's version. Plantinga begins by defining two properties, the property of maximal greatness and the property of maximal excellence, as follows:

  1. A being is maximally excellent in a world W if and only if it is omnipotent, omniscient, and morally perfect in W; and
  2. A being is maximally great in a world W if and only if it is maximally excellent in every possible world.

Thus, maximal greatness entails existence in every possible world: since a being that is maximally great at W is omnipotent at every possible world and non-existent beings can't be omnipotent, it follows that a maximally great being exists in every logically possible world.

Accordingly, the trick is to show that a maximally great being exists in some world W because it immediately follows from this claim that such a being exists in every world, including our own. But notice that the claim that a maximally great being exists in some world is logically equivalent to the claim that the concept of a maximally great being is not self-contradictory; for the only things that don't exist in any possible world are things that are conceptually defined in terms of contradictory properties. There is no logically possible world in which a square circle exists (given the relevant concepts) because the property of being square is inconsistent with the property of being circular.

Since, on Plantinga's view, the concept of a maximally great being is consistent and hence possibly instantiated, it follows that such a being, i.e., God, exists in every possible world. Here is a schematic representation of the argument:

  1. The concept of a maximally great being is self-consistent.
  2. If 1, then there is at least one logically possible world in which a maximally great being exists.
  3. Therefore, there is at least one logically possible world in which a maximally great being exists.
  4. If a maximally great being exists in one logically possible world, it exists in every logically possible world.
  5. Therefore, a maximally great being (that is, God) exists in every logically possible world.

It is sometimes objected that Plantinga's Premise 4 is an instance of a controversial general modal principle. The S5 system of modal logic includes an axiom that looks suspiciously similar to Premise 4:

AxS5: If A is possible, then it is necessarily true that A is possible.

The intuition underlying AxS5 is, as James Sennett puts it, that "all propositions bear their modal status necessarily." But, according to this line of criticism, Plantinga's version is unconvincing insofar as it rests on a controversial principle of modal logic.

To see that this criticism is unfounded, it suffices to make two observations. First, notice that the following propositions are not logically equivalent:

PL4 If "A maximally great being exists" is possible, then "A maximally great being exists" is necessarily true.

PL4* If "A maximally great being exists" is possible, then it is necessarily true that "A maximally great being exists" is possible.

PL4 is, of course, Plantinga's Premise 4 slightly reworded, while PL4* is simply a straightforward instance of AxS5. While PL4 implies PL4* (since if A is true at every world, it is possible at every world), PL4* doesn't imply PL4; for PL4 clearly makes a much stronger claim than PL4*.

Second, notice that the argument for Premise 4 does not make any reference to the claim that all propositions bear their modal status necessarily. Plantinga simply builds necessary existence into the very notion of maximal greatness. Since, by definition, a being that is maximally great at W is omnipotent at every possible worldand a being that does not exist at some world W' cannot be omnipotent at W', it straightforwardly follows, without the help of anything like the controversial S5 axiom, that a maximally great being exists in every logically possible world.

Indeed, it is for this very reason that Plantinga avoids the objection to Malcolm's argument that was considered above. Since the notion of maximal greatness, in contrast to the notion of an unlimited being as Malcolm defines it, is conceived in terms that straightforwardly entail existence in every logically possible world (and hence eternal existence in every logically possible world), there are no worries about whether maximal greatness, in contrast to unlimitedness, entails something stronger than eternal existence.

IV. Is the Concept of a Maximally Great Being Coherent?

As is readily evident, each version of the ontological argument rests on the assumption that the concept of God, as it is described in the argument, is self-consistent. Both versions of Anselm's argument rely on the claim that the idea of God (that is, a being than which none greater can be conceived) "exists as an idea in the understanding." Similarly, Plantinga's version relies on the more transparent claim that the concept of maximal greatness is self-consistent.

But many philosophers are skeptical about the underlying assumption, as Leibniz describes it, "that this idea of the all-great or all-perfect being is possible and implies no contradiction." Here is the problem as C.D. Broad expresses it:

Let us suppose, e.g., that there were just three positive properties X, Y, and Z; that any two of them are compatible with each other; but that the presence of any two excludes the remaining one. Then there would be three possible beings, namely, one which combines X and Y, one which combines Y and Z, and one which combines Z and X, each of which would be such that nothing … superior to it is logically possible. For the only kind of being which would be … superior to any of these would be one which had all three properties, X, Y, and Z; and, by hypothesis, this combination is logically impossible.… It is now plain that, unless all positive properties be compatible with each other, this phrase [i.e., "a being than which none greater can be imagined"] is just meaningless verbiage like the phrase "the greatest possible integer."

Thus, if there are two great-making characteristics essential to the classically theistic notion of an all-perfect God that are logically incompatible, it follows that this notion is incoherent.

Here it is important to note that all versions of the ontological argument assume that God is simultaneously omnipotent, omniscient, and morally perfect. As we have seen, Plantinga expressly defines maximal excellence in such terms. Though Anselm doesn't expressly address the issue, it is clear (1) that he is attempting to show the existence of the God of classical theism; and (2) that the great-making properties include those of omnipotence, omniscience, and moral perfection.

There are a number of plausible arguments for thinking that even this restricted set of properties is logically inconsistent. For example, moral perfection is thought to entail being both perfectly merciful and perfectly just. But these two properties seem to contradict each other. To be perfectly just is always to give every person exactly what she deserves. But to be perfectly merciful is to give at least some persons less punishment than they deserve. If so, then a being cannot be perfectly just and perfectly merciful. Thus, if moral perfection entails, as seems reasonable, being perfectly just and merciful, then the concept of moral perfection is inconsistent.

The problem of divine foreknowledge can also be seen as denying that omniscience, omnipotence, and moral perfection constitute a coherent set. Roughly put, the problem of divine foreknowledge is as follows. If God is omniscient, then God knows what every person will do at every moment t. To say that a person p has free will is to say that there is at least one moment t at which p does A but could have done other than A. But if a person p who does A at t has the ability to do other than A at t, then it follows that p has the ability to bring it about that an omniscient God has a false belief - and this is clearly impossible.

On this line of analysis, then, it follows that it is logically impossible for a being to simultaneously instantiate omniscience and omnipotence. Omnipotence entails the power to create free beings, but omniscience rules out the possibility that such beings exist. Thus, a being that is omniscient lacks the ability to create free beings and is hence not omnipotent. Conversely, a being that is omnipotent has the power to create free beings and hence does not know what such beings would do if they existed. Thus, the argument concludes that omniscience and omnipotence are logically incompatible. If this is correct, then all versions of the ontological argument fail.

5. References and Further Reading

  • Anselm, St., Anselm's Basic Writings, translated by S.W. Deane, 2nd Ed. (La Salle, IL: Open Court Publishing Co., 1962)
  • Aquinas, Thomas, St., Summa Theologica (1a Q2), "Whether the Existence of God is Self-Evident (Thomas More Publishing, 1981)
  • Barnes, Jonathan, The Ontological Argument (London: MacMillan Publishing Co., 1972)
  • Broad, C.D., Religion, Philosophy and Psychical Research (New York: Routledge & Kegan Paul, 1953)
  • Findlay, J.N., "God's Existence is Necessarily Impossible," from Flew, Antony and MacIntyre, Alasdair, New Essays in Philosophical Theology (New York: MacMillan Publishing Co., 1955)
  • Gale, Richard, On the Nature and Existence of God (Cambridge: Cambridge University Press, 1991)
  • Hartshore, Charles, The Logic of Perfection (LaSalle, IL: Open Court, 1962)
  • Hegel, Georg Wilhelm Friedrich, Lectures on the History of Philosophy, translated by E.S. Haldane and F.H. Simson (London, Kegan Paul, 1896)
  • Kant, Immanuel, Critique of Pure Reason, translated by J.M.D. Meiklejohn (New York: Colonial Press, 1900)
  • Leibniz, Gottfried Wilhelm, New Essays Concerning Human Understanding, translated by A.G. Langley (Chicago, IL: Open Court Publishing, 1896).
  • Malcolm, Norman, "Anselm's Ontological Argument," Philosophical Review, vol. 69, no. 1 (1960), 41-62
  • Miller, Ed L., God and Reason, 2nd Ed. (Upper Saddle River, NJ: Prentice-Hall, Inc., 1995)
  • Pike, Nelson, "Divine Omniscience and Voluntary Action," Philosophical Review, vol. 74 (1965)
  • Plantinga, Alvin, God, Freedom, and Evil (New York: Harper and Row, 1974)
  • Plantinga, Alvin, The Ontological Argument from St. Anselm to Contemporary Philosophers (Garden City, NY: Doubleday, 1965)
  • Pojman, Louis, Philosophy of Religion (London: Mayfield Publishing Co., 2001)
  • Rowe, William, "Modal Versions of the Ontological Argument," in Pojman, Louis (ed.), Philosophy of Religion, 3rd Ed. (Belmont, CA: Wadsworth Publishing Co., 1998)
  • Sennett, James F., "Universe Indexed Properties and the Fate of the Ontological Argument," Religious Studies, vol. 27 (1991), 65-79

Author Information

Kenneth Einar Himma
Email: himma@spu.edu
Seattle Pacific University
U. S. A.

