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Ontological Arguments

Ontological arguments are arguments, for the conclusion that God exists, from premises which are supposed to derive from some source other than observation of the world—e.g., from reason alone. In other words, ontological arguments are arguments from what are typically alleged to be none but analytic, a priori and necessary premises to the conclusion that God exists.

The first, and best-known, ontological argument was proposed by St. Anselm of Canterbury in the 11th century C.E. 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 real 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.

In various ways, the account provided to this point is rough, and susceptible of improvement. Sections 1–6 in what follows provide some of the requisite embellishments, though—as is usually the case in philosophy—there are many issues taken up here which could be pursued at much greater length. Sections 7–9 take up some of the central questions at a slightly more sophisticated level of discussion. Section 10 is a quick overview of very recent work on ontological arguments:

1. History of Ontological Arguments

2. taxonomy of ontological arguments, 3. characterisation of ontological arguments, 4. uses of ontological arguments, 5. objections to ontological arguments, 6. parodies of ontological arguments, 7. gödel’s ontological argument, 8. a victorious ontological argument, 9. st. anselm’s ontological argument, 10. ontological arguments in the 21st century, primary texts, other texts, other internet resources, related entries.

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

According to a modification of the taxonomy of Oppy 1995, there are eight 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;
• higher-order 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: No example is provided of a ‘Hegelian’ ontological argument. There is no extant discussion that states clearly the full set of premises of a ‘Hegelian’ ontological argument. (See Redding and Bubbio 2014 for recent discussion of this point.)

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

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.

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.)

[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.)

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.)

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.

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.)

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.

Before we turn to assessment of ontological arguments, we need to get clear about what the proper intended goals of ontological arguments can be. Suppose we think of arguments as having advocates and targets: when an advocate presents an argument to a target, the goal of the advocate is to bring about some change in the target. What might be the targets of ontological arguments, and what might be the changes that advocates of these arguments aim to bring about in those targets?

Here are some proposals; no doubt the reader can think of others:

• The targets might be atheists, and the goal might be to turn them into theists.
• The targets might be agnostics, and the goal might be to turn them into theists.
• The targets might be theists, and the goal might be to improve the doxastic position of theists.
• The targets might be professional philosophers, and the goal might be to advance understanding of the consequences of adopting particular logical rules, or treating existence as a real predicate, or allowing definitions to have existential import, or the like.
• The targets might be undergraduate philosophy students, and the goal might be to give them some sufficiently frustrating examples on which to cut their critical teeth.

In the coming discussion, it will be supposed that the targets are atheists and agnostics, and that the goal is to turn them into theists. Suppose that an advocate presents an ontological argument to a target. What conditions must that arguments satisfy if it is fit for its intended purpose? A plausible suggestion is that, minimally, it should make the targets recognise that they have good reason to accept the conclusion of the argument that they did not recognise that they have prior to the presentation of the argument. Adopting this plausible suggestion provides the following criterion: a successful ontological argument is one that should make atheists and agnostics recognise that they have good reason to believe that God exists that they did not recognise that they have prior to the presentation of the argument. Note that this criterion has a normative dimension: it adverts to what atheists and agnostics should do when presented with the argument.

There is an important discussion to be had about whether we should suppose that the targets of ontological arguments are atheists and agnostics, and that the goal is to turn them into theists. However, it is simply beyond the scope of this entry to pursue that discussion here.

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 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 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 cannot accept both of these premises – they entail that God exists in every possible world whereas a minimally rational non-theist maintains that there is at least one possible world in which God does not exist. Given that a minimally rational non-theist says that there is at least one possible world in which God does not exist, such a non-theist can offer a parallel counterargument with the following two premises:

• God fails to exist in at least one possible world.

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 sophisticated 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 pejorative 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 inconsistent—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).

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 (usually 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 of 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 interpreted classically: “Either 2+2=5, or God exists. Not 2+2=5. Hence God exists.” This argument contributes nothing positive to any case for theism, just as the argument “Either 2+2=5, or God does not exist. Not 2+2=5. Hence God does not exist.” contributes nothing positive to the case for non-theism.)

There are many parodic discussions of Ontological Arguments in the literature. See, for example, the parody provided by 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):

• 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—is 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 interesting recent discussions of Gaunilo’s parody of the Proslogion II 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, we 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 , G 1 , G 2 , …} 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. G 1 , G 2 , … are further properties, of which we require at least two.) Consider any proper subset of the set { G 1 , G 2 , …}—{ H 1 , H 2 , …}, say—and define a new generating set { I *, H 1 , H 2 , …}, 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.

For detailed recent discussion of Gödel’s argument, see Kovac (2003), Pruss (2009) (2018), and Swietorzecka (2016).

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, omniscient, 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 possesses 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 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 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 ”, just as it is a mistake for a non-theist to say that the argument “Either God does not exist, or 2+2=5. It is not the case that 2+2=5. So God does not exist.” shows that God does not exist. Similarly, it is a mistake for a theist to say: “Since it is rational to accept the premises (and the argument is valid), this argument shows that it is rational to accept the claim that God exists”, just as it is a mistake for the non-theist to say: “Since it is rational to accept the premises of the non-theistic argument (and that argument is valid), the non-theistic argument shows that it is rational to accept the claim that God does not exist”. While there is room for dispute about exactly why all of this is so, it is plausible to say 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 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), Rasmussen (2018), Tooley 1981, and van Inwagen 1977).

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. In what follows, we ignore this aspect of the controversy about the Proslogion . Instead, we focus just 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.)

9.1 Formulation 1

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

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

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

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

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

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

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

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

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

See Plantinga 1967.

9.2 Formulation 2

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

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

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

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

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

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)

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.

9.3 Formulation 3

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)

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)

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)

(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.

9.4 Formulation 4

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

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)

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)

(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, these 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.)

9.5 Formulation 5

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

(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.)

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

(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.)

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)

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

(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, it won't be considered further here.

9.6 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:

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

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

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.

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

(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.)

Many recent discussions of ontological arguments are in compendiums, companions, encyclopedias, 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, encyclopedias, 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.

Szatkowski (2012) is a 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).) The most recent collection is Oppy (2018).

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 is Pruss 2010, which provides a novel defence of the key possibility premise in modal ontological arguments. There is also a chain of papers in Analysis initiated by Matthews and Baker (2010)

Relatively recent work on ontological arguments by women includes: Anscombe (1993), Antognazza (2018), Crocker (1972), Diamond (1977), Ferreira (1983), Garcia (2008), [Haight and] Haight (1970), [Matthews and] Baker (2011), Wilson (1978) and Zagzebski (1984).

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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Medieval Sourcebook: Philosophers’ Criticisms of Anslem’s Ontological Argument for the Being of God (Paul Halsell, Fordham University)
• Ontological Argument Revisited by Two Ottoman Muslim Scholars (Umit Dericioglu)
• The Ontological Argument (Kenneth Himma, University of Washington)
• Hegel and Kant on the Ontological Argument (Maria de Lourdes Borges, Federal University of Santa Catarina)
• Ontological Argument (links to papers on ontological arguments)
• “ Formalization, Mechanization and Automation of Gödel’s Proof of God’s Existence ”, unpublished manuscript.
• “ Automating Gödel’s Ontological Proof of God’s Existence with Higher-order Automated Theorem Provers ”, published in ECAI 2014, T. Schaub et al . (eds.), IOS Press.

Anselm of Canterbury [Anselm of Bec] | a priori justification and knowledge | Descartes, René | existence | God: and other ultimates | Gödel, Kurt | Hegel, Georg Wilhelm Friedrich | Kant, Immanuel | logic: informal | logic: modal | Meinong, Alexius

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A Level Philosophy & Religious Studies

The Ontological Argument

Introduction.

“it is easier to feel convinced that [the Ontological Argument] must be fallacious than it is to find out precisely where the fallacy lies.” – Bertrand Russell

Ontological arguments are a priori. They are based on an analysis of the concept of God. They essentially argue that if you think carefully about what God is, you’ll understand that God must exist.

Ontological arguments are deductive. The truth of the premises logically entails the truth of the conclusion.

St Anselm’s Ontological argument

P1. God is the greatest conceivable being (by definition) P2. It is greater to exist in reality than the mind alone P3. God exists in the mind C1. Therefore, God exists in reality

Anselm uses the illustration of a painter who has an idea of what they will paint in their mind before painting it in reality. This shows that ideas can exist in the mind.

Anselm points to Psalm 14:1 “the fool says in his heart, ‘there is no God’.”

An atheist says they do not believe in God, but they must therefore have an idea of God in their mind.

The force of Anselm’s argument is then that it would be incoherent to think that God exists in the mind alone, since then we could conceive of something greater, i.e., God also existing in reality. Yet, God is the greatest being, so conceiving of anything greater is incoherent. So, our idea of God must therefore be of a being that exists in reality. To say that God does not exist in reality is to say that the greatest being is not the greatest being. It is self-contradictory.

“that, than which nothing greater can be conceived, cannot exist 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 reality.” – Anselm.

Whether God is within our understanding

A strength of the ontological argument its definition of God

Anselm uses a theologically and philosophically convincing definition of God, carefully designed to avoid the problem of defining something that is beyond our understanding. Anselm presents an analogy. We can’t fully look at the sun but can still see daylight. Similarly, we can’t fully know God, but can at least understand that he is the greatest conceivable being.

“If you say that what is not entirely understood is not understood and is not in the understanding: say, then, that since someone is not able to gaze upon the purest light of the sun does not see light that is nothing but sunlight.”  – Anselm

Weakness: God is not ‘in’ the mind/understanding

Gaunilo raises an objection to P3; the premise that the greatest conceivable being exists in the mind/understanding. Gaunilo draws on the traditional Christian premise that God is beyond our understanding to argue that God therefore cannot be in the understanding.

Anselm cannot then proceed to reason about whether it would be greater also in reality. The ontological argument seems to fail because it relies on our ability to understand and reason about things that are beyond our ability to understand or reason about.

Aquinas also made this argument against Anselm – that God’s nature, such as the ‘eternal law’ is beyond our understanding and that people have different understandings of God.

“Perhaps not everyone who hears this word “God” understands it to signify something than which nothing greater can be thought” – Aquinas.

Gaunilo even doubts that we can understand this idea of the greatest conceivable being:  

“of God, or a being greater than all others, I could not conceive at all” – Gaunilo.

“So much for the assertion that this supreme nature already is in my understanding.” – Gaunilo.

Evaluation defending the ontological argument

However, Gaunilo’s argument is unsuccessful because a full understanding of the greatest conceivable being or of God’s nature is not required for the ontological argument to work.

Peter van Inwagen explains that Anselm would not accept that we either understand God fully or not at all. Our limited understanding of God is enough to justify attributing the name “that than which nothing greater can be conceived” to God.

God has traits but infinitely, i.e., omnipotence, omniscience etc. It is impossible to conceive of anything greater. So, we can understand enough of that idea. We may not be able to conceive of the ‘being’ itself, as Gaunilo says, but that seems to commit a straw man fallacy. Anselm doesn’t rely on conceiving the being itself. We can grasp the concept of a being greater than which none may be conceived. We can then follow Anselm’s reasoning that since it is greater to exist, that being must exist.

Evaluation criticizing the ontological argument

Gaunilo has a point. When we think about the concept of a being greater than anything we could possibly imagine, the idea of that actual being is not in our understanding.

