Part 1 of 2: The Ontological Argument For the Existence of God

Posted By Thomas Perez. August 10, 2010 at 10:57pm. Copyright 2010.

The Ontological Argument

The ontological argument is an argument for God’s existence and can be stated in this way: “God is the greatest being imaginable. One of the aspects of perfection or greatness is existence. Thus, God exists.” Or put another way—“The fact that God can be conceived means that he must exist.”

This argument for God’s existence was developed by the twelfth century theologian and philosopher, Anselm. It is based on Anselm’s declaration that God is “that which nothing greater can be conceived.”

The ontological argument is unlike the cosmological and teleological arguments in that it does not argue from evidence in the natural world. Thus, it is not a “cause and effect” argument. The famous French philosopher, Rene Descartes, believed in the validity of the ontological argument.

The first, and best-known, ontological argument was proposed by St. Anselm of Canterbury in the 11th. century A.D. In his Proslogion, St. Anselm claims to derive the existence of God from the concept of a being than which no greater can be conceived. St. Anselm reasoned that, if such a being fails to exist, then a greater being—namely, a being than which no greater can be conceived, and which exists—can be conceived. But this would be absurd: nothing can be greater than a being than which no greater can be conceived. So a being than which no greater can be conceived—i.e., God—exists.

In the seventeenth century, René Descartes defended a family of similar arguments. For instance, in the Fifth Meditation, Descartes claims to provide a proof demonstrating the existence of God from the idea of a supremely perfect being. Descartes argues that there is no less contradiction in conceiving a supremely perfect being who lacks existence than there is in conceiving a triangle whose interior angles do not sum to 180 degrees. Hence, he supposes, since we do conceive a supremely perfect being—we do have the idea of a supremely perfect being—we must conclude that a supremely perfect being exists.

In the early eighteenth century, Gottfried Leibniz attempted to fill what he took to be a shortcoming in Descartes’ view. According to Leibniz, Descartes’ arguments fail unless one first shows that the idea of a supremely perfect being is coherent, or that it is possible for there to be a supremely perfect being. Leibniz argued that, since perfections are unanalysable, it is impossible to demonstrate that perfections are incompatible—and he concluded from this that all perfections can co-exist together in a single entity.

In more recent times, Kurt Gödel, Charles Hartshorne, Norman Malcolm and Alvin Plantinga have all presented much-discussed ontological arguments which bear interesting connections to the earlier arguments of St. Anselm, Descartes and Leibniz. Of these, the most interesting are those of Gödel and Plantinga; in these cases, however, it is unclear whether we should really say that these authors claim that the arguments are proofs of the existence of God.

Critiques of ontological arguments begin with Gaunilo, a contemporary of St. Anselm. Perhaps the best known criticisms of ontological arguments are due to Immanuel Kant, in his Critique of Pure Reason. Most famously, Kant claims that ontological arguments are vitiated by their reliance upon the implicit assumption that “existence” is a predicate. However, as Bertrand Russell observed, it is much easier to be persuaded that ontological arguments are no good than it is to say exactly what is wrong with them. This helps to explain why ontological arguments have fascinated philosophers for almost a thousand years.

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, 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 famous ordinary 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

Taxonomy of Ontological Arguments

According to the taxonomy of Oppy (1995), there are seven major kinds of ontological arguments, viz:

definitional ontological arguments; conceptual (or hyperintensional) ontological arguments; modal ontological arguments; Meinongian ontological arguments experiential ontological arguments mereological ontological arguments; and ‘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. Here, in my view, they follow Hegel’s own precedent: his lectures on ‘the ontological argument’ are full of assertions that there is a successful ontological argument, but he gives no argumentative support for those assertions, not any indication of what the premises of the target argument might be.

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.

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 Part 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 license 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 hyper-intentional 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. Non-theists do not accept the claim that God exists in the actual world. Plainly enough, non-theists and necessitarian theists disagree about the layout of logical space, i.e., the space of possible worlds. The sample argument consists, in effect, of two premises: one which says that God exists in at least one possible world; and one which says that God exists in all possible worlds if God exists in any. It is perfectly obvious that no non-theist can accept this pair of premises. Of course, a non-theist can allow—if they wish—that there are possible worlds in which there are contingent Gods. However, it is quite clear that no rational, reflective, etc. non-theist will accept the pair of premises in the sample argument.

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 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.

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).

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 some very nice parodic discussions of Ontological Arguments in the literature. A particularly pretty one is due to Raymond Smullyan, in 5000 BC and Other Philosophical Fantasies, 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):

The creation of the world is the most marvellous achievement imaginable.
The merit of an achievement is the product of (a) its intrinsic quality, and (b) the ability of its creator.
The greater the disability or handicap of the creator, the more impressive the achievement.
The most formidable handicap for a creator would be non-existence.
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.
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.
Hence God does not exist.

This parody—at least in its current state—seems to me to be 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.)

Godel’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:

If a property belongs to the set, then its negation does not belong to the set.
The set is closed under entailment.
The property of having as essential properties just those properties which are in the set is itself a member of the set.
The set has exactly the same members in all possible worlds.
The property of necessary existence is in the set.
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, …}, which 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.

Plantinga’s 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:

There is a possible world in which there is an entity which possesses maximal greatness.
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.

There is no entity which possesses maximal greatness.
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 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 there is an entity which possesses maximal greatness, will have exactly the same doubts about the claim 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)).

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).

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