1. History of Ontological Arguments

1078:St. Anselm, Proslogion. Followed soon after by Gaunilo’s critique In Behalf of the Fool.
1264:St. Thomas Aquinas, Summa. Criticises an argument which somehow descends from St. Anselm.
1637:Descartes, Discourse on Method. The argument of Discourse 4 is further elaborated in the Meditations. The Objections—particularly those of Caterus and Gassendi—and the Replies contain much valuable discussion of the Cartesian arguments.
c1680:Spinoza, Ethics. Intimations of a defensible mereological ontological argument, albeit one whose conclusion is not (obviously) endowed with religious significance.
1709:Leibniz, New Essays Concerning Human Understanding. Contains Leibniz’s attempt to complete the Cartesian argument by showing that the Cartesian conception of God is not inconsistent.
1776:Hume, Dialogues Concerning Natural Religion. Part IX is a general attack on a priori arguments (both analytic and synthetic). Includes a purported demonstration that no such arguments can be any good.
1787:Kant, Critique of Pure Reason. Contains famous attack on traditional theistic arguments. Three objections to “the ontological argument”, including the famous objection based on the dictum that existence is not a predicate.
1831:Hegel, Lectures of 1831. Hegel makes repeated assertions in these lectures that there is a successful ontological argument, though he nowhere says what the argument actually is. Some scholars have claimed that the entire Hegelian corpus constitutes an ontological argument. Since no one has ever said what the premises of this alleged argument are, there is good reason for scepticism about this scholarly claim.
1884:Frege, Foundations of Arithmetic. Existence is a second-order predicate. First-order existence claims are meaningless. So ontological arguments—whose conclusions are first-order existence claims—are doomed.
1941:Hartshorne, Man’s Vision of God. Defence of modal ontological arguments, allegedly derived from Proslogion 3.
1960:Malcolm, “Anselm’s Ontological Argument”. Defence of modal ontological arguments by a well-known ordinary language philosopher.
1970:Lewis, “Anselm and Actuality”. The key critique of ontological arguments. All ontological arguments are either invalid or question-begging; moreover, in many cases, they have two closely related readings, one of which falls into each of the above categories.
1974:Plantinga, The Nature of Necessity. Plantinga’s “victorious” modal ontological argument.
1995:Gödel, Collected Works Volume III. Gödel’s ontological argument.
2004:Sobel, Logic and Theism. Detailed critique of ontological arguments. See, especially, chapters 2–4, pp. 29–167.

For a useful discussion of the history of ontological arguments in the modern period, see Harrelson 2009.

2. Taxonomy of Ontological Arguments

According to a modification of the taxonomy of Oppy 1995, there are eight major kinds of ontological arguments, viz:

  1. definitional ontological arguments;
  2. conceptual (or hyperintensional) ontological arguments;
  3. modal ontological arguments;
  4. Meinongian ontological arguments;
  5. experiential ontological arguments;
  6. mereological ontological arguments;
  7. higher-order ontological arguments; and
  8. ‘Hegelian’ ontological arguments;

Examples of all but the last follow. These are mostly toy examples. But they serve to highlight the deficiencies which more complex examples also share.

Note: I provide no example of a ‘Hegelian’ ontological argument because I know of no formulation of such an argument. Many people assert that Hegel provided an ontological argument; but, when pressed for a list of the premises of the argument, Hegel’s friends fail to deliver. (For a defense of Hegel against these charges—but not for a supply of the premises of ‘the Hegelian ontological argument’—see Redding and Bubbio 2014.)

  1. God is a being which has every perfection. (This is true as a matter of definition.) Existence is a perfection. Hence God exists.

  2. I conceive of a being than which no greater can be conceived. If a being than which no greater can be conceived does not exist, then I can conceive of a being greater than a being than which no greater can be conceived—namely, a being than which no greater can be conceived that exists. I cannot conceive of a being greater than a being than which no greater can be conceived. Hence, a being than which no greater can be conceived exists.

  3. It is possible that that God exists. God is not a contingent being, i.e., either it is not possible that God exists, or it is necessary that God exists. Hence, it is necessary that God exists. Hence, God exists. (See Malcolm 1960, Hartshorne 1965, and Plantinga 1974 for closely related arguments.)

  4. [It is analytic, necessary and a priori that] Each instance of the schema “The F G is F” expresses a truth. Hence the sentence “The existent perfect being is existent” expresses a truth. Hence, the existent perfect being is existent. Hence, God is existent, i.e. God exists. (The last step is justified by the observation that, as a matter of definition, if there is exactly one existent perfect being, then that being is God.)

  5. The word ‘God’ has a meaning that is revealed in religious experience. The word ‘God’ has a meaning only if God exists. Hence, God exists. (See Rescher 1959 for a live version of this argument.)

  6. I exist. Therefore something exists. Whenever a bunch of things exist, their mereological sum also exists. Therefore the sum of all things exists. Therefore God—the sum of all things—exists.

  7. Say that a God-property is a property that is possessed by God in all and only those worlds in which God exists. Not all properties are God properties. Any property entailed by a collection of God-properties is itself a God-property. The God-properties include necessary existence, necessary omnipotence, necessary omniscience, and necessary perfect goodness. Hence, there is a necessarily existent, necessarily omnipotent, necessarily omniscient, and necessarily perfectly good being (namely, God).

Of course, this taxonomy is not exclusive: an argument can belong to several categories at once. Moreover, an argument can be ambiguous between a range of readings, each of which belongs to different categories. This latter fact may help to explain part of the curious fascination of ontological arguments. Finally, the taxonomy can be further specialised: there are, for example, at least four importantly different kinds of modal ontological arguments which should be distinguished. (See, e.g., Ross 1969 for a rather different kind of modal ontological argument.)

3. Characterisation of Ontological Arguments

It is not easy to give a good characterisation of ontological arguments. The traditional characterisation involves the use of problematic notions—analyticity, necessity, and a priority—and also fails to apply to many arguments to which defenders have affixed the label “ontological”. (Consider, for example, the claim that I conceive of a being than which no greater can be conceived. This claim is clearly not analytic (its truth doesn’t follow immediately from the meanings of the words used to express it), nor necessary (I might never have entertained the concept), nor a priori (except perhaps in my own case, though even this is unclear—perhaps even I don’t know independently of experience that I have this concept.)) However, it is unclear how that traditional characterisation should be improved upon.

Perhaps one might resolve to use the label “ontological argument” for any argument which gets classified as “an ontological argument” by its proponent(s). This procedure would make good sense if one thought that there is a natural kind—ontological arguments—which our practice carves out, but for which is hard to specify defining conditions. Moreover, this procedure can be adapted as a pro tem stop gap: when there is a better definition to hand, that definition will be adopted instead. On the other hand, it seems worthwhile to attempt a more informative definition.

Focus on the case of ontological arguments for the conclusion that God exists. One characteristic feature of these arguments is the use which they make of “referential vocabulary”—names, definite descriptions, indefinite descriptions, quantified noun phrases, etc.—whose ontological commitments—for occurrences of this vocabulary in “referential position”—non-theists do not accept.

Theists and non-theists alike (can) agree that there is spatio-temporal, or causal, or nomic, or modal structure to the world (the basis for cosmological arguments); and that there are certain kinds of complexity of organisation, structure and function in the world (the basis for teleological arguments); and so on. But theists and non-theists are in dispute about whether there are perfect beings, or beings than which no greater can be conceived, or … ; thus, theists and non-theists are in dispute about the indirect subject matter of the premises of ontological arguments.