Furthermore, the insights of Apophatic theology show that reasoning about God is impossible. Pseudo-Dionysius argues that if we are true to God’s transcendent unknowability, we would recognize that God is simply beyond any human concepts that we can understand. God therefore cannot be grasped by the understanding and so cannot be ‘in’ the understanding.

Pseudo-Dionysius explicitly says that God is ‘beyond assertion and denial’. So although the atheist is indeed wrong to deny God, proponents of the ontological argument are also wrong to assert God. God is beyond all these philosophical terms, even beyond truth and falsity itself.

Gaunilo’s ‘lost island’ response to Anselm

Deductive arguments are strong because the only way to attack them is to deny the truth of the premises (soundness). This is stronger than inductive arguments because they can also be attacked by arguing that the conclusion is false even if the premises are true.

Weakness: Gaunilo denies that the ontological argument is actually a valid deductive argument, attacking the inference from the premises to the conclusion of God existing in reality

“I have in my understanding all manner of unreal objects” – Gaunilo.

“I should not admit that this being is in my understanding and concept even in the way in which many objects whose real existence is uncertain and doubtful, are in my understanding and concept. For it should be proved first that this being itself really exists somewhere; and then, from the fact that it is greater than all, we shall not hesitate to infer that it also subsists in itself.” – Gaunilo.

Anselm’s argument could succeed in showing that if God exists, then God is the greatest being and even that it subsists in itself, i.e., has necessary existence. However, this is not enough to show that God does exist necessarily.

“he who says that this being exists, because otherwise the being which is greater than all will not be greater than all, does not attend strictly enough to what he is saying. – Gaunilo.

Gaunilo then illustrates this with the case of a perfect lost island, which is an illustration of a thing whose real existence is ‘uncertain and doubtful’ yet is in his understanding as a concept.

Applying the logic of Anselm’s argument to this island has an absurd result (reductio ad absurdum). It is greater for this island to exist in reality, so it must exist. This would work not just for an island. The greatest or supremely perfect member of every category must exist. This is sometimes called the ‘overload’ objection because it suggests that reality would be overloaded with greatest/perfect things.

In response to Gaunilo, Anselm strengthened his argument into a 2 nd form.

Something is greater if it doesn’t depend on anything for its existence. An Island by definition is land enclosed by water, so part of the concept of an Island involves a dependence on things such as an ocean or a planet to exist. So, the greatest possible Island will still be contingent, which means by definition it could either exist or not.

This is why a priori analysis of its definition cannot prove its existence. The existence of contingent beings cannot be proven a priori since their existence is not a matter of definition. Their existence is a matter of whether what they depend on exists.

There is nothing in the concept of the greatest being that involves dependence, making it a necessary being. So, Anselm can now argue that this is why the argument works for God but is absurd when applied to anything contingent.

Anselm’s 2 nd form of his argument successfully refutes the relevance of the perfect island. A priori arguments cannot prove the existence of contingent things like islands since their existence is not a matter of definition. However, the greatest being is necessary, so its existence can be prove a priori.

However, Anselm arguably failed to respond to Gaunilo’s central contention.

Even if Anselm is right that we cannot conceive of God without existence, that only proves that God is a necessary being, such that if God existed it would be in a special way where God could not cease to exist. This is not the same as proving that this necessary being actually does exist. Anselm doesn’t deal with this point.

Descartes & Anselm vs Kant’s development of Gaunilo

Descartes’ Ontological argument

Descartes aims to strengthen the ontological argument with his rationalist epistemology. This claims that we can gain certain knowledge of some truths a priori, through rational intuition. This involves our mind’s ability to simply know certain truths. We can simply think about the concept of God as the supremely perfect being. We then rationally appreciate that God contains the perfection of existence. This is similar to how a rational understanding of a triangle reveals that it contains three sides.

“t he idea of God, or a supremely perfect being, is one that I find within me just as surely as the idea of any shape or number. And my understanding that it belongs to his nature that he always exists is no less clear and distinct than is the case when I prove of any shape or number that some property belongs to its nature” – Descartes

Descartes’ ontological argument functions through intuition rather than argument. Nonetheless he did put it into the form of a deductive argument:

P1 – I have an idea of a supremely perfect being which contains all perfections P2 – Existence is a perfection C3 – God exists

Descartes argument is notable for its simplicity. We know mathematical truths about triangles by simply thinking about our clear and distinct concept of a triangle. Similarly, we can know God exists by thinking about our clear and distinct concept of a supremely perfect being.

The argument is deliberately short, highlighting that its main point is that God’s existence can be known intuitively, not requiring a process of reasoning.

Weakness: Kant’s 1st objection: A priori reasoning cannot establish existence

Gaunilo tried to show that Anselm only succeeds in showing that if God exists, then God exists necessarily. The ontological argument has not shown that God-the-necessary-being does exist. Kant developed this type of objection.

Kant argues that Anselm and Descartes treat ‘existence’ as a predicate, as a description of God. Descartes implies that perfection is an ‘attribute’ of God. Anselm argues God must exist in order to be God. They try to show that you cannot think of God without existence, because it is a defining quality of God. The idea of ‘God’ and the idea of ‘existence’ are necessarily connected.

Kant objects that existence being a predicate of God does not establish God’s existence in reality. He Descartes example of a triangle. It is necessary that ‘having three sides’ is part of the concept of a triangle. This shows that if a triangle exists, it must have three sides.

Similarly, we could grant that the ontological argument shows that ‘necessary existence’ is part of the concept of God. Kant’s objection is that this only shows that if God exists, then God exists necessarily. It doesn’t show that God-the-necessary-being does exist.

Existence necessarily being part of the definition of God only shows that God is the idea of a necessary being. We can still deny that this necessary being or being greater than which cannot be conceived or maximally great or unlimited being actually exists.

Like Gaunilo, Kant is drawing a distinction between judgement and reality. A priori reasoning showing that existence is necessary to the definition of God in our minds is not the same as showing that necessary being actually exists in reality.

“The unconditioned necessity of judgements is not the same as an absolute necessity of things” – Kant.

“the illusion of this logical necessity has proved so powerful that when one has made a concept a priori of a thing that was set up so that its existence was comprehended within the range of its meaning, one believed one could infer with certainty that because existence necessarily pertains to the object of this concept, i.e., under the condition that I posit this thing as given (existing), its existence can also be posited necessarily” – Kant.

Kant’s first critique is unsuccessful because it is self-contradictory.

“ I think that Caterus, Kant, and numerous other philosophers have been mistaken in supposing that the proposition ‘God is a necessary being’ (or “God necessarily exists”) is equivalent to the conditional proposition ‘If God exists then He necessarily exists’ … Can anything be clearer than that the conjunction ‘God necessarily exists but it is possible that He does not exist’ is self-contradictory?” – Malcolm

Kant’s 1st objection seems to accept that the ontological argument shows that God is necessary. So, Kant must then accept that God is a being which contains its own reason for existence and is thus defined by the impossibility of non-existence.

It’s incoherent of Kant to grant God’s necessity while maintaining the possibility of God’s non-existence. So, the Ontological argument does show that God-the-necessary-being actually exists.

Malcolm tries to object that it’s incoherent to say God necessarily exists, but possibly doesn’t exist. However, that misunderstands Kant’s argument.

The issue is, Malcolm has only shown that God is a non-dependent being. In his ontological argument, Malcolm argued that if God exists, God exists necessarily because nothing could cause God to cease existing, as God is unlimited and non-dependent. This is what Malcolm established as God’s necessity. But this only establishes that God is necessary in the sense of being non-dependent, not in the sense of must exist. A being could be non-dependent and yet not exist. If it existed, then it would be necessary.

So, the necessity of God’s existence established by the ontological argument only relates to the manner of God’s existence if God exists. 

Ontological arguments cannot show that God actually exists, then.

The most famous modern defender on the ontological argument is Plantinga. Even he admits that this critique from Kant cannot really be solved and that at most the ontological argument can make religious belief rational – it cannot prove that God actually does exist, however. Very few people defend the ontological argument these days except for Plantinga, and even he doesn’t defend it as actually proving that God actually exists necessarily.

“reformulated versions of St. Anselm’s argument … 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.

Whether existence is a predicate

Strength: Anselm strengthens his argument in Proslogion chapter 3 to include necessary existence.

In chapter 2 Anselm spoke of existence being greater than non-existence. In chapter 3 he better justifies that premise. Existence is greater than non-existence because a being is greater if it cannot cease existing. A being whose nonexistence is impossible is greater than a being whose non-existence is possible.

If a being can cease to exist, that is because it depends on something else for its existence. Malcolm points out that dependence is a kind of limitation and in common language these concepts are linked to inferiority. A being which doesn’t depend on anything else (is necessary) is therefore unlimited and so is the greatest conceivable being.

This is Anselm’s argument in its strongest form. A being greater than which cannot be conceived must be one whose nonexistence is impossible.

Weakness: Kant’s 2 nd objection: existence is not a predicate.  

Anselm argues that if God didn’t exist, God wouldn’t be what God is; the greatest conceivable being. Descartes says that existence is part of what God is. Kant thinks they both assume that existence is a predicate, a description of a quality that God possesses.

Kant objects that existence is not a quality or attribute that defines a thing. To say something exists is not to describe that thing. If I say my cat exists, I do not describe a feature of the cat. I may be describing reality in a general sense, but I am not describing a defining quality of the cat. So existence isn’t a predicate.

Kant’s illustration is 100 thalers (coins). Imagine you have 100 thalers in your mind as a mere concept. Then imagine you also have 100 thalers in existence, not only in the mind. You have two cases of 100 thalers, one which exists in reality and the other which only exists in your mind.

If Anselm was correct that existence is part of the definition of the concept of a thing, then the thalers which exist should be conceptually different to the thalers that do not.

However, the concept 100 thalers is no different whether a mere concept in your mind or instantiated in reality. 100 thalers is just 100 thalers. It has the predicates of shininess, roundness and 100 etc. Being only in the mind doesn’t make the concept somehow less of a complete description of what 100 thalers is. So, existence is not part of the definition of a thing. It is not a predicate or property of the definition of a thing.

So, Anselm and Descartes are wrong when they claim it’s incoherent to think of God without existence.

Malcolm criticised Kant, arguing that Anselm’s second form had been right all along. Kant’s argument worked regarding contingent but not necessary existence. He made the same mistake Gaunilo’s lost island argument made, which was to think we could test the logic of the ontological argument through application to contingent things, such as islands or thalers.

Something is contingent if it is dependent on something else for its existence. The reason for the existence of a contingent thing is therefore external to it and so does not describe or define it. However, a necessary being doesn’t depend on anything else for its existence, so it contains the reason for its existence within itself. Since the reason for its existence is contained within itself, necessary existence must be a defining part of a thing in a way that contingent existence is not. So, necessary existence is a predicate. The ontological argument, which relies on necessary existence, is therefore defended from Kant’s critique.

Anselm and Malcolm seem correct that necessary existence is a predicate of God. Contingent existence of things like cats and coins is not a predicate, since their reason for existence is something else. However, necessary existence does define and describe a thing.

However, Kant’s first criticism might still succeed:

Even if necessary existence were a predicate of God, that only shows that if God exists, then God necessarily exists. It doesn’t show that God does exist.