Of course, the premises of ontological arguments often do not deal directly with perfect beings, beings than which no greater can be conceived, etc.; rather, they deal with descriptions of, or ideas of, or concepts of, or the possibility of the existence of, these things. However, the basic point remains: ontological arguments require the use of vocabulary which non-theists should certainly find problematic when it is used in ontologically committing contexts (i.e not inside the scope of prophylactic operators—such as “according to the story” or “by the lights of theists” or “by the definition”—which can be taken to afford protection against unwanted commitments).

Note that this characterisation does not beg the question against the possibility of the construction of a successful ontological argument—i.e., it does not lead immediately to the conclusion that all ontological arguments are question-begging (in virtue of the ontologically committing vocabulary which they employ). For it may be that the vocabulary in question only gets used in premises under the protection of prophylactic operators (which ward off the unwanted commitments.) Of course, there will then be questions about whether the resulting arguments can possibly be valid—how could the commitments turn up in the conclusion if they are not there in the premises?—but those are further questions, which would remain to be addressed.

4. Objections to Ontological Arguments

Objections to ontological arguments take many forms. Some objections are intended to apply only to particular ontological arguments, or particular forms of ontological arguments; other objections are intended to apply to all ontological arguments. It is a controversial question whether there are any successful general objections to ontological arguments.

One general criticism of ontological arguments which have appeared hitherto is this: none of them is persuasive, i.e., none of them provides those who do not already accept the conclusion that God exists—and who are reasonable, reflective, well-informed, etc.—with either a pro tanto reason or an all-things-considered reason to accept that conclusion. Any reading of any ontological argument which has been produced so far which is sufficiently clearly stated to admit of evaluation yields a result which is invalid, or possesses a set of premises which it is clear in advance that no reasonable, reflective, well-informed, etc. non-theists will accept, or has a benign conclusion which has no religious significance, or else falls prey to more than one of the above failings.

For each of the families of arguments introduced in the earlier taxonomy, we can give general reasons why arguments of that family fall under the general criticism. In what follows, we shall apply these general considerations to the exemplar arguments introduced in section 2.

(1) Definitional arguments: These are arguments in which ontologically committing vocabulary is introduced solely via a definition. An obvious problem is that claims involving that vocabulary cannot then be non-question-beggingly detached from the scope of that definition. (The inference from ‘By definition, God is an existent being’ to ‘God exists’ is patently invalid; while the inference to ‘By definition, God exists’ is valid, but uninteresting. In the example given earlier, the premises licence the claim that, as a matter of definition, God possesses the perfection of existence. But, as just noted, there is no valid inference from this claim to the further claim that God exists.)

(2) Conceptual arguments: These are arguments in which ontologically committing vocabulary is introduced solely within the scope of hyperintensional operators (e.g. ‘believes that’, ‘conceives of’, etc.). Often, these operators have two readings, one of which can cancel ontological commitment, and the other of which cannot. On the reading which can give cancellation (as in the most likely reading of ‘John believes in Santa Claus’), the inference to a conclusion in which the ontological commitment is not cancelled will be invalid. On the reading which cannot cancel ontological commitment (as in that reading of ‘John thinks about God’ which can only be true if there is a God to think about), the premises are question-begging: they incur ontological commitments which non-theists reject. In our sample argument, the claim, that I conceive of an existent being than which no greater being can be conceived, admits of the two kinds of readings just distinguished. On the one hand, on the reading which gives cancellation, the inference to the conclusion that there is a being than which no greater can be conceived is plainly invalid. On the other hand, on the reading in which there is no cancellation, it is clear that this claim is one which no reasonable, etc. non-theist will accept: if you doubt that there is a being than which no greater can be conceived, then, of course, you doubt whether you can have thoughts about such a being.

(3) Modal arguments: These are arguments with premises which concern modal claims about God, i.e., claims about the possibility or necessity of God’s attributes and existence. Suppose that we agree to think about possibility and necessity in terms of possible worlds: a claim is possibly true just in case it is true in at least one possible world; a claim is necessarily true just in case it is true in every possible world; and a claim is contingent just in case it is true in some possible worlds and false in others. Some theists hold that God is a necessarily existent being, i.e., that God exists in every possible world; all non-theists reject the claim that God exists in the actual world. The sample argument consists, in effect, of two premises:

  • God exists in at least one possible world.
  • God exists in all possible worlds if God exists in any.

A minimally rational non-theist would not accept both of these premises – they entail that God exists in every possible world whereas a minimally rational non-theists would insist that there is at least one possible world in which God does not exist. Given that that a minimally rational non-theist accepts that there is at least one possible world in which God does not exist, such a non-theist could offer the following counterargument:

  • God fails to exist in at least one possible world.
  • God exists in all possible worlds if God exists in any.

These premises entail that God exists in no possible world, and hence that God does not exist in the actual world. Considered together, the argument and the counterargument just mentioned plainly do not give anyone a reason to prefer theism to non-theism, and nor do they give anyone a reason to prefer non-theism to theism. So the sample argument is unsuccessful: it doesn’t supply an all-things-considered reason to prefer theism to non-theism (just as the counterargument doesn’t supply an all-things-considered reason to prefer non-theism to theism).

(4) Meinongian arguments: These are arguments which depend somehow or other on Meinongian theories of objects. Consider the schema ‘The F G is F’. Naive Meinongians will suppose that if F is instantiated with any property, then the result is true (and, quite likely, necessary, analytic and a priori). So, for example, the round square is round; the bald current King of France is bald; and so on. However, more sophisticiated Meinongians will insist that there must be some restriction on the substitution instances for F, in order to allow one to draw the obvious and important ontological distinction between the following two groups: {Bill Clinton, the sun, the Eiffel Tower} and {Santa Claus, Mickey Mouse, the round square}. Choice of vocabulary here is controversial: Let us suppose (for the sake of example) that the right thing to say is that the former things exist and the latter do not. Under this supposition, ‘existent’ will not be a suitable substitution instance for F—obviously, since we all agree that there is no existent round square. Of course, nothing hangs on the choice of ‘existent’ as the crucial piece of vocabulary. The point is that non-theists are not prepared to include god(s) in the former group of objects—and hence will be unpersuaded by any argument which tries to use whatever vocabulary is used to discriminate between the two classes as the basis for an argument that god(s) belong to the former group. (Cognoscenti will recognise that the crucial point is that Meinongian ontological arguments fail to respect the distinction between nuclear (assumptible, characterising) properties and non-nuclear (non-assumptible, non-characterising) properties. It should, of course, be noted that neither Meinong, nor any of his well-known modern supporters—e.g. Terence Parsons, Richard Sylvan—ever endorses a Meinongian ontological argument; and it should also be noted that most motivate the distinction between nuclear and non-nuclear properties in part by a need to avoid Meinongian ontological arguments. The reason for calling these arguments “Meinongian” is that they rely on quantification over—or reference to—non-existent objects; there is no perjorative intent in the use of this label.)

(5) Experiential arguments: These are arguments which try to make use of ‘externalist’ or ‘object-involving’ accounts of content. It should not be surprising that they fail. After all, those accounts of content need to have something to say about expressions which fail to refer (‘Santa Claus’, ‘phlogiston’, etc.). But, however the account goes, non-theists will insist that expressions which purport to refer to god(s) should be given exactly the same kind of treatment.

(6) Mereological arguments: Those who dislike mereology will not be impressed by these arguments. However, even those who accept principles of unrestricted composition—i.e., who accept principles which claim, e.g., that, whenever there are some things, there is something which is the sum or fusion of all of those things—need not be perturbed by them: for it is plausible to think that the conclusions of these arguments have no religious significance whatsoever—they are merely arguments for, e.g., the existence of the physical universe.

(7) Higher-Order arguments: The key to these arguments is the observation that any collection of properties, that (a) does not include all properties and (b) is closed under entailment, is possibly jointly instantiated. If it is impossible that God exists — as all who deny that God exists suppose, on the further assumption that, were God to exist, God would exist of necessity — then it cannot be true both that the God-properties are closed under entailment and that there are properties that are not God-properties. Those who take themselves to have good independent reason to deny that there are any gods will take themselves to have good independent reason to deny that there are God-properties that form a non-trivial collection that is closed under entailment.