Malcolm’s ontological argument

N. Malcolm’s created his own version of the ontological argument, referring to God as an unlimited being.

P1. God either exists or does not exist. P2. If God exists, God cannot go out of existence as that would require dependence on something else. So, if God exists, God’s existence is necessarily P3. If God does not exist, God cannot come into existence as that would make God dependent on whatever brought God into existence. So, if God does not exist, God’s existence is impossible. C1. So, God’s existence is either necessary or impossible P4. The concept of God is not self-contradictory (like a four-sided triangle), therefore God’s existence is not impossible. C2. Therefore, God exists necessarily.

In P4, Malcolm’s ontological argument most clearly shows how all versions of the argument rely on the concept of God being coherent. Nonetheless, there are numerous philosophical debates about that, including:

• The paradox of the stone
• The Euthyphro dilemma
• The incompatibility of free will and omniscience
• The logical problem of evil

Empiricist response: Hume on the impossibility of a necessary being

“there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori” – Hume.

A necessary being must exist – it cannot be the case that it does not exist. This means that we shouldn’t even be able to conceive of a necessary being not existing without contradiction. However, Hume claims that whatever we conceive of as existing, we can conceive of as not existing. It follows that there is no being that we cannot conceive to not exist, so no being can exist necessarily. Hume concludes:

“The words, therefore, necessary existence, have no meaning.”  

This argument references “Hume’s fork”:

A priori reasoning can only tell us about the relations between ideas , i.e. analytic knowledge (true by definition). E.g. “a bachelor is an unmarried man”.

A posteriori reasoning can only tell us about matters of fact , i.e. synthetic knowledge (true by the way the world is). E.g. “The sun will rise tomorrow”.

Matters of fact, such as whether a being exists, cannot be established a priori, according to this argument. Hume’s basis for the fork is that if a particular truth is a matter of logic/definition, then it will be true or false no matter the factual state of the universe. E.g., one plus one will always equal two, regardless of what happens to be factually true of the universe. This suggests there is a disconnect between logical truth and factual truth. The term “necessary existence” seem to ignore this disconnect. A being having necessary existence does not seem to be a matter of fact since it must exist, regardless of the factual state of the universe. Yet, what exists is a matter of fact, not relations of ideas. It’s invalid to claim that a being’s existence is logically necessary since a being’s existence cannot be established through logic. Since Hume’s fork has shown that logical truth is disconnected from factual truth, the idea that something could necessarily exist is incoherent.

The ontological argument therefore fails because it attempts to establish a matter of fact (God’s existence) through a priori reasoning.

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4 The Ontological Argument

Brian Leftow is the Nolloth Professor of Philosophy of the Christian Religion at the University of Oxford.

• Published: 02 September 2009
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The term “ontological argument” was Kant's name for one member of a family of arguments that began with Anselm of Canterbury. These arguments all try to prove God's existence a priori, via reasoning about the entailments of a particular description of God. The description almost always involves God's greatness or perfection. Where it does not, the argument has a premise justified by God's greatness or perfection. So these arguments might better be called arguments from perfection. This article deals with the main arguments from perfection and criticisms thereof in historical order. It first explicates Anselm's key phrase “something than which no greater can be thought” and then takes up his reasoning, then the question of whether its premises are true.

The term “ontological argument” was Kant's name for one member of a family of arguments that began with Anselm of Canterbury. These arguments all try to prove God's existence a priori, via reasoning about the entailments of a particular description of God. The description almost always involves God's greatness or perfection. Where it does not, the argument has a premise justified by God's greatness or perfection. 1 So these arguments might better be called arguments from perfection.

I deal with the main arguments from perfection and criticisms thereof in historical order.

Anselm: Proslogion 2

Anselm gave the first argument from perfection in his Proslogion (1078). The key passage (in ch. 2) is this:

We believe [God] to be something than which nothing greater can be thoughtThe Foolwhen he hears“something than which nothing greater can be thought,” understands what he hears, and what he understands is in his intellect. (But) it cannot exist in the intellect alone. For if it exists only in the intellect, it can be thought to exist also in reality, which is greater. If therefore itexists only in the intellect, this same thing than which a greater cannot be thought, is a thing than which a greater can be thought. But this surely cannot be. So something than which no greater can be thoughtexistsboth in the intellect and in reality. (Charlesworth 1965 , 116, my translation)

I first explicate Anselm's key phrase “something than which no greater can be thought” (henceforth “a G”). I then take up his reasoning, then the question of whether its premises are true.

“A G” is an indefinite description. Its form lets many things satisfy it (as with “something brown and red” and “something canine”). What the Fool understands is this description. A natural thought would be that what is “in his intellect,” if not just a token string of words, is the property the description expresses, being a G . But as the argument proceeds, it supposes that the Fool “has in mind” some particular thing that has the property, an “it” that cannot exist in the mind alone. Anselm seems to suppose, in short, that by understanding the description a G , one comes into some sort of direct cognitive relation with something that is a G: one thinks of or refers to a particular G. For Anselm, then, being such that no greater can be thought means being such that no one nondivine can refer to a greater possible object, under any description. 2 A G is a greatest possible being to which we can refer. If there is hierarchy of greatness with a topmost level to which we can refer, then, “a G” automatically picks out only something(s) on the topmost level. If we can refer to an unending progression of ever greater possible beings, “a G” does not refer.

“A G” has a modal element: it speaks of items to which we can refer. To make sense of this “can,” I now introduce a bit of technical terminology that will be repeatedly useful. The sentence “Possibly there are ostriches” asserts that in at least one history the universe could have, ostriches would exist. In fact, one such history has taken place. “Possibly Churchill runs a three-minute mile” asserts that in at least one history the universe could have, Churchill pulls off this surprising feat. Churchill has not yet done this, and barring reincarnation or resurrection, he will not. So it appears that actual history is not any of those in which Churchill does this: no such history has taken place. But still, it's in some sense possible that he do so. Every sentence instancing the form possibly P asserts the existence of at least one history the universe could have in which P. Every sentence instancing the form necessarily P asserts that there is no history the universe could have in which ¬P. The sentence “necessarily 2+2=4” asserts that there is no history the universe could have in which this is false; that is that in every possible history, 2+2=4. Every sentence using “can,” of course, is equivalent to one using “possibly” (e.g., “There can be ostriches”).

Philosophers call histories the universe could have possible worlds . So we can now explicate Anselm this way: something x is a G only if no nondivine being in any possible world can refer to any being greater than x actually is. Now surely, for every possible being, possibly someone or other nondivine refers to it. If that's so, then possibly something is greater than x only if possibly someone refers to that greater thing. If so, we can simplify our account of a G , for being a G is equivalent to being something than which there can be no greater. From now on, let's take Anselm to be talking of this property.

In Proslogion 5, Anselm reasons that unless it is to be less than we can think it to be, a G must be “whatever it is better to be than not to be” (Charlesworth 1965 , 120), that is, have every attribute F such that having F is better than lacking F. Now if something had every such attribute, it would be a G (a G being one thing it is better to be than not to be). So if something is not a G, it lacks some F a G has, such that having this F is better than lacking F. Thus, Proslogion 5 implies that a G is greater than any possible non-G in at least one respect. Further, there is no respect in which a non-G surpasses a G: if a non-G has some attribute it is better to have than to lack, any G has this too, and only such attributes are respects in which something might surpass a G. 3 So overall, any G is greater than any non-G. As it's obvious that nothing in the material world is a G, we can infer that a G must at least be greater than any actual material object—including the universe. Here is a particularly impressive attribute: being greater than every other possible being in some respect and equaled by no other possible being in any respect. Such a G would be a most perfect possible being. Anselm would almost certainly hold that a G must be a most perfect possible being: if a G were not so, we could apparently think of a greater, namely one that was so. But his argument doesn't make use of this description.

Talk of Gs naturally raises questions like What is greatness? or Greater in what way? Anselm doesn't answer. But he clearly means greatness or being greater to be or involve some sort of value-property the God of Western theism has supremely. So Findlay's ( 1955 ) suggestion that we take these in terms of worthiness of worship can't be too far off the mark: let's say that greatness is either desert of worship or some combination of attributes on which this supervenes. 4 As it turns out, we needn't be more specific than this.

In Proslogion 4, Anselm asserts that

Df. God = that than which no greater can be thought,

the definite description implying that there is just one G. Anselm nowhere argues that there is just one. And this is not obvious. Something without a greater might nonetheless have an equal. If Anselm cannot rule it out that there could be two or more equal Gs, he faces a problem. For his argument will apply to as many possible Gs as there are, prima facie, and so if it works will prove that there are many Gs. If there are, the definite description “ that than which no greater” will not refer—in which case, Anselm's argument will prove that God does not exist, given (Df). Why just one possible G? One can only speculate:

i. Anselm argues that being a G entails being intrinsically simple, that is, not having distinct purely intrinsic attributes ( Proslogion 12; see Monologion 16–17). Suppose that this is so. For any x, being x is intrinsic to x: it is a matter settled entirely within x's boundaries, so to speak. Being simple is also intrinsic. So for any x, if x is simple, being simple and being x must be the same attribute. But then any simple being will be identical to x. So there can be at most one simple being. So if being a G entails being simple, there can be at most one G—and if attribute-identities are necessary, at most one possible G. Thus, there is at least a good argument from premises Anselm clearly accepted to back his belief that at most one possible being is a G.

ii. As the doctrine of divine simplicity is controversial, perhaps a better answer lies with what Anselm means by “greatness.” It's axiomatic in Western theism that whatever precisely worship is , at most one thing deserves it, and this thing coexists with no rivals for worship (see, e.g., Isaiah 40:25, 44:6–7, 46:5, 9). Anselm argues that any G must as such exist necessarily and necessarily be a G. If he's right, and it's also the case that maximal greatness in a possible world W excludes having a rival in W, then in no possible world does a G coexist with another G, and there is at most one possible G.

I now turn to Anselm's reasoning.

The Reasoning

On one reading, Anselm's premises are

1. Someone thinks of a possible object which is a G, and 2. If any possible G is thought of but not actual, it could have been greater than it actually is.

The reductio runs this way. By definition, if a possible object g is a G, no possible object in any possible state is greater than g actually is: g is in a state than which there is no greater. Let g be the G someone thinks of. Then, as a G, g is in a state than which there is no greater. Per (2), if g is not actual, g could have been greater than g actually is. So if g is not actual, g is not in a state than which there is no greater. So if g is not actual, g both is and is not in such a state. So g is actual. So a G exists.

The argument is valid. So let us ask if its premises are true.

Ontological Commitments?

(1) is not innocent. It asserts a relation between a thinker and a possible object that is actually a G, and so brings an object into our ontology. Anselm needs it to do so if (1) is to give him a G to which to apply (2). But then if he is not blatantly to beg the question of God's existence, Anselm must also assume that this possible object is there, and is a G, even if it does not exist. And odds are that Anselm did believe in nonexistent objects. 5 But this puts an unflattering gloss on his argument. For then it seems to amount to: grant that something actually is in a state with no greater. This thing either does or doesn't exist. But how could something that didn't so much as exist be as great as all that? And of course, if that's what the argument amounts to, it's hard to see why one should grant that something actually is in such a state. The step from this admission to the conclusion seems vanishingly small.

But Anselm's argument doesn't require his ontology. One could instead read (1) in light of non-Anselmian semantic assumptions. Suppose that one denied nonexistent objects, but held that one can use satisfiable descriptions as if they refer, whether or not they do, and can properly use claims like (2) to reason about satisfiers of descriptions, whether or not the descriptions are satisfied. This would amount to running Anselm's argument within a “free” logic. Such logics carry no ontological commitments. Taken in light of these new assumptions, (1) asserts only that someone tokens an indefinite description that is possibly satisfied. (1), then, turns out no more or less problematic than the claim that

1a. Possibly something is a G.

(2) assigns a degree of greatness to an object even if it does not actually exist; like (1), it must allow for nonexistent objects with greatness if it is not to beg the question. Even if the degree were automatically zero, this would still entail that nonexistents have properties. So we must replace (2) with a premise assigning greatness to nonexistents only in worlds in which they exist. The most straightforward replacement is probably

2a. If possibly something is a G, but actually nothing is a G, then in any possible world W in which something is a G, that G could be greater than it is in W.

If possibly something is a G, there is a world W in which something is a G. So (2a) immediately yields

2b. If possibly something is a G, but actually nothing is a G, then in some possible world W, something is a G but could be greater than it is in W.

Free logics let one use names or descriptions that do not refer as if they refer. So they reject the logical rules of universal instantiation (from “for all x, Φx,” infer Φs for any singular term s) and existential generalization (from any statement Fs, infer that there is something which is F; Lambert 1983 , 106–7). Thus, to show that Anselm's argument can go free-logical, one must state his reductio without using these rules. So here it is: given (1a) and (2b), if nothing is a G, then in some possible world W, something is a G but could be greater than it is in W. But it cannot be the case that in some world, a G could be greater than it is in that world: being a G is being in a state with no greater in any world. So it is not the case that nothing is a G. As far as I can see, then, given a free logic, Anselm's reductio goes through.

The Premises

If an argument is valid and its premises are true, its conclusion is true. I will not try to settle whether (1a) is true. But there is a case for (2a). For a G could be greater than it is in W just in case G lacks in W some great-making property compatible with the rest of its attributes in W. If no G exists, any G in any W lacks the property of existing in @, the actual world. But

3. For a G, for any W, existing in @ is great-making in W.

And if it is possible that a G exists, then for some G in some W, existing in @ is compatible with the rest of its attributes.

The controversial premise here is of course (3). There are two cases to consider here: W = @ and W ≠ @. For the first, I support (3) in two ways. One appeals to a general claim,

4. For any F and x, if x would be F were it to exist, then for x, existing in @ is F-making.

Suppose that Leftow would be human were he to exist. Then whoever gives Leftow existence ipso facto makes him be human. So for Leftow, existence is human-making: it makes him actually what he would be were he actual, and so human. But the properties a G would have if actual include being great. So for a G, existing in @ is great-making. Oppy ( 1995 ) suggests that (3) must rest on or be supplanted by some more general principle connecting greatness and existence, which atheists and agnostics would be reasonable to reject: “After all, there seems to be no good reason to suppose that existence in reality is a great-making property solely in the case of a [G]” (10, cf. 11). 6 But the only general principle needed is (4). (4) does not connect existence with greatness any more than with any other property, and I cannot see that atheists or agnostics have any particular reason to object to it.

The second line of argument begins that surely

5. Nothing that doesn't exist ought to be worshipped.

For worship is a kind of talking to, and it makes no sense to talk to something that isn't there. Atheists and agnostics will of course insist on (5). If (5) is true, then any G would be more deserving of worship if actual than if merely possible. For a merely possible G does not deserve worship at all, and an actual G does deserve worship. If greatness is worthiness of worship or whatever property(-ies) would subvene it, this implies that any G would be greater if actual than if merely possible, and because it is actual, not merely possible. So a G's being actual surely moves it at least a bit in the direction of maximal greatness. In fact, it moves it all the way, if (as it were) the G is all set to be great save for the little detail of actually existing. But then existing in @ is great-making for Gs.

Suppose, on the other hand, that W ≠ @. We then must ask why existing in some other world contributes to a G's greatness in W. One sort of reply appeals to arguments that necessary existence is great-making: if it is, then a fortiori existing in another world is. Now the claim that being a G entails existing necessarily leads to its own sort of argument from perfection. But it does so only given certain principles of modal logic. Pros. 2 does not commit itself to any such principles. So this sort of support would not make Pros. 2 depend on modal perfection-arguments. It would at most show that Pros . 2 has one root these other arguments do.

Another sort of response begins with two premises: that worship consists largely of giving thanks and praise, and that @, as it happens, contains concrete things whose maker might in some circumstance deserve thanks and praise for them, and for whose existence a G would account if it existed. A being that can have no greater is one than which none can be more worship-worthy. So it must deserve the greatest thanks and praise compatible with its nature. Those who worship, thank and praise God for their existence and for items in the world around them if they seem good. So if a G is to deserve maximal thanks and praise, it must be such as to deserve thanks and praise for whatever should inspire these in worlds it graces. All things in any way good in these worlds thus must owe it their very being; its contribution must suffice for their existence. The more complete this dependence, the greater the thanks and praise deserved. So another axis along which to magnify the thanks/praise a G is owed is depth of dependence: the deeper it is, the greater the thanks/praise deserved. One way dependence can be deeper is this: an item depending on the G could depend on it so thoroughly that it could not exist without the G's causal support. So via “perfect being” reasoning, we can conclude that whatever in any way ought to inspire thanks and praise and coexists with a G depends so completely on it for existence that it could not exist without the G.

Turning now to our G in W, @, again, contains many things warranting thanks and praise. Either some of these also exist in W, or none do. Suppose that some do. Then if the G does not exist in @, some things in W could have existed without depending on a G's contribution to their existence. But we've just ruled this out. And so if a G exists in W but not in @, nothing warranting thanks and praise in @ exists in W. If a G exists in W but not in @, nothing in @ could have depended on that G. For if it did, in any world, it would there depend on that G so completely that it could not exist without the G in any world—including @. So if the G does not exist in @, everything in @ is such that that G does not possibly account for its existence. If so, the G of W is not omnipotent: there are perfectly possible contingent beings for whose existence it cannot account. Surely omnipotence is great-making and exemplifiable; surely nothing can be a G without it. So existence in @ follows from a clearly great-making property. This may well make existing in @ great-making. In any case, on the present argument, nothing that does not exist in @ can be a G in any world. And so any G in any world, including W, exists in @.

I submit, then, that the amended, free-logical version of Proslogion 2's argument is valid, and one of its two premises has strong support.

Proslogion 3

In Proslogion 3, Anselm reasons that

something can be thought to be, which cannot be thought not to be. This is greater than what can be thought not to be. Whence if that than which no greater can be thought, can be thought not to be, itis not that than which no greater can be thoughtSo truly does something than which no greater can be thought exist, therefore, that it cannot be thought not to exist. (Charlesworth 1965 , 118)

Some claim that here Anselm gives a second argument for God's existence. They do so by reading Anselm this way:

6. Possibly something is a G, and 7. Being a G entails existing necessarily. So 8. Possibly a G exists necessarily. So 9. A G exists necessarily. So 10. A G exists.

I doubt on exegetical grounds that Anselm actually means to give this argument. But as Proslogion 3 has led some to this argument, we can discuss it here.

(6)–(10) is a valid argument in the S5 system of modal logic. Systems of modal logic—the logic of inferences involving “possibly” and “necessarily”—differ in the claims they make about the relations between possible worlds. The distinctive feature of the S5 system of modal logic is that in it, every world is possible relative to every other world: no matter which world were actual, the same set of worlds would be possible. To see how (6)–(10) works in such a set of worlds, let the boxes below represent all the worlds that are possible:

Let existing in at least one box represent being possible, and existing in all the boxes represent existing necessarily. (6) asserts that possibly a G exists. To represent this, we enter a G in one box:

Now (8) asserts not just that it's possible that a G exist, but that it's possible that a G exist necessarily . What this means, in terms of our boxes, is that a G is in one box, and in that box, it's true of the G that it exists in all the boxes (more precisely, all the boxes possible relative to it, which in S5 are all the boxes). So if (8) is true, G is in W1, and in W1 it's true that if G is in W1, it is also in W2–4, so that we have

Thus, given an S5 system of relations among the boxes, (8) does entail (9): G exists necessarily (in all boxes). Now if W1–4 are all the worlds there are, then one of them will turn out to be actual. G is in all of them, so no matter which one is actual, G will be actual with it. So (9) entails (10). In S5, this modal argument from perfection is valid.

Anselm's Real Argument

While Anselm probably did not intend (6)–(10), he did develop the first modal argument from perfection, in a slightly later work, the Reply to Gaunilo :

Whatever can be thought and does not exist, if it existed, would be ablenot to exist. (But) something than which no greater can be thoughtif it existed, would not be ablenot to exist—for which reason if it can be thought, it cannot not exist. (Charlesworth 1965 , 60)

Anselm's reasoning is this:

11. If it can be thought that a G exists and no G exists, any G would exist contingently if it did exist. 12. It is not possible that a G exist contingently. So 13. It is not the case that it can be thought that a G exists and no G exists.

14. If it can be thought that a G exists, some G exists. 15. It can be thought that a G exists. 16. Some G exists.

There are strong a priori arguments for (12). We can recast (11) as

17. If it is possible that a G exists and no G exists, any G would exist contingently if it did exist.

and alter the rest of the argument accordingly. The advantage of doing so is that (17) comes out true within the Brouwer system of modal logic, a weaker system S5 includes. The Brouwer system is weaker than S5 because it makes a weaker claim about possible worlds: rather than assert that every world is possible relative to every other, it asserts that relative possibility is symmetric: that if A is possible relative to B, B is possible relative to A. To see that (17) is true in Brouwer, suppose that these boxes represent all the possible worlds there are:

Let's say that W1 is actual, and relative to W1, W2 is possible. Our G, God, exists only in W2. So actually, God does not exist. But W2 is possible. So it's possible that God exist. Now suppose that W2 had been actual instead of W1. In that case, God would have been actual. But if relative possibility is symmetric, then because W2 is possible relative to W1, had W2 been actual, W1 would have been possible. So had W2 been actual, a world would have been possible in which God did not exist. So had W2 been actual, God would have existed contingently: which is to say that if our G possibly exists and does not, it would exist contingently if it did exist, assuming what the Brouwer system says about relations among possible worlds.

It's also worth noting that (6) and (12) suffice on their own to prove God's existence if the correct system of modal logic for metaphysical possibility includes Brouwer. To see this, suppose that these boxes represent all the possible worlds there are:

If W4 is actual, of course, God exists. Suppose instead that W3 is actual. Then if possibly God exists, God exists in at least one box possible relative to W3, and so God exists in W4. Per (12), God exists necessarily in W4. So if W4 were actual, God would exist necessarily, that is, in every world possible relative to W4. Per Brouwer, if W4 is possible relative to W3, W3 is also possible relative to W4. So God is necessary in W4 only if God also exists in W3. So if W3 is actual, God actually exists. So whether W3 or W4 is actual, God exists, and so given (6), (12), and Brouwer, God exists.

Modulo the change from (11) to (17), then, we can credit Anselm with the first valid modal argument from perfection.