Even if the forgoing analyses are correct, it is important to note that no argument has been given for the conclusion that no ontological argument can be successful. Even if all of the kinds of arguments produced to date are pretty clearly unsuccessful—i.e., not such as ought to give non-theists reason to accept the conclusion that God exists—it remains an open question whether there is some other kind of hitherto undiscovered ontological argument which does succeed. (Perhaps it is worth adding here that there is fairly widespread consensus, even amongst theists, that no known ontological arguments for the existence of God are persuasive. Most categories of ontological argument have some actual defenders; but none has a large following.)

Many other objections to (some) ontological arguments have been proposed. All of the following have been alleged to be the key to the explanation of the failure of (at least some) ontological arguments: (1) existence is not a predicate (see, e.g., Kant, Smart 1955, Alston 1960); (2) the concept of god is meaningless/incoherent/ inconsistent (see, e.g., Findlay 1949); (3) ontological arguments are ruled out by “the missing explanation argument” (see Johnston 1992; (4) ontological arguments all trade on mistaken uses of singular terms (see, e.g., Barnes 1972; (5) existence is not a perfection (see almost any textbook in philosophy of religion); (6) ontological arguments presuppose a Meinongian approach to ontology (see, e.g., Dummett 1993); and (7) ontological arguments are question-begging, i.e., presuppose what they set out to prove (see, e.g., Rowe 1989). There are many things to say about these objections: the most important point is that almost all of them require far more controversial assumptions than non-theists require in order to be able to reject ontological arguments with good conscience. Trying to support most of these claims merely in order to beat up on ontological arguments is like using a steamroller to crack a nut (in circumstances in which one is unsure that one can get the steamroller to move!).

Of course, all of the above discussion is directed merely to the claim that ontological arguments are not dialectically efficacious—i.e., they give reasonable non-theists no reason to change their views. It might be wondered whether there is some other use which ontological arguments have—e.g., as Plantinga claims, in establishing the reasonableness of theism. This seems unlikely. After all, at best these arguments show that certain sets of sentences (beliefs, etc.) are incompatible—one cannot reject the conclusions of these arguments while accepting their premises. But the arguments themselves say nothing about the reasonableness of accepting the premisses. So the arguments themselves say nothing about the (unconditional) reasonableness of accepting the conclusions of these arguments. Those who are disposed to think that theism is irrational need find nothing in ontological arguments to make them change their minds (and those who are disposed to think that theism is true should take no comfort from them either).

5. Parodies of Ontological Arguments

Positive ontological arguments—i.e., arguments FOR the existence of god(s)—invariably admit of various kinds of parodies, i.e., parallel arguments which seem at least equally acceptable to non-theists, but which establish absurd or contradictory conclusions. For many positive ontological arguments, there are parodies which purport to establish the non-existence of god(s); and for many positive ontological arguments there are lots (usually a large infinity!) of similar arguments which purport to establish the existence of lots (usally a large infinity) of distinct god-like beings. Here are some modest examples:

(1) By definition, God is a non-existent being who has every (other) perfection. Hence God does not exist.

(2) I conceive of a being than which no greater can be conceived except that it only ever creates n universes. If such a being does not exist, then we can conceive of a greater being—namely, one exactly like it which does exist. But I cannot conceive of a being which is greater in this way. Hence, a being than which no greater can be conceived except that it only ever creates n universes exists.

(3) It is possible that God does not exist. God is not a contingent being, i.e., either it is not possible that God exists, or it is necessary that God exists. Hence it is not possible that God exists. Hence God does not exist.

(4) It is analytic, necessary, and a priori that the F G is F. Hence, the existent perfect being who creates exactly n universes is existent. Hence the perfect being who creates exactly n universes exists.

There are many kinds of parodies on Ontological Arguments. The aim is to construct arguments which non-theists can reasonably claim to have no more reason to accept than the original Ontological Arguments themselves. Of course, theists may well be able to hold that the originals are sound, and the parodies not—but that is an entirely unrelated issue. (All theists—and no non-theists—should grant that the following argument is sound, given that the connectives are to be interpretted classically: “Either 2+2=5, or God exists. Not 2+2=5. Hence God exists.” It should be completely obvious that this argument is useless.)

There are many parodic discussions of Ontological Arguments in the literature. A particularly pretty one is due to Raymond Smullyan (1984), in which the argument is attributed to “the unknown Dutch theologian van Dollard”. A relatively recent addition to the genre is described in Grey 2000, though the date of its construction is uncertain. It is the work of Douglas Gasking, one-time Professor of Philosophy at the University of Melbourne (with emendations by William Grey and Denis Robinson):

  1. The creation of the world is the most marvellous achievement imaginable.
  2. The merit of an achievement is the product of (a) its intrinsic quality, and (b) the ability of its creator.
  3. The greater the disability or handicap of the creator, the more impressive the achievement.
  4. The most formidable handicap for a creator would be non-existence.
  5. Therefore, if we suppose that the universe is the product of an existent creator, we can conceive a greater being—namely, one who created everything while not existing.
  6. An existing God, therefore, would not be a being than which a greater cannot be conceived, because an even more formidable and incredible creator would be a God which did not exist.
  7. (Hence) God does not exist.

This parody—at least in its current state—seems inferior to other parodies in the literature, including the early parodies of Gaunilo and Caterus. To mention but one difficulty, while we might suppose that it would be a greater achievement to create something if one did not exist than if one did exist, it doesn’t follow from this that a non-existent creator is greater (qua being) than an existent creator. Perhaps it might be replied that this objection fails to take the first premise into account: if the creation of the world really is “the most marvellous achievement imaginable”, then surely there is some plausibility to the claim that the creator must have been non-existent (since that would make the achievement more marvellous than it would otherwise have been). But what reason is there to believe that the creation of the world is “the most marvellous achievement imaginable”, in the sense which is required for this argument? Surely it is quite easy to imagine even more marvellous achievements—e.g., the creation of many worlds at least as good as this one! (Of course, one might also want to say that, in fact, one cannot conceive of a non-existent being’s actually creating something: that is literally inconceivable. Etc.)

Chambers 2000 and Siegwart 2014 provide nice, recent discussions of Gaunilo’s parody of the Proslogion II argument.

6. Gödel’s Ontological Argument

There is a small, but steadily growing, literature on the ontological arguments which Gödel developed in his notebooks, but which did not appear in print until well after his death. These arguments have been discussed, annotated and amended by various leading logicians: the upshot is a family of arguments with impeccable logical credentials. (Interested readers are referred to Sobel 1987, Anderson 1990, Adams 1995b, and Hazen 1999 for the history of these arguments, and for the scholarly annotations and emendations.) Here, I shall give a brief presentation of the version of the argument which is developed by Anderson, and then make some comments on that version. This discussion follows the presentation and discussion in Oppy 1996, 2000.

Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive

Definition 2: 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 3: x necessarily exists if and only if every essence of x is necessarily exemplified

Axiom 1: If a property is positive, then its negation is not positive.

Axiom 2: Any property entailed by—i.e., strictly implied by—a positive property is positive

Axiom 3: The property of being God-like is positive

Axiom 4: If a property is positive, then it is necessarily positive

Axiom 5: Necessary existence is positive

Axiom 6: For any property P, if P is positive, then being necessarily P is positive.

Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.

Corollary 1: The property of being God-like is consistent.

Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.

Theorem 3: Necessarily, the property of being God-like is exemplified.

Given a sufficiently generous conception of properties, and granted the acceptability of the underlying modal logic, the listed theorems do follow from the axioms. (This point was argued in detail by Dana Scott, in lecture notes which circulated for many years and which were transcribed in Sobel 1987 and published in Sobel 2004. It is also made by Sobel, Anderson, and Adams.) So, criticisms of the argument are bound to focus on the axioms, or on the other assumptions which are required in order to construct the proof.

Some philosophers have denied the acceptability of the underlying modal logic. And some philosophers have rejected generous conceptions of properties in favour of sparse conceptions according to which only some predicates express properties. But suppose that we adopt neither of these avenues of potential criticism of the proof. What else might we say against it?