Modal arguments from perfection face two difficulties. One lies in showing that the modal systems they invoke really are the correct logics for real metaphysical possibility. The other is epistemological. Consider Plantinga's (1974a) attribute of no-maximality, or being such that one does not coexist with a G. If this attribute is possibly exemplified, then given (12) and S5, being a G is not. A modal argument gives one reason to become a theist only if its proponent offers one not just the argument but some reason to believe the claim that being a G is possibly exemplified rather than the claim that no-maximality is. Many claim that modal arguments from perfection “beg the question” by asserting that being a G rather than no-maximality is possibly exemplified. They do not. Every argument asserts rather than justifies its own premises. If we need reason to believe in being a G rather than no-maximality, this shows not that a modal argument begs the question, but merely that another argument is needed, on behalf of one of its premises.

Gaunilo and Parody

Shortly after Anselm published the Proslogion , Gaunilo of Marmoutiers replied with a parody of the Proslogion 2 argument:

(An) island more excellent than all other lands truly exists somewhere in reality (if it exists) in your mind. For it is more excellent to exist not only in the mind but also in reality. So it must necessarily exist. For if it did not, any other land existing in reality would be more excellent. And so the island you conceived to be more excellent will not be more excellent. (Charlesworth 1965 , 164)

This parody isn't quite right, but we can construct the right sort on Gaunilo's behalf: let's take him to have meant that if we replace “a G” with “an island than which no greater can be thought,” the resulting argument works as well as Anselm's. There is no such island. So (says Gaunilo) we know the argument isn't sound, even if we can't pinpoint its flaw.

Unfortunately for Gaunilo, some sorts of parody are easily dismissed. There is no greatest possible island, for there can always be another island better at least for containing more of what makes any other island good (Plantinga 1974b, 91–92). 7 Oppy suggests that perhaps “the greatest possible island will have an infinite surface area andsupply of banana trees (etc.)Given (this) it will not be the case that it could have a greater supply of these things” ( 1995 , 165). Not so: for every order of infinity, there is a higher order. Oppy also suggests that traditional theists must concede the possibility of a greatest island, for their heaven is in effect an island than which no greater is possible, whose greatness lies inter alia in conferring “eternal life and infinite attributes on its inhabitants” (165). But on traditional theist belief, not heaven but God confers eternal life, and heaven is not surrounded by water. A physical heaven might be more like a new universe. But traditional theists don't hold that heaven is a best possible physical universe, only that being in heaven is the best possible state for us—and that it is so because heaven affords each of us our closest contact with God. Further, if greatness is (roughly) worship-worthiness, it's not true that a greatest possible island would be still greater if it existed. Nonexistent islands don't deserve worship, but neither do real ones, however lovely. Here, however, Oppy has a countersuggestion. Perhaps, he wonders, a greatest possible island would have “Godlike powers of providing for its inhabitants,” in which case, theists can rule out a greatest possible island only if they can rule out the possibility of “limited—localized—pantheism” (166). Oppy might have made this particularly pointed by asking Christians whether God could incarnate Himself in an island. But a divine island is great qua divine, not qua island. Despite Oppy, it remains the case that islands as such don't deserve worship. So Oppy has left the realm of Gaunilo's original parody, and moved into talk of what I call almost-Gods.

Deity is a kind. Most kinds can have more than one member: there are many cows. If deity is a kind, perhaps it can have many members, or could have had a different one. If it can or could have, parallel arguments from perfection will work for all possible Gods, yielding more Gods than monotheists want. So Anselm needs to show that

NO. There cannot in one possible world be two instances of deity .

One good argument for (NO) stems from a claim argued earlier, that a G must account for the existence of all good things with which it coexists. Gs are good things. So were there two Gs at once, each would have to account for the other's existence. Because —— accounts for ——'s existence is a transitive relation, this would entail that each accounts for its own existence. But this is impossible. Again, we saw earlier that a G's contribution must be both sufficient and necessary for the existence of all good things with which it coexists. If so, there cannot be two Gs at once. For suppose that A and B each suffice on their own for C's existence. Then without B's contribution, C could still exist, if A were still making its contribution. But then it's false that B's contribution is necessary for C's existence.

(NO) is true, and so multiple-G parodies are ruled out. So let's consider parodies via almost-Gods, deities whose only greater is God. Let's call one such being Zod, and say that Zod is just like God save for a slight difference in perfection we cannot conceive. Zod is to us indiscernible from God. But Zod cannot coexist with God. For God is uncreatable and has made everything other than Himself, and Zod would duplicate Him in these respects. And so we cannot accept arguments for both Zod and God. But we might read “a G” as “an almost-God than whom no greater can be thought”—describing a being whose only greater is God, who is not an almost-God. If Anselm can't explain why we should accept (1) and (2) on his reading of them but not on a parody-reading, we ought not assent to them on either reading. Further, if God is a necessary being, so is Zod. So given a modal logic including Brouwer, it's not the case both that Zod and that God possibly exist. 8 But if we can't tell Zod from God, how could we have reason to think one but not the other possible? Thus, parody yields reason to be agnostic about such claims as that being a G is possibly exemplified.

Almost-Gods threaten to multiply: perhaps for any particular degree of likeness to God, an almost-God like Him to that degree would be more worship-worthy if it existed than if it were merely possible. Whether it would, though, depends on what worship is. At least within Western monotheism, whose concept of worship Anselm presumably had in mind, worship is or includes praise without qualification or limit. What deserves only qualified or limited praise thus does not deserve worship. And anything that can have a superior can deserve only qualified or limited praise. It is great—but there can be a greater, and so its praise ought to be qualified accordingly. “O god, you are great—but there can be greater”: this does not sound like worship. If it isn't, and yet someone surpassable can deserve no more, nobody surpassable can deserve worship. Nothing can unless it has no possible greater simpliciter. And now here's the rub: an almost-God has no possible greater simpliciter only if it isn't possible that there be an Anselmian G. For as we've seen, a G is greater overall than any other possible being. If a G is possible, then, no almost-God can deserve worship, and so none can be more worship-worthy if actual. And so if a G is possible, one can dismiss this sort of parody—any reason to think a G possible gives one reason simply to ignore it. Perhaps, then, one can so tweak Anselm's property of greatness as to make parody difficult.

Here an objection arises. Polytheists worshipped; what they felt, did, and said is enough like what monotheists feel, do, and say to deserve the label. Some worshipped gods other gods outranked. So one can worship something surpassed. And so there is room for worship of almost-Gods. The tweaking move is at best trivial and at worst question-begging, for it so defines worship that only God can deserve it.

This objection is confused on at least two levels. For one thing, even if polytheists did worship, nothing follows about what deserved their worship: that something is worshipped implies nothing about whether it ought to be. And no polytheist god could deserve what monotheists call worship. In worship, monotheists give all their religious thanks and praise to God. So deserving worship in the Western-monotheist sense includes deserving all of one's religious thanks and praise. No polytheist god deserves all religious thanks and praise, for none is responsible for all of our blessings. So either polytheists misdirected monotheist worship at their gods or, more charitably, what polytheists did “in church” does not count as worship in the sense discussed above . Further, worship for Western monotheists includes the giving of thanks and praise without limit or qualification. Polytheists, just as such, cannot consistently do this for any single god. They must limit and qualify their praise for any god in light of what they must say to other gods: they should not praise Zeus for blessings Hera gave or praise Hera to a degree only Zeus deserves. In worship, monotheists give God all their religious loyalty. Polytheists, as such, cannot give all their religious loyalty in any act of worship. Polytheists' religious loyalties compete: time spent in Venus's temple is not spent in Mars's. Monotheists have only one temple to attend. If polytheists worship, then, their worship differs from monotheists'. There is a kind of worship only monotheists can give, for there are attitudes one can have only to a sole object of worship.

Next epicycle: perhaps one can define the almost-greatness of almost-Gods in terms of deserving almost-worship (or almost-sole-worship, etc.), and say that almost-Gods would be almost-greater if actual. What then? Well, the problem for a Pros . 2 parody comes in applying the parallel to (2a). There is no maximal degree of deserving almost-worship (as vs. worship). There is no state than which there is no almost-greater. So for every state an almost-God might be in, there is an almost-greater state something could be in, and so the parody-argument will fail. I now argue the no-maximal-degree claim.

God deserves worship. Maximal likeness to God would be duplication, and so would yield something deserving worship, not almost-worship. If likeness to God is graded on a dense or continuous scale, then there is no maximum likeness to God short of duplication: for every nonduplicate of God, something can be more like God than it is. If God deserves worship, becoming more like God is coming closer to deserving worship. So plausibly, becoming more like God is also coming closer to deserving almost-worship, or (once over the threshold for this) deserving ever more almost-worship. If likeness to God has no maximum short of deserving worship (by duplication), there is no maximum state of almost deserving worship (almost duplicating God). This doesn't entail that there's no maximum state of deserving almost-worship, but it surely suggests it.

Still, it's not implausible that in some cases likeness to God is a granular matter, that is, comes in discrete degrees, with a maximum just shy of duplication. For we can describe such a scale: just like God save for knowing four public truths God knows, or three, or twoOn such scales, if there are maximal states, they are along the lines of being just like God save for not knowing one public truth an omniscient being would know, or being unable to do one task omnipotence, could accomplish, or being able to commit one sin. I doubt that beings like this really are possible—what could keep someone who has all eternity to figure things out, is omnipotent, and knows all the other public truths from learning the last? Be that as it may, someone with just one of these defects would be more like God than someone with all three. But which defect leaves one closest to God? Would someone not quite omnipotent be more like God than someone not quite omniscient? Someone is most like a perfect being if he or she is unlike it only in the least important (“perfecting”) respect, and so this amounts to the question Which is least important: omniscience, omnipotence, or moral perfection? Given the shakiness of all intuitions here, the best reply may be that each one-defect being is more like God in his or her nondefective respects than anything defective in these respects is, but there's no answer to the question Which is most like God overall? This sparks a suggestion: perhaps each one-defect being is in a state with no greater short of being God, and so is maximally Godlike short of duplication. But this suggestion is correct only if there are no relevant gradations within each one-defect state, and that's questionable.

Consider possible beings just one truth short of public-truth omniscience. Some don't know this truth, some that. Which truth they don't know can affect their Godlikeness. Some truths are more important than others. So the lack of some truths is more important than the lack of others: it seems less important that God know the weight of a particular gnat in early Mesopotamia than that God know that floods kill. It's more Godlike (“perfecting”) to get important things right. So beings are less Godlike the more important the truths they lack. Again, lacking some truths entails greater cognitive defect than lacking others: not knowing about the gnat is minor, while not knowing that modus ponens is valid is major. But it would take some doing to show that there are least important truths or lacks or defects. If some truths or lacks are more important than others, none are least important, and a being is the more Godlike in knowledge the less important the truth it lacks (or the less important the lack of this truth, or the defect it entails), then not all not-quite-omniscient beings are equally Godlike and there probably is no such thing as a most-Godlike not-quite-omniscient being. Like comments apply to lacks of power and abilities to sin.

The more like God in greatness-relevant ways, the closer to deserving worship. So if there is no greatest nonduplicative likeness to God, for every possible being deserving almost-worship, there is a state something can be in that would put it closer to deserving worship, and so make it deserve more or greater almost-worship. If possibly God exists, then, there is no state than which there is no greater for almost-Gods. Of course, if God is impossible, then again no possible being can duplicate Him, and the points just made about greater likeness to God remain, for they did not turn on the claim that God possibly exists. Possible items can be graded for likeness with impossible ones; the more nearly circular a thing, the more it is like a circular square.

So the last-epicycle parodic argument doesn't go through. On the other hand, almost-Gods make harder the epistemic problem modal arguments face: it's hard to see how to back belief that possibly God exists over belief that possibly Zod exists. And with the modal arguments there in the background, one wonders how well one can argue for (1a). For (it seems) any reason to accept (1a) would have also to be a reason to favor God over Zod. But in fact, the dialectical situation is this. To take a modal argument as reason to believe in God, one must have reason to believe that God rather than Zod is possible. For modal arguments from perfection will work as well for Zod as for God. But to take the Pros . 2 argument as a reason, one need only have reason to believe that God is possible, rather than more reason to believe this than to believe that Zod is.

Considering parodies for the modal argument shows that the existence of God (or Zod) would have modal consequences. If God exists, then given Brouwer, it is not so much as possible that Zod does: it's necessarily false that Zod exists. So the existence of God would have consequences for modal truths not involving the concept of God: God would have a modal footprint. And Anselm in fact held that what necessary truths there are depends on God ( Cur Deus Homo II, 17).

The Fifth of Descartes' Meditations on First Philosophy ([ 1641 ] 1993 ) offers the last fully original argument from perfection. It begins from a general attempt to show that some conceptual truths are not just conceptual truths, but rather reveal facts about natures independent of the mind:

I find within meideas of certain things that, even if perhaps they do not exist anywhere outside me, still cannot be said to be nothing. And althoughI think them at will, nevertheless they are not something I have fabricated; rather they have their own true and immutable natures. For example, when I imagine a triangle, even if perhaps no such figure exists outside my thought anywhere in the world and never has, the triangle still has a certain determinate nature, essence or form which is unchangeable and eternal, which I did not fabricate, and which does not depend on my mind. This is evident from the fact that various properties can be demonstrated regarding this triangle (which) Iclearly acknowledge, whether I want to or not. For this reason they were not fabricated by meAll these properties are patently trueand thus they are something and not nothing. (42–43)

Descartes then suggests that the nature of God is akin to the nature of a triangle in being something mind-independent which the mind grasps:

The idea of God, that isof a supremely perfect being, is one I discover to be no less within me than the idea of any figurethat it belongs to God's nature that he always existsI understand no less clearly and distinctly thanwhen I demonstrate in regard to some figurethat somethingbelongs to the nature of that figureThusthe existence of God ought to have for me at least thecertainty that truths of mathematics (have). (43–44)

This promises a quasi-mathematical demonstration. Descartes' attempt to keep the promise runs this way:

Existence can no more be separated from the essence of God than the fact that its three angles equal two right angles can be separated from the essence of a triangleit isa contradiction to think of God (that is, a supremely perfect being) lacking existence (that is, lacking a perfection)it isnecessary for me to suppose God exists, once I have made the supposition that he has all perfections (since existence is one of the perfections)Not that my thought brings this about or imposes any necessity on anything, but rather the necessity of the thing itselfforces me to think this. (44)

Descartes then adds further reasons to believe that his idea of God is “an image of a true and immutable nature” (45). The broad outline of Descartes' argument, then, is this: he grasps what he claims are mind-independent truths about the kind of thing God would be if there were one. And uniquely, in the case of God, the mind-independent truths about the kind require that the kind has an instance. To try to show why, Descartes tries to show that “God does not exist” entails a contradiction.

It is surprisingly hard to say exactly what this last phase of Descartes' argument is up to. I offer three readings of it, one of which subdivides.

Meditation V: One Reading

On one reading, Descartes' premises are that

18. If God does not exist, a being with all perfections lacks a perfection, and 19. A being with all perfections lacks a perfection entails a contradiction.

If both are true, Descartes may think, then if God does not exist, a contradiction is true. But (18) is ambiguous, between

18a. If God does not exist, then if anything has all perfections, it lacks a perfection, and 18b. If God does not exist, there is something with all perfections which lacks a perfection. (Van Inwagen 1993 , 80–81)

To get a valid argument with (18a), we must read (19) as

19a. If anything has all perfections, it lacks a perfection entails a contradiction.

But (19a) is false. That conditional does not by itself entail a contradiction. It entails only that nothing has all perfections, which is what one would expect if a perfect being does not exist. So if the argument including (18a) is valid, it is unsound.

For Descartes, God is the sole possible being with all perfections, and so (18b) amounts to

20. If God does not exist, God exists and lacks a perfection.

(20) is false unless God actually does exist necessarily, in which case “God does not exist” is impossible and so implies anything. But then why should an atheist or agnostic accept (20)? It is on its face quite unintuitive. On another reading, (18b) asserts that if God does not exist, He “is” there, in some sense of “is” compatible with nonexistence, and has contradictory properties. This reading clearly commits us to a Meinongian ontology of nonexistent impossible objects, for it asserts that if God does not exist, He is one. On such views, “there is” in “there is something with all perfections which lacks a perfection” does not express existence. It is instead a “wide” quantifier ranging over existent and nonexistent objects. To get a valid argument with (18b), we must read (19) as

19b. There is something with all perfections which lacks a perfection entails a contradiction.

But with the quantifier read “widely,” (19b) is false. On a Meinongian ontology, it is no contradiction for there to “be” contradictory nonexistent objects. Such objects are perfectly normal features of reality. What would be contradictory would be for one of them to exist . So the (18)–(19) argument is unsound on two readings, and on a third has a counterintuitive premise supporting which would require another, independent argument for God's (necessary) existence. Let's therefore consider a different analysis.

Meditation V: Second Try

Med . V speaks of what we do and must suppose, that is, of what our idea of God includes. Descartes later offered a “synthetic” presentation of material from his Meditations, and as an argument to what he seems to claim is to the same effect as Meditation V gave:

To say that something is contained in the nature or concept of anything is the same as to say that it is true of that thing. But necessary existence is contained in the concept of God. Hence it is true to affirm that necessary existence exists in Him, or God Himself exists. (HR II 57)

Here the argument is in terms of concepts. There is also a reference to necessary existence, which suggests a modal argument. But by “necessary existence” Descartes means only actual existence the nature of the thing guarantees: that “actual existence is necessarilylinked to God's other attributes” (HR II 20). So Descartes may here suggest that the Med . V argument is really this:

21. For all x, if being F is part of the concept of x, then Fx. 22. It is part of the concept of God that if God's nature is what it is, God exists. So 23. If God's nature is what it is, God exists. 24. God's nature is what it is. So 25. God exists.

The problem here is that (21) is false. It's part of the concept of Santa that he has a beard, but it's false that Santa has a beard, for it's false that anything really both is Santa and is bearded. “Santa is bearded” doesn't say anything true. It is just the right thing to say if you're telling Santa stories.

But perhaps (21) is dispensable. All Descartes really needs is

21a. For all x, if being F is part of the concept of God, then Fgod.

One can read Descartes' Meditation III argument about the concept of God as an attempt to warrant (21a). It is, in effect, an argument that the concept of God has contents such that nobody has this concept unless it has an instance—that the causal story behind anyone's having that concept must include a God. If recent externalists are right, there are many such concepts, for example, water . And if the concept of a sort of item is externally determined in the right way, then something like (21a) will hold for it. Suppose that an appropriate externalist story about natural kind concepts is correct, and that water is a natural kind. Then because the concept of water is determined by the real external nature of water, if being H 2 O is part of that concept, it follows that water is H 2 O. It's not clear a priori why God or perfect being could not be an externally determined concept. And that Descartes was in general the patron saint of anti-externalism hardly precludes his claiming that there is one exception to it, which the argument from perfection reveals. On the other hand, any argument that externalism holds for the concept of God is ipso facto one that God really exists. If to back a premise in an argument for God, one needs a second, discrete argument for God, then the first argument cannot be stronger than the second and is not independent of it. So if it took such an argument to back (21a), an argument resting on (21a) would be useless.

Meditation V: Third Try

Our third reading of Meditation V begins by noting again its talk of God's essence and what it includes. Descartes later claimed that the Meditation V argument is:

That which we clearly and distinctly understand to belong to the true and immutable nature of anything, its essence, can be truly affirmed of that thingto exist belongs to [God]'s true and immutable nature; thereforeHe exists. (HR II 19)

In accord with this, we might render the Med . V argument as

26. If the “true and immutable nature” of x includes being F, then Fx. 27. The “true and immutable nature” of God includes existence. So 28. God exists.

To respect Descartes' claim that this somehow encapsulates Med . V, we might expand the argument by deriving (27) from

29. The “true and immutable nature” of God includes having all perfections, and 30. Existence is a perfection.

Perhaps Descartes did not see (21)–(25) and (26)–(30) as distinct. He distinguishes ideas that grasp “true and immutable natures” from ideas that are just “fictitiousdue to a mental synthesis” (HR II 20). If an idea does not have its content simply due to a mental operation, it grasps a mind-independent truth. That is, it has its content by grasping something that is somehow also extramentally the case. Descartes' thought, then, seems to be that some ideas grasp “natures” that have some status beyond them, the idea of God being one; for these ideas, the “nature” is just the idea's content, and so we can switch indifferently between nature-talk and talk of concepts (ideas' contents).

Descartes' talk of “true and immutable natures” has two functions in (26)–(30). One is trying to lend credibility to (29). If it's part of a thing's nature that it is F, says Descartes, we did not simply dream this up, and so we can trust our impression that such a thing would be F. But apart from this, it also sets up the claim that (27) and (29) concern some entity or truth independent of the mind. If there really is some entity or truth that logically requires that God exist, then there would be a contradiction in objective reality (not just in our ideas about it) if God did not.

Like (21), (26) is dubious but dispensable. All Descartes needs is (27), which we can recast as

27a. There is a “true and immutable nature” P which includes all perfections and is (uniquely) such that if it exists, it has an instance,

whence he can reason that

31. P exists. (27a, simplification) 32. If P exists, it has an instance. (27a, simplification) 33. P has an instance. (31, 32, MP)

Traits of our idea of God are supposed to assure us that it captures a “true and immutable nature.” Why is (27a)'s second conjunct supposed to be true? One story Descartes tells is the (18)–(19) argument. But in at least one place, he tells another story about why existence is uniquely inseparable from the divine essence:

It is not true that essence and existence can be thought the one apart from the other in Godbecause God is His existence. (HR II 228)

That God = God's existence explains the inseparability of God's essence and God's existence only if God = God's essence—a standard part of the doctrine of divine simplicity Descartes inherited from his Jesuit education. So what Descartes is really saying here is that the divine essence = the divine existence. The reason (27a) is true, then, could be that if there is a divine nature, it is identical with the existence of God. If this is so, then if there is in extramental reality such a nature, there is also such an existence—and so God exists. Perhaps Descartes' doctrine of divine simplicity, asserted in Meditation III, can help his argument in Meditation V.