One important point to note is that no definition of the notion of “positive property” is supplied with the proof. At most, the various axioms which involve this concept can be taken to provide a partial implicit definition. If we suppose that the “positive properties” form a set, then the axioms provide us with the following information about this set:

  1. If a property belongs to the set, then its negation does not belong to the set.
  2. The set is closed under entailment.
  3. The property of having as essential properties just those properties which are in the set is itself a member of the set.
  4. The set has exactly the same members in all possible worlds.
  5. The property of necessary existence is in the set.
  6. If a property is in the set, then the property of having that property necessarily is also in the set.

On Gödel’s theoretical assumptions, we can show that any set which conforms to (1)–(6) is such that the property of having as essential properties just those properties which are in that set is exemplified. Gödel wants us to conclude that there is just one intuitive, theologically interesting set of properties which is such that the property of having as essential properties just the properties in that set is exemplified. But, on the one hand, what reason do we have to think that there is any theologically interesting set of properties which conforms to the Gödelian specification? And, on the other hand, what reason do we have to deny that, if there is one set of theologically interesting set of properties which conforms to the Gödelian specification, then there are many theologically threatening sets of properties which also conform to that specification?

In particular, there is some reason to think that the Gödelian ontological argument goes through just as well—or just as badly—with respect to other sets of properties (and in ways which are damaging to the original argument). Suppose that there is some set of independent properties {I, G1, G2, …} which can be used to generate the set of positive properties by closure under entailment and “necessitation”. (“Independence” means: no one of the properties in the set is entailed by all the rest. “Necessitation” means: if P is in the set, then so is necessarily having P. I is the property of having as essential properties just those properties which are in the set. G1, G2, … are further properties, of which we require at least two.) Consider any proper subset of the set {G1, G2, …}—{H1, H2, …}, say—and define a new generating set {I*, H1, H2, …}, where I* is the property of having as essential properties just those properties which are in the newly generated set. A “proof” parallel to that offered by Gödel “establishes” that there is a being which has as essential properties just those properties in this new set. If there are as few as 7 independent properties in the original generating set, then we shall be able to establish the existence of 720 distinct“God-like” creatures by the kind of argument which Gödel offers. (The creatures are distinct because each has a different set of essential properties.)

Even if the above considerations are sufficient to cast doubt on the credentials of Gödel’s “proof”, they do not pinpoint where the “proof” goes wrong. If we accept that the role of Axioms 1, 2, 4, and 6 is really just to constrain the notion of “positive property” in the right way—or, in other words, if we suppose that Axioms 1, 2, 4, and 6 are “analytic truths” about “positive properties”—then there is good reason for opponents of the “proof” to be sceptical about Axioms 3 and 5. Kant would not have been happy with Axiom 5; and there is at least some reason to think that whether the property of being God-like is “positive” ought to depend upon whether or not there is a God-like being.

7. A Victorious Ontological Argument?

The “victorious” modal ontological argument of Plantinga 1974 goes roughly as follows: Say that an entity possesses “maximal excellence” if and only if it is omnipotent, omnscient, and morally perfect. Say, further, that an entity possesses “maximal greatness” if and only if it possesses maximal excellence in every possible world—that is, if and only if it is necessarily existent and necessarily maximally excellent. Then consider the following argument:

  1. There is a possible world in which there is an entity which possesses maximal greatness.
  2. (Hence) There is an entity which possesses maximal greatness.

Under suitable assumptions about the nature of accessibility relations between possible worlds, this argument is valid: from it is possible that it is necessary that p, one can infer that it is necessary that p. Setting aside the possibility that one might challenge this widely accepted modal principle, it seems that opponents of the argument are bound to challenge the acceptability of the premise.

And, of course, they do. Let’s just run the argument in reverse.

  1. There is no entity which possesses maximal greatness.
  2. (Hence) There is no possible world in which there is an entity which possesses maximal greatness.

Plainly enough, if you do not already accept the claim that there is an entity which possesses maximal greatness, then you won’t agree that the first of these arguments is more acceptable than the second. So, as a proof of the existence of a being which posseses maximal greatness, Plantinga’s argument seems to be a non-starter.

Perhaps somewhat surprisingly, Plantinga himself agrees: the “victorious” modal ontological argument is not a proof of the existence of a being which possesses maximal greatness. But how, then, is it “victorious”? Plantinga writes: “Our verdict on these reformulated versions of St. Anselm’s argument must be as follows. They cannot, perhaps, be said to prove or establish their conclusion. But since it is rational to accept their central premise, they do show that it is rational to accept that conclusion” (Plantinga 1974, 221).

It is pretty clear that Plantinga’s argument does not show what he claims that it shows. Consider, again, the argument: “Either God exists, or 2+2=5. It is not the case that 2+2=5. So God exists.” It is just a mistake for a theist to say: “Since the premise is true (and the argument is valid), this argument shows that the conclusion of the argument is true”. No-one thinks that that argument shows any such thing. Similarly, it is just a mistake for a theist to say: “Since it is rational to accept the premise (and the argument is valid), this argument shows that it is rational to accept the conclusion of the argument”. Again, no one thinks that that argument shows any such thing. But why don’t these arguments show the things in question? There is room for argument about this. But it is at least plausible to claim that, in each case, any even minimally rational person who has doubts about the claimed status of the conclusion of the argument will have exactly the same doubts about the claimed status of the premise. If, for example, I doubt that it is rational to accept the claim that God exists, then you can be quite sure that I will doubt that it is rational to accept the claim that either 2+2=5 or God exists. But, of course, the very same point can be made about Plantinga’s argument: anyone with even minimal rationality who understands the premise and the conclusion of the argument, and who has doubts about the claim that it is rationally permissible to believe that there is an entity which possesses maximal greatness, will have exactly the same doubts about the claim that it is rationally permissible to believe that there is a possible world in which there is an entity which possesses maximal greatness.

For further discussion of Plantinga’s argument, see—for example—Adams 1988, Chandler 1993, Oppy 1995 (70–78, 248–259), Tooley 1981, and van Inwagen 1977).

8. St. Anselm’s Ontological Argument

There is an enormous literature on the material in Proslogion II-III. Some commentators deny that St. Anselm tried to put forward any proofs of the existence of God. Even among commentators who agree that St. Anselm intended to prove the existence of God, there is disagreement about where the proof is located. Some commentators claim that the main proof is in Proslogion II, and that the rest of the work draws out corollaries of that proof (see, e.g., Charlesworth 1965). Other commentators claim that the main proof is in Prologion III, and that the proof in Proslogion II is merely an inferior first attempt (see, e.g., Malcolm 1960). Yet other commentators claim that there is a single proof which spans at least Proslogion II-III—see, e.g., Campbell 1976 and, perhaps, the entire work—see, e.g., La Croix 1972. I shall ignore this aspect of the controversy about the Proslogion. Instead, I shall just focus on the question of the analysis of the material in Proslogion II on the assumption that there is an independent argument for the existence of God which is given therein.

Here is one translation of the crucial part of Proslogion II (due to William Mann (1972, 260–1); alternative translations can be found in Barnes 1972, Campbell 1976, Charlesworth 1965, and elsewhere):

Thus even the fool is convinced that something than which nothing greater can be conceived is in the understanding, since when he hears this, he understands it; and whatever is understood is in the understanding. And certainly that than which a greater cannot be conceived cannot be in the understanding alone. For if it is even in the understanding alone, it can be conceived to exist in reality also, which is greater. Thus if that than which a greater cannot be conceived is in the understanding alone, then that than which a greater cannot be conceived is itself that than which a greater can be conceived. But surely this cannot be. Thus without doubt something than which a greater cannot be conceived exists, both in the understanding and in reality.

There have been many ingenious attempts to find an argument which can be expressed in modern logical formalism, which is logically valid, and which might plausibly be claimed to be the argument which is expressed in this passage. To take a few prime examples, Adams 1971, Barnes 1972 and Oppenheimer and Zalta 1991 have all produced formally valid analyses of the argument in this passage. We begin with a brief presentation of each of these analyses, preceded by a presentation of the formulation of the argument given by Plantinga 1967, and including a presentation of some of the formulations of Lewis 1970. (Chambers 2000 works with the analysis of Adams 1971.)

8.1 Formulation 1

  1. God exists in the understanding but not in reality. (Assumption for reductio)

  2. Existence in reality is greater than existence in the understanding alone. (Premise)

  3. A being having all of God’s properties plus existence in reality can be conceived. (Premise)

  4. A being having all of God’s properties plus existence in reality is greater than God. (From (1) and (2).)

  5. A being greater than God can be conceived. (From (3) and (4).)

  6. It is false that a being greater than God can be conceived. (From definition of “God”.)

  7. Hence, it is false that God exists in the understanding but not in reality. (From (1), (5), (6).)

  8. God exists in the understanding. (Premise, to which even the Fool agrees.)

  9. Hence God exists in reality. (From (7), (8).)

See Plantinga 1967.

8.2 Formulation 2

  1. The Fool understands the expression “the being than which no greater can be conceived”. (Premise)

  2. If a person understands an expression “b”, then b is in that person’s understanding. (Premise)

  3. If a thing is in a person’s understanding, then the person can conceive of that thing’s existing in reality. (Premise)

  4. Each thing which exists in reality is greater than any thing which exists only in the understanding. (Premise)

  5. If a person can conceive of something, and that thing entails something else, then the person can also conceive of that other thing. (Premise)

  6. If a person can conceive that a specified object has a given property, then that person can conceive that something or other has that property. (Premise)

  7. Hence the being than which no greater can be conceived exists in reality. (From (1)-(6), by a complex series of steps here omitted.)

See Barnes 1972.

8.3 Formulation 3

  1. There is a thing x, and a magnitude m, such that x exists in the understanding, m is the magnitude of x, and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n>m. (Premise)

  2. For any thing x and magnitude m, if x exists in the understanding, m is the magnitude of x, and it is not possible that there is a thing y and magnitude n such that n is the magnitude of y and n>m, then it is possible that x exists in reality. (Premise)

  3. For any thing x and magnitude m, if m is the magnitude of x, and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n>m, and x does not exist in reality, then it is not possible that if x exists in reality then there is a magnitude n such that n is greater than m and n is the magnitude of x. (Premise)

  4. (Hence) There is a thing x and a magnitude m such that x exist in the understanding, and x exists in reality, and m is the magnitude of x, and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n>m. (From 1, 2, 3)

See Adams 1971.

8.4 Formulation 4

  1. For any understandable being x, there is a world w such that x exists in w. (Premise)

  2. For any understandable being x, and for any worlds w and v, if x exists in w, but x does not exist in v, then the greatness of x in w exceeds the greatness of x in v. (Premise)

  3. There is an understandable being x such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. (Premise)

  4. (Hence) There is a being x existing in the actual world such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. (From (1)-(3).)

See Lewis 1970.

Lewis also suggests an alternative to (3) which yields a valid argument:

(3′) There is an understandable being x such that for no worlds v and w and being y does the greatness of y in w exceed the greatness of x in v.

and two alternatives to (3)—not presented here—which yield invalid arguments. (Of course, there further two alternatives are crucial to Lewis’ overall analysis of the passage: essentially, Lewis suggests that Anselm equivocates between an invalid argument with plausible premises and a valid argument with question-begging premises. In this respect, Lewis’ analysis is quite different from the other analyses currently under discussion.)

8.5 Formulation 5

  1. There is (in the understanding) something than which there is no greater. (Premise)

  2. (Hence) There is (in the understanding) a unique thing than which there is no greater. (From (1), assuming that the “greater-than” relation is connected.)

  3. (Hence) There is (in the understanding) something which is the thing than which there is no greater. (From (2), by a theorem about descriptions.)

  4. (Hence) There is (in the understanding) nothing which is greater than the thing than which there is no greater. (From (3), by another theorem about descriptions.)

  5. If that thing than which there is no greater does not exist (in reality), then there is (in the understanding) something which is greater than that thing than which there is no greater. (Premise)

  6. (Hence) That thing than which there is no greater exists (in reality). (From (4) and (5).)

  7. (Hence) God exists. (From (6).)

See Oppenheimer and Zalta 1991.

Oppenheimer and Zalta 2011 provides a “simplified” version of this argument, in which the number of controversial assumptions is reduced. Since they also provide a clear reason for thinking that this new version of the argument is not persuasive, I shall not consider it further here.

8.6 Critical Appraisal

Considered as interpretations of the argument presented in the Proslogion, these formulations are subject to various kinds of criticisms.

First, the modal interpretations of Lewis 1970 and Adams 1971 don’t square very well with the rest of the Proslogion: the claim that “being than which no greater can be conceived” should be read as “being than which no greater is possible” would have us render the claim of Proslogion 15 to be that God is a being greater than any which is possible. And that is surely a bad result.

Second, the Meinongian interpretations of Barnes 1972, Adams 1971 and Oppenheimer and Zalta 1991 produce arguments which, given the principles involved, could easily be much simplified, and which are obviously vulnerable to Gaunilo-type objections.

Consider, for example, the case of Oppenheimer and Zalta. They have Anselm committed to the claim that if anyone can understand the phrase “that than which F”, then there is something in the understanding such that F (see their footnote 25); and they also have him committed to the claim that if there is something which is the F-thing, then it—i.e., the F-thing—has the property F (see page 7). Plainly though, if Anselm is really committed to these principles, then he could hardly fail to be committed to the more general principles: (1) if anyone can understand the phrase “an F”, then there is at least one F-thing in the understanding; and (2) if there are some things which are the F-things, then they—i.e., the F-things—must have the property F. (It would surely be absurd to claim that Anselm is only committed to the less general principles: what could possibly have justified the restrictions to the special cases?)

But, then, mark the consequences. We all understand the expression “an existent perfect being”. So, by the first claim, there is at least one existent perfect being in the understanding. And, by the second claim, any existent perfect being is existent. So, from these two claims combined, there is—in reality—at least one existent perfect being.

This argument gives Anselm everything that he wants, and very much more briefly. (The Proslogion goes on and on, trying to establish the properties of that than which no greater can be conceived. How much easier if we can just explicitly build all of the properties which want to “derive” into the initial description.) So, if Anselm really were committed to the principles which Oppenheimer and Zalta appear to attribute to him, it is hard to understand why he didn’t give the simpler argument. And, of course, it is also hard to understand why he didn’t take Gaunilo’s criticism. After all, when it is set out in this way, it is obvious that the argument proves far too much.

Third, some of the arguments have Anselm committed to claims about greatness which do not seem to correspond with what he actually says. The natural reading of the text is that, if two beings are identical save that one exists only in the understanding and the other exists in reality as well, then the latter is greater than the former. But Barnes 1971, for example, has Anselm committed to the much stronger claim that any existing thing is greater than every non-existent thing.

Given these kinds of considerations, it is natural to wonder whether there are better interpretations of Proslogion II according to which the argument in question turns out NOT to be logically valid. Here is a modest attempt to provide such an analysis:

We start with the claim that the Fool understands the expression “being than which no greater can be conceived”, i.e., even the Fool can entertain the idea or possess the concept of a being than which no greater can be conceived. Now, entertaining this idea or possessing this concept requires the entertainer or possessor to recognise certain relationships which hold between given properties and the idea or concept in question. For example, given that you possess the concept of, or entertain the idea of, a smallest really existent Martian, it follows that you must recognise some kind of connection between the properties of being a Martian, really existing, and being smaller than other really existing Martians, and the concept or idea in question.

Following Anselm, we might say that, since you understand the expression “smallest really existent Martian”, there is, in your understanding, at least one smallest really existent Martian. (Or, apparently following Descartes, one might say that real existence is “part of”—or “contained in”—the idea of a smallest really existent Martian.) However, in saying this, it must be understood that we are not actually predicating properties of anything: we aren’t supposing that there is something which possesses the properties of being a Martian, really existing, and being no larger than any other Martian. (After all, we can safely suppose, we don’t think that any Martians really exist.) In other words, we must be able to have the concept of, or entertain the idea of, a smallest really existing Martian without believing that there really are any smallest Martians. Indeed, more strongly, we must be able to entertain the concept of a smallest really existent Martian—and to recognise that the property of “really existing” is part of this concept—while nonetheless maintaining that there are no smallest existent Martians.

It will be useful to introduce vocabulary to mark the point which is being made here. We could, for instance, distinguish between the properties which are encoded in an idea or concept, and the properties which are attributed in positive atomic beliefs which have that idea or concept as an ingredient. The idea “really existent Santa Claus” encodes the property of real existence; but it is perfectly possible to entertain this idea without attributing real existence to Santa Claus, i.e., without believing that Santa Claus really exists.