Descartes: Objections and Replies

Publication of the Meditations led to a series of exchanges between Descartes and prominent intellectuals. The best criticisms of Descartes' argument from perfection came from Pierre Gassendi and Johannes Caterus. Caterus wrote:

Though it be conceded that an entity of the highest perfection implies existence by its very name, yet it does not follow that that very existence is anything actual in the real world, but merely that the concept of existence is insepatably united with the concept of highest being. (The) complex “existing lion” includes both lion andexistence, and includes them essentially, for if you take away either it will not be the same complexdoes not its existence flow from the essence of this composite “existent lion”? Yet (this) does not constrain either part of the complex to existTherefore, also, even thougha being of supreme perfection includes existence in the concept of its essence, yet it does not follow that its existence is anything actual. (HR II, 7–8)

One can put Caterus's thought this way: from premises about the content of a concept, only conclusions about the content of a concept can validly follow.

Descartes' reply in a nutshell is that his premises deal in “what belongs to the true and immutable essence of a thing,” not “what is attributed to it merely by a fiction of the intellect” (HR II 19)—that is, are not merely about concepts' contents, but about extramental facts. His criterion for this seems to be that elements of a “merely fictitious” nature can rightly be separated conceptually: winged horse is “fictitious” because we can rightly conceive of horses without wings (HR II 20). On the other hand, if elements FG belong together as part of a “true and immutable nature,” we cannot rightly conceive them apart: being F entails being G, or conversely (HR II 21). Thus, Descartes goes on to try to show that existence really does belong to God's “true and immutable nature” without merely reiterating his Med . V argument, by arguing that the nature of God's power itself entails His existence (HR II 21). But if one must show that some divine attribute entails God's existence to show that existence is of God's nature, Descartes has a problem. For if the Med . V argument really does include a premise about God's true, immutable nature including existence, it is then an argument for God the defense of whose premises requires another, independent argument for God's existence. If it is, it is dialectically useless. For if one can demonstrate God's existence a priori in another way, the Med . V argument is unneeded: it can't yield any further, independent warrant for belief in God. If one can't, it has an indefensible premise.

Gassendi wrote:

Existence is a perfection neither in God nor in anything else; it is rather that in the absence of which there is no perfectionthat which does not exist has neither perfection nor imperfection, and that which exists (has) its existenceas that by means of which the thing itself equally with its perfections is in existencenor if the thing lacks existence is it said to be imperfect, (but rather) to be nothing. (HR II 186)

Descartes' reply is that possible existence is a perfection in the case of a triangle, making “the idea of a triangle superior to the ideas of chimeras,” and similarly necessary existence is a perfection in God's case, making the idea of God superior to other ideas (HR II 228–29). This does not immediately address Gassendi's point about mere existence; perhaps Descartes means to add that any property a perfection entails is itself a perfection. This claim would not be implausible, as we see below in discussing Gödel.

Gassendi's second major argument was this:

Although you say that existence quite as much as other perfections is included in the idea of a being of the highest perfection, you (just) affirm what has to be proved, and assume your conclusion as a premise. For I might alsosay that in the idea of a perfect Pegasus (is) contained not only the perfection of having wings but also that of existing. For just as God is thought to be perfect in every kind of perfection, so is Pegasus thought to be perfect in its own kind. (HR II 187)

Descartes offers no reply to the parody. Perhaps he would treat “existing Pegasus” as he did Caterus's “existing lion”: the “complex” captures no “true, immutable nature”—since it's not the case that the attribute of being Pegasus is such that necessarily, if it exists, it has an instance—and so here we do not escape the conceptual order. The Pegasus argument from perfection, Descartes might say, falls to the Caterus objection. But if Descartes cannot support his claim that God's nature includes existence without independent a priori proof that God exists, Gassendi is right that it begs the question.

Leibniz worked intensely on arguments from perfection in the 1670s. He held that Descartes' argument was valid but incomplete, needing the addition of a proof that it is at least possible that God exists. His own preferred argument was modal:

If a being from whose essence existence follows is possibleit existsGod is a being from whose essence existence followsTherefore if God is possible, He exists. (Adams 1994 , 137, n.9)

“A being from whose essence existence follows” is just a necessary being. So Leibniz's argument is really that

If possibly a necessary being exists, it exists. God is by nature a necessary being. So If possibly God exists, God exists.

The first premise is just an instance of the characteristic axiom of the Brouwer system of modal logic; the argument is sound in Brouwer. The conclusion leaves Leibniz's case for God incomplete, needing, as Leibniz said of Descartes, a proof that possibly God exists. Leibniz tries to provide one.

Leibniz's possibility-argument (Plantinga 1965 , 54–56) treats God as the being whose nature is a conjunction of all and only perfections, perfections being properties that are “simple,” “positive,” and “absolute.” Simple properties do not consist of other properties. They are primitive. Positive properties are those whose natures do not include the negation of other properties. If the property F is a constituent of the property ¬F, every simple property is positive. Positive properties needn't be simple, though. F • G is a positive property if F and G are positive. A property is absolute if and only if its nature involves no limitations of any sort. Leibniz's argument, then, is in essence this: it's possible that God exist just in case all properties in the nature He'd have if actual are compatible. But if properties are simple, they cannot be incompatible because properties of which they consist are incompatible. If properties are positive, their natures do not include the negations of other properties. That is, for all FG, if F and G are positive, F's nature is not and does not include not having G, and G's is not and does not include not having F. But properties F and G are incompatible, thinks Leibniz, only if F includes ¬G, G includes ¬F, some property F includes includes ¬G, or some property G includes includes ¬F. Thus, if any absolute properties are simple and positive, they are compatible.

Leibniz's argument raises a number of questions: Are there simple, absolute, positive qualities? Do they include necessary existence? Do they include colors, and do colors pose a problem for the argument? Can the argument be parodied? And what about the gap between consistency and metaphysical possibility?

Simple, Positive Properties

Leibniz wanted this to come out a proof that God possibly exists, and so presumably took perfections to include such properties as omnipotence, omniscience, and perfect benevolence. These involve no limits of quantity or degree. Presumably they need not be instanced by an imperfect subject—they are compatible with “infinity” and “perfection.” So their natures involve no limitations in that respect. It is a limitation to be something with knowledge and will only if there is something better to be, and this is not at all clear. But these are not obviously unanalyzable; plausible accounts of each abound. Leibniz's likely reply would be to say that perfect power, knowledge, and goodness are primitive properties—that although we offer accounts of them in terms of (say) generic power, knowledge, and goodness, in metaphysical fact power (for instance) in general consists in a likeness to the perfect exemplar of power, which thus figures as a primitive constituent in the general, shareable attribute of power. This amounts to applying a resemblance-nominalist account of attributes to the divine case, letting God serve as the paradigm instance: and Leibniz was indeed a nominalist, and speaks of created attributes as imperfect imitations of divine attributes in his Monadology (#48). If the standard divine attributes come out primitive, then they are also positive, and we've already seen that they're “absolute.” Perhaps Leibniz can claim that necessary existence is the paradigm of which nonnecessary existence is an imperfect imitation. This claim is at least standard in theological tradition; one finds it, for example, in Anselm.

Colors are a problem for Leibniz. Phenomenal redness and greenness seem unanalyzable. They are also positive qualities of experience. They also seem absolute. For what limits are involved in seeming red? Not materiality: a discarnate soul could hallucinate in color, and plausibly in a hallucination something appears red. But no spot in any visual field can have both properties: they are incompatible. Now here Leibniz could perhaps reply that just for this reason, colors are not positive in his sense. Each is, after all, a determinate of a determinable, phenomenal color. And the nature of determinables may come to Leibniz's aid. For a plausible view of determinables would see them as simply disjunctions of their determinates, such that each n-tuple of the properties of which a determinable consists is internally inconsistent—in which case, each determinate implies the negation of each other determinate. If this is correct, the phenomenal colors are not Leibniz-positive. Each's nature in some manner contains the negation of the rest: certainly it entails these. So perhaps Leibniz's cause is not utterly hopeless here.

Parody and Possibility

Leibniz's argument does seem vulnerable to parody (Adams 1994 , 150–51). Nothing he says indicates that his simple perfections entail one another. And it's hard to see how he could allow this. If omniscience did entail omnipotence, say, it would not be in virtue of “containing” the negation of nonomnipotence (since it doesn't contain the negation of any property). If the perfections do not entail each other, it seems possible to conjoin all save omniscience with almost-omniscience. For as none contain the negation of any other property, none contain the negation of almost-omniscience. But then the other perfections are consistent with almost-omniscience—or at least Leibniz's argument gives us as much reason to think this as to think that the perfections are all consistent. And so the argument gives us as much reason to grant the possibility of a necessarily existing almost-omniscient almost-God as we do the existence of God. But they can't both be possible. Just because we do see that it is vulnerable to parody, it's clear that Leibniz has a problem with the gap between consistency and real metaphysical possibility. The concepts of God and almost-God are equally consistent, on his showing. But it cannot be that both are possible, for at most one of these beings really exists. So we can't take Leibniz to have shown that it is possible that God or an absolutely perfect being exists.

Kant's Critique of Pure Reason ([ 1781 ] 1956 ) is often treated as the death knell of arguments from perfection. Kant claimed against Descartes that “ ‘being’ isnota predicatewhich could be added to the concept of a thingIt is merely the positing of a thing” (A598/B626). This denies (30), at least if we assume that every perfection is expressed by a “predicate,” something that describes or characterizes an object. On this assumption, it is very nearly one of Gassendi's moves. Kant also argued this way:

34. All necessary truths are really conditional in form (“The absolute necessity of the judgment is only a conditioned necessity ofthe predicate in the judgment” [A703–4/B621–22]). 35. Any conditional expansion of a purported necessary existential truth would be analytic as well as existential. 36. There are no analytic existential propositions (A708/B626). 9 37. So no necessary proposition asserts the existence of anything.

(36) and (37) follow Hume. But Kant's way of supporting them is, for better or worse, his own. If (36) or (37) is true, then Descartes' argument cannot be sound, if its contention is in effect that “God exists” is analytic. If an argument is unsound, it either has a false premise or makes an invalid inference, and one who asserts that an argument is unsound must back the claim by showing one or the other. Kant's denial of (30) does this.

Kant supports (34) with only an example, that “necessarily a triangle has three sides” is really “necessarily, for all x, if x is a triangle, x has three sides” (A704/B622). His case for (35) is left implicit. In parallel to the triangle example, “necessarily, God exists” would on Kant's account really assert “necessarily, for all x, if x is a God, x exists.” This is an “identical proposition” (A704/B622), since “x is a God” includes the note that x exists, at least on the plausible assumption that only existing things have any attributes at all. If this is an “identical proposition,” it is also an analytic proposition, because its consequent merely makes explicit something its antecedent clearly includes. So if Kant's conditional account of necessity-claims is correct, then any necessary existential proposition is analytic. Kant's denial that existence is a “predicate”—by which he means something that describes or characterizes an object—helps back (36). Analytic propositions unfold the contents of a concept of some item. Concepts characterize their objects, that is, ascribe to them conjunctions of characterizing properties. So analytic propositions can only ascribe characterizing properties. So if existence is not a characterizing property, there can be no analytic existentials.