We can then apply this distinction to Anselm’s argument. On the one hand, the idea “being than which no greater can be conceived” encodes the property of real existence—this is what the reductio argument establishes (if it establishes anything at all). On the other hand, it is perfectly possible to entertain the idea of a being than which no greater can be conceived—and to recognise that this idea encodes the property of real existence—without attributing real existence to a being than which no greater can be conceived, i.e., without believing that a being than which no greater can be conceived really exists.

Of course, the argument which Anselm actually presents pays no attention to this distinction between encoding and attributing—i.e., between entertaining an idea and holding a belief—and nor does it pay attention to various other niceties. We begin from the point that the Fool entertains the idea of that than which no greater can be conceived (because the Fool understands the words “that than which no greater can be conceived”). From this, we move quickly to the claim that even the Fool is “convinced”—i.e., believes—that that than which no greater can be conceived possesses the property of existing in the understanding. And then the reductio argument is produced to establish that that than which no greater can be conceived cannot exist only in the understanding but must also possess the property of existing in reality as well (and all mention of the Fool, and what it is that the Fool believes, disappears).

As it stands, this is deeply problematic. How are we supposed to regiment the references to the Fool in the argument? Is the reductio argument supposed to tell us something about what even the Fool believes, or ought to believe? Are the earlier references to the Fool supposed to be inessential and eliminable? How are we so much as to understand the claim that even the Fool believes that that than which no greater can be conceived exists in the understanding? And how do we get from the Fool’s understanding the words “that than which no greater can be conceived” to his believing that that than which no greater can be conceived possesses the property of existing in the understanding?

Following the earlier line of thought, it seems that the argument might go something like this:

  1. (Even) the Fool has the concept of that than which no greater can be conceived.

  2. (Hence) (Even) the Fool believes that that than which no greater can be conceived exists in the understanding.

  3. No one who believes that that than which no greater can be conceived exists in the understanding can reasonably believe that that than which no greater can be conceived exists only in the understanding.

  4. (Hence) (Even) the Fool cannot reasonably deny that that than which no greater can be conceived exists in reality

  5. (Hence) That than which no greater can be conceived exists in reality.

While this is not a good argument, it could appear compelling to one who failed to attend to the distinction between entertaining ideas and holding beliefs and who was a bit hazy on the distinction between the vehicles of belief and their contents. When the Fool entertains the concept of that than which no greater can be conceived he recognises that he is entertaining this concept (i.e., he believes that he is entertaining the concept of that than which no greater can be conceived—or, as we might say, that the concept is in his understanding). Conflating the concept with its object, this gives us the belief that than which no greater can be conceived possesses the property of existing in the understanding. Now, suppose as hypothesis for reductio, that we can reasonably believe that that than which no greater can be conceived possesses the property of existing only in the understanding. Ignoring the distinction between entertaining ideas and holding beliefs, this means that we when we entertain the idea of that than which no greater can be conceived, we entertain the idea of a being which exists only in the understanding. But that is absurd: when we entertain the idea of that than which no greater can be conceived, our idea encodes the property of existing in reality. So there is a contradiction, and we can conclude that, in order to be reasonable, we must believe that that than which no greater can be conceived exists in reality. But if any reasonable person must believe that that than which no greater can be conceived exists in reality, then surely it is the case that that than which no greater can be conceived exists in reality. And so we are done.

No doubt this suggestion about the interpretation of Anselm’s argument is deficient in various ways. However, the point of including it is illustrative rather than dogmatic. In the literature, there has been great resistance to the idea that the argument which Anselm gives is one which modern logicians would not hesitate to pronounce invalid. But it is very hard to see why there should be this resistance. (Certainly, it is not something for which there is much argument in the literature.) The text of the Proslogion is so rough, and so much in need of polishing, that we should not be too quick to dismiss the suggestion that Anselm’s argument is rather more like the argument most recently sketched than it is like the logically valid demonstrations provided by commentators such as Barnes, Adams, and Oppenheimer and Zalta. (For a more complex analysis of Proslogion II that has it yielding a valid argument, see Hinst 2014.)

9. Ontological Arguments in the 21st Century

Many recent discussions of ontological arguments are in compendiums, companions, encylopedias, and the like. So, for example, there are review discussions of ontological arguments in: Leftow 2005, Matthews 2005, Lowe 2007, Oppy 2007, and Maydole 2009. While the ambitions of these review discussions vary, many of them are designed to introduce neophytes to the arguments and their history. Given the current explosion of enthusiasm for compendiums, companions, encylopedias, and the like, in philosophy of religion, it is likely that many more such discussions will appear in the immediate future.

Some recent discussions of ontological arguments have been placed in more synoptic treatments of arguments about the existence of God. So, for example, there are extended discussions of ontological arguments in Everitt 2004, Sobel 2004, and Oppy 2006. Sobel’s examination of ontological arguments is exemplary. He provides one chapter on ‘classical ontological arguments’: Anselm, Descartes, Spinoza, and Kant’s critique of ontological arguments; one chapter on ‘modern modal ontological arguments’: Hartshorne, Malcolm and Plantinga; and one chapter on Gödel’s ontological argument. His analyses are very careful, and make heavy use of the tools of modern philosophical logic.

There has been one recent monograph devoted exclusively to the analysis of ontological arguments: Dombrowski 2006. Dombrowski is a fan of Hartshorne: the aim of his book is to defend the claim that Hartshorne’s ontological argument is a success. While Dombrowski’s book is a useful addition to the literature because of the scope of its discussion of ontological arguments—for example, it contains a chapter on Rorty on ontological arguments, and another chapter on John Taylor on ontological arguments—even reviewers sympathetic to process theism have not been persuaded that it makes a strong case for its central thesis.

Swatkowski (2012) is the most recent collection of papers on ontological arguments. A significant proportion of papers in this collection take up technical questions about logics that support ontological derivations. (Those interested in technical questions may also be interested in the topic taken up in Oppenheimer and Zalta (2011) and Gorbacz (2012).)

Finally, there has been some activity in journals. The most significant of these pieces is Millican 2004, the first article on ontological arguments in recent memory to appear in Mind. Millican argues for a novel interpretation of Anselm’s argument, and for a new critique of ontological arguments deriving from this interpretation. Needless to say, both the interpretation and the critique are controversial, but they are also worthy of attention. Among other journal articles, perhaps the most interesting are Pruss 2010, which provides a novel defence of the key possibility premise in modal ontological arguments, and Pruss 2009, which kick-started recent discussion of higher-order ontological arguments. There is also a chain of papers in Analysis initiated by Matthews and Baker (2010)

Bibliography

Primary Texts

  • Anselm, St., Proslogion, in St. Anselm’s Proslogion, M. Charlesworth (ed.), Oxford: OUP, 1965
    [Available online, in the Internet Medieval Sourcebook, Paul Halsall (ed.), Fordham University Center for Medieval Studies, translation by David Burr].
  • Aquinas, T., Summa Theologica, 1272, literally translated by Fathers of the English Dominican Province, London: Burn, Oates & Washbourne, 1920
    [Available online, in the Internet Medieval Sourcebook, Paul Halsall (ed.), Fordham University Center for Medieval Studies, translation by David Burr].
  • Ayer, A., Language, Truth and Logic , second edition, London: Gollancz, 1948.
  • Descartes, R., Discourse on Method and The Meditations, translated with an introduction by F. Sutcliffe, Harmondsworth: Penguin, 1968
    [Translation of The Meditations by John Veitch, LL.D. available online].
  • Frege, G., Die Grundlagen der Arithmetik, Bresnau: Koebner, 1884; translated as The Foundations of Arithmetic, J.L. Austin (trans), Oxford: Blackwell, 1974, 2nd rev edition;
    Original German text available online, (628 KB PDF file), maintained by Alain Blachair, Académie de Nancy-Metz.
  • Gaunilo, “On Behalf of the Fool”, in St. Anselm’s Proslogion, M. Charlesworth (ed.), Oxford: OUP, 1965
    [Available online in the Internet Medieval Sourcebook, Paul Halsall (ed.), Fordham Universit\ y Center for Medieval Studies, translation by David Burr].
  • Hegel, G., The Ontological Proof According to the Lectures of 1831, in P. Hodgson (ed.), Lectures on the Philosophy of Religion, Vol. III Berkeley: University of California Press, 1985, pp. 351–8.
  • Hume, D., Dialogues Concerning Natural Religion, 1779, edited with an introduction by H. Aiken, London: Macmillan, 1948.
  • Kant, I., Critique of Pure Reason, 1787, second edition, translated by N. Kemp-Smith, London: Macmillan, 1933.
  • Leibniz, G., New Essay Concerning Human Understanding, 1709, translated by A. Langley, New York: Macmillan, 1896.
  • Spinoza, B., The Ethics, 1677, translation of 1883 by R. Elwes, New York: Dover, 1955
    [Available online, prepared by R. Bombardi, for the Philosophy Web Works project, Middle Tennessee State Univerity].