How much did Kant actually achieve? As to the claim that existence is not a predicate, Anselm's backing for (2), as explained above, does not involve any particular doctrine about the logical status of existence, nor even the claim that existence has some general great-making or perfective aspect. The point about existence doesn't even really cut against Descartes. One version of his argument uses the premise that existence is a perfection, but the having of a perfection could be expressed other than by what Kant would call a “real predicate.” Another version claims that necessary existence is a perfection—but to claim that necessary existence is a property is not to claim that any existential proposition is necessary. Propositions predicating such a property need not be quantified at all. In any case, the claims that existence is not a predicate or a characterizing predicate are quite likely false. We can well understand a woman who concedes that her hus band, Harvey, is not as brave as Batman or as brilliant as Lex Luthor, then adds “But at least Harvey exists!” This claim predicates existence of Harvey, telling us something substantive about him that “enlarges our concept” of Harvey, namely, that he is not a fictional character.

As to Kant's other line of attack, mathematics features numerous apparent necessary and nonconditional existential truths, for example, that there is a prime number between one and ten. (Kant's friends might dig their heels in and insist that this is really something like a claim that if anything is a series of natural numbers, it includesBut this would pretty plainly be stretching things.) Note that worries about the ontological status of numbers aren't really to the point here: the truths involved are of this form, whatever precisely it is that makes them true, and even if one assigns some unusual interpretation to the existential quantifier in mathematical contexts. So Kant's (34) seems frail indeed, and without it, (35) is at best irrelevant. If the logicists are right, these necessary truths are all analytic. If they are not, these are synthetic propositions which ( pace Kant) do not concern how things must appear to us. Either way, Kant's theory of necessity is in serious trouble.

Kant actually said little that earlier writers had not already said, and Kant's objections (I've claimed) were duds. But they were not thought so, and so arguments from perfection found few friends for the next two centuries. In 1970, mathematician Kurt Gödel developed an argument related to Leibniz's. The reasoning keys on a concept of a “positive” property that Gödel did not explain well. C. Anthony Anderson suggests that we take being positive as being “necessary for and compatible with perfection,” or such that “its absence in an entity entails that the entity is imperfect and its presence does not entail (this)” ( 1990 , 297). The two descriptions are equivalent. If a property is necessary for perfection, its absence in A entails that A is imperfect, and conversely. If a property is compatible with perfection, its presence in A does not entail that A is imperfect, and conversely. Gödel's proof (as Anderson emends it) makes these assumptions:

Definition 1. X is divine if and only if x has as essential properties all and only positive properties. Definition 2. A is an essence of x if and only if for every property B, x has B necessarily just in case x's having A entails x's having B. Definition 3. X necessarily exists if and only if every essence of x is necessarily exemplified. Axiom 1. If a property is positive, its negation is not positive. Axiom 2. Any property a positive property entails is positive. Axiom 3. The property of being divine is positive. Axiom 4. If a property is positive, it is necessarily positive. Axiom 5. Necessary existence is positive.

Since being perfect is necessary for and compatible with perfection, on Anderson's reading, Definition 1 yields the claim that anything divine is by nature a perfect being. Again, on D. 1, a divine being has essentially every property necessary for perfection. Presumably having every property necessary for perfection suffices for perfection. (If it did not, something more would be necessary to attain perfection.) So D. 1 licenses the use of “perfect being theology” to fill out the concept of a divine being. If entailment is strict implication, Definition 2 encapsulates one standard account of what an essence is. Given D. 2, Definition 3 follows at once.

I now present the argument. Axiom 3 has it that the property of being divine is positive. D. 1 has it that every positive property is essential to a divine being. So being divine is essential to a divine being. D. 2 entails that any being has each of its essential properties in every world in which it exists, for if x has B necessarily, x's having A entails x's having B only if x has A necessarily. So per D. 2, any divine being is necessarily divine—divine in all possible worlds in which it exists. Per D. 1 and A. 5, any divine being is essentially a necessary existent. So any divine being is by nature divine and necessary in every possible world.

Axioms 1 and 2 jointly entail that any positive property is consistent. For a property is inconsistent just in case it entails its own negation. Per Axiom 1, if a property is positive, its negation is not positive. But per Axiom 2, if a property is positive, it entails only positive properties. So no positive property entails its own negation.

If every positive property is consistent, and being divine is positive, being divine is consistent. It is necessarily so per A. 4. We can confirm this another way: being divine is having all and only positive properties essentially. But if positive properties entail only positive properties (A. 2), and no negation of any positive property is positive (A. 1), no positive property entails the negation of any positive property. But then the set of all positive properties is consistent; none of its members entails the negation of any of its members. 10 Suppose now that if being divine is consistent, it is instanced in some possible world. Then given what we've argued so far, there is in some possible world a necessarily existent necessarily divine being: that is, it is possibly necessary that “a divine being exists” is true. Given this and the Brouwer axiom, it follows that a divine being exists.

Gödel's argument faces two basic questions. One is whether there is a con‐ tentful, theologically appropriate gloss of “positive” on which the axioms are true. The other is whether there is a sort of possibility such that (a) a concept's being syntactically consistent entails that it is possible in that sense that it be instanced, and (b) the Brouwer axiom is true for that sort of possibility and necessity.

The answer to the first question is yes. Talk of God as a perfect being is certainly appropriate theologically, and perfect being theology has been the main tool to give content to the concept of God philosophically almost as long as there has been philosophical theology. And on Anderson's gloss, the axioms come out true.

Anderson's gloss validates Axiom 1. Suppose that a property F is positive. Then by Anderson's gloss, if A lacks F, A is imperfect. If A has not-F, A lacks F. So if A has not-F, A is imperfect, and so not-F is not compatible with perfection, and so not positive. Anderson's gloss validates Axiom 2. On Anderson's gloss, if a property is not positive, either it is not necessary for or it is not compatible with perfection. If having a property F entails having some property that is not compatible with perfection, having F is not compatible with perfection—and so any property that entails something for this reason nonpositive is itself nonpositive. If a property entails a property not necessary for perfection, it entails a property a divine being can lack. Any property a divine being can lack is not part of its essence. A divine being's essence includes or entails whatever properties it has necessarily (D. 2); so any property a divine being can lack is contingent. But only properties had contingently entail the having of contingent properties. So any property that entails a property not necessary for perfection is itself contingent and not part of a divine being's essence. But a divine being's essence includes all positive properties (D. 1). So any property entailing a property that is not positive in this second way is itself not positive. Axiom 3 seems patent, for given D. 1, being divine amounts to a conjunction of all positive properties, and it's hard to see how such a conjunction could fail to be positive. As to Axiom 4, on Anderson's gloss, a property's being positive consists in two facts about property-entailment. It's plausible that properties entail what they do necessarily. As to Axiom 5, necessary existence is certainly compatible with perfection, and perfect being reasoning suggests that it is necessary for it.

There remains the modal question, of whether a concept of possibility and necessity such that being syntactically consistent (entailing no explicit contradiction) entails being in this way possible also conforms to the Brouwer axiom. Syntactic consistency amounts to “logical possibility,” in one sense of the term. But not all that is possible in this narrow logical sense is really or metaphysically possible: there is no formal, explicit contradiction in the claim that something is red and green all over at once, and yet this claim is not metaphysically possible. So there is a gap between what Gödel establishes and its being metaphysically possible that a divine being exist. And it's a substantive question whether the Brouwer axiom governs real metaphysical possibility. We can describe coherently a set of possible worlds in which the Brouwer axiom doesn't hold, and in which, while it's possibly necessary that God exists, God does not exist. We need only two worlds to do so, in fact:

Suppose that W2 is actual, and W1 is possible relative to W2 but not vice versa. Then were W2 actual, W1 would be possible. As we're supposing that there are only these two worlds, a God who exists in W1 exists in every world possible relative to W1, if W2 is not possible relative to W1. So in W1, God exists necessarily (and W2 is impossible). Thus, since W1 is possible relative to W2, in this setup, God is possibly necessary and yet does not exist.

Gödel's argument (as emended) shows us that the concepts of a perfect being and of divinity are consistent, given a reasonable concept of perfection. But the gap between consistency and metaphysical possibility and the need to establish that the logic of metaphysical possibility includes the Brouwer axiom stand between it and the Holy Grail of proving God's existence. As well, as a modal argument, Gödel's faces the epistemic problems we've observed: the portion of the argument that contends that possibly a divine being exists may admit of significant parody. On the other hand, consistency is evidence for possibility, though defeasibly so, and if I've assessed Proslogion 2 correctly, that argument is promising and does not require us to deal with the epistemic problems the modal argument faces. There is (I think) little good to be said for Descartes' argument. But the Pros . 2 argument appears to survive objections; to accept its premise (1a) we needn't have more reason to believe in God's possibility than in Zod's; and we do have evidence that possibly God exists. So while there is of course much more to be said here, perhaps Anselm's argument has a future.

Leibniz's argument, for instance, reasons simply from the claim that God is a necessary being (see below). But the latter rests on the claims that necessary existence is a perfection and that God is a perfect being.

Nobody nondivine is clumsy but necessary. Proslogion 15 asserts that God is greater than can be thought, using the same language involved in a G . Anselm could not mean to say that God is too great to be thought of or described simpliciter, since he surely thinks that God thinks of Himself. So he must mean a G in terms of thinkers other than God. But Anselm wouldn't want to read a G simply in terms of what we can describe or refer to, for he believes in angels, and surely he'd hold that God is too great for angels as well as humans to describe adequately. Still, since “nobody nondivine” is clumsy, I henceforth replace it with “we.”

If it is better to lack than to have F—that is, if F is an imperfection—then it is better to have than to lack ¬F, and so a G has ¬F. So a G has no imperfections. So nothing could surpass a G by surpassing one of its imperfections. If an attribute is neither a perfection nor an imperfection—neither raises nor lowers greatness—it's hard to see how it could be a respect in which one being could surpass another. For if being F makes A greater than G, presumably being F raises A's greatness past B's.

Oppy ( 1995 ) suggests that we need reason to think that a G, if actual, would be “a being of religious significance” since there may well be numbers too great (large) for us to “form a positive conception of” (16). Agreed. The only nonlogical vocabulary in “a G” is “thought of” and “greater.” Since no religious significance attaches to the first, the second must provide some. The Findlay suggestion in effect stipulates that it does. And why not?

Anselm's argument requires that understanding “the G” puts one in cognitive relation to an entity, the G, which then “exists in intellectu .” On this general approach, understanding “Santa Claus” puts one in cognitive relation with Santa Claus. Santa Claus then is the object of one's thought. But Santa Claus does not exist.

But see also p. 68, where Oppy ( 1995 ) seems to waver.

Can there also always be another being a bit better than any being we pick (Oppy 1995 , 19)? We have the concept of God, which has a number of notes and is supposed in virtue of them to be a concept of the greatest possible being. And we find this connection intuitive: it's pretty hard to think of something better than being necessary, omnipotent, omniscient, morally perfect, and so on. So if one can show it possible that God exist, one can answer the question no. Those who offer arguments from perfection must show that this is possible anyway. So “Is it the case that for any possible being, there is always a greater?” adds nothing to their argumentative task. Moreover, —— is a greatest possible island wears its unsatisfiability on its sleeve. —— is a greatest possible being does not, if only because we're less clear on what makes beings as such “great,” or what greatness is in beings. Further, on the reading of greatness I've suggested, it turns out trivially true that God is the greatest being possible, if God possibly exists.

To see the need for Brouwer, suppose (contra Brouwer) that relative possibility is not symmetric. Then