Other Texts

  • Adams, R., 1971, “The Logical Structure of Anselm’s Argument”, Philosophical Review, 80: 28–54.
  • –––, 1988, “Presumption and the Necessary Existence of God”, Noûs, 22: 19–34.
  • –––, 1995a, Leibniz: Determinist, Theist, Idealist, Oxford: Oxford University Press.
  • –––, 1995b, “Introductory Note to *1970” in K. Gödel Collected Works Volume III: Unpublished essays and lectures, S. Feferman, et al. (eds.), New York: Oxford University Press, pp. 388–402.
  • Alston, W., 1960, “The Ontological Argument Revisited” Philosophical Review, 69: 452–74.
  • Anderson, C., 1990, “Some Emendations on Gödel’s Ontological Proof”, Faith and Philosophy, 7: 291–303.
  • Barnes, J., 1972, The Ontological Argument, London: Macmillan.
  • Campbell, R., 1976, From Belief to Understanding, Canberra: ANU Press.
  • Chambers, T., 2000, “On Behalf of the Devil: A Parody of St. Anselm Revisited”, Proceedings of the Aristotelian Society (New Series), 100: 93–113.
  • Chandler, H., 1993, “Some Ontological Arguments”, Faith and Philosophy, 10: 18–32.
  • Charlesworth, M., 1965, Anselm’s Proslogion, Oxford: Oxford University Press.
  • Dombrowski, D., 2006, Rethinking the Ontological Argument: A Neoclassical Theistic Response, Cambridge: Cambridge University Press.
  • Dummett, M., 1993, “Existence”, in The Seas of Language, Oxford: Oxford University Press.
  • Everitt, N., 2004, The Non-Existence of God, London: Blackwell
  • Findlay, J., 1949, “Can God’s Existence Be Disproved?”, Mind, 57: 176–83.
  • Gorbacz, P., 2012, “PROVER9’s Simplification Explained Away”, Australasian Journal of Philosophy, 90: 585–96.
  • Grey, W., 2000, “Gasking’s Proof”, Analysis, 60: 368–370.
  • Harrelson, K., 2009, The Ontological Argument from Descartes to Hegel, New York: Humanity Books.
  • Hartshorne, C., 1965, Anselm’s Discovery: A Re-Examination of the Ontological Proof for God’s Existence, La Salle, IL: Open Court.
  • Hazen, A., 1999, “On Gödel’s Ontological Proof”, Australasian Journal of Philosophy, 76: 361–377.
  • Henle, P., 1961, “Uses of the Ontological Argument”, Philosophical Review, 70: 102–9.
  • Hinst, P., 2014, “A Logical Analysis of the Main Argument in Chapter 2 of the Proslogion by Anselm of Canterbury”, Philosophiegeschichte Und Logische Analyse, 17: 22–44.
  • Johnston, M., 1992, “Explanation, Response-Dependence, and Judgement-Dependence”, in P. Menzies (ed.), Response-Dependent Concepts, Canberra: ANU/RSSS Working Papers in Philosophy, 123–83.
  • La Croix, R., 1972, Proslogion II and III: A Third Interpretation of Anselm’s Argument, Leiden: Brill.
  • Leftow, B., 2005, “The Ontological Argument”, in The Oxford Handbook of Philosophy of Religion, W. Wainwright (ed.), Oxford: Oxford University Press, pp. 80–115.
  • Lewis, D., 1970, “Anselm and Actuality”, Noûs, 4: 175–88.
  • Lowe, E., 2007, “The Ontological Argument”, in The Routledge Companion to Philosophy of Religion, P. Copan and C. Meister (eds.), London: Routledge.
  • Malcolm, N., 1960, “Anselm’s Ontological Arguments”, Philosophical Review, 69: 41–62.
  • Mann, W., 1972, “The Ontological Presuppositions of the Ontological Argument”, Review of Metaphysics, 26: 260–77.
  • Matthews, G., 2005, “The Ontological Argument”, in The Blackwell Guide to the Philosophy of Religion, W. Mann (ed.), Oxford: Blackwell, pp. 81–102.
  • Matthews, G., and Baker, L., 2010 “The Ontological Argument Simplified”, Analysis, 70: 210–212.
  • Maydole, R., 2009, “The Ontological Argument”, in The Blackwell Companion to Natural Theology, W. Craig and J. Moreland (ed.), Oxford: Blackwell, pp. 553–592.
  • Millican, P., 2004, “The One Fatal Flaw in Anselm’s Argument”, Mind, 113: 437–76.
  • Oppenheimer, P., and Zalta, E., 1991, “On the Logic of the Ontological Argument”, in J. Tomberlin (ed.) Philosophical Perspectives 5: The Philosophy of Religion, Atascadero: Ridgeview, pp. 509–29 [Preprint available online].
  • –––, 2011, “A Computationally-Discovered Simplification of the Ontological Argument”, Australasian Journal of Philosophy, 89: 333–349.
  • Oppy, G., 1995, Ontological Arguments and Belief in God, New York: Cambridge University Press.
  • –––, 1996, “Gödelian Ontological Arguments”, Analysis, 56: 226–230.
  • –––, 2000, “Response to Gettings”, Analysis, 60: 363–367.
  • –––, 2006, Arguing about Gods, Cambridge: Cambridge University Press.
  • –––, 2007, “The Ontological Argument” in P. Copan and C. Meister (eds.), Philosophy of Religion: Classic and Contemporary Issues, Oxford: Blackwell.
  • Plantinga, A., 1967, God and Other Minds, Ithaca: Cornell University Press.
  • –––, 1974, The Nature of Necessity, Oxford: Oxford University Press.
  • Pruss, A., 2009, “A Gödelian Ontological Argument Improved”, Religious Studies, 45: 347–353.
  • –––, 2010,“The Ontological Argument and the Motivational Centres of Lives”, Religious Studies, 46: 233–249.
  • Redding, P. and Bubbio, P., 2014 “Hegel and the Ontological Argument for the Existence of God”, Religious Studies, 50: 465–86.
  • Rescher, N., 1959, “The Ontological Proof Revisited”, Australasian Journal of Philosophy, 37: 138–48.
  • Ross, J., 1969, Philosophical Theology, New York: Bobbs-Merrill.
  • Rowe, W., 1989, “The Ontological Argument”, in J. Feinberg (ed.), Reason and Responsibility, seventh edition, Belmont, CA: Wadsworth, pp. 8–17.
  • Salmon, N., 1987, “Existence”, in J. Tomberlin (ed.), Philosophical Perspectives 1: Metaphysics, Atascadero, CA: Ridgeview: 49–108.
  • Siegwart, G., 2014, “Gaunilo Parodies Anselm: An Extraordinary Job for the Interpreter”, Philosophiegeschichte Und Logische Analyse, 17: 45–71.
  • Smart, J., 1955, “The Existence of God”, in A. Flew and A. MacIntyre (eds.), New Essays in Philosophical Theology, London: SCM Press: 500–509.
  • Sobel, J., 1987, “Gödel’s Ontological Proof”, in On Being and Saying: Essays for Richard Cartwright, J. Thomson (ed.), Cambridge, MA: MIT Press, pp. 241–61.
  • Sobel, J., 2004, Logic and Theism, New York: Cambridge University Press.
  • Smullyan, R., 1984, 5000 BC and Other Philosophical Fantasies, New York: St. Martins Press.
  • Szatkowski, M. (ed.), 2012, Ontological Proofs Today, Frankfurt: Ontos Verlag.
  • Tooley, M., 1981, “Plantinga’s Defence of the Ontological Argument”, Mind, 90: 422–7.
  • van Inwagen, P., 1977, “Ontological Arguments”, Noûs, 11: 375–395.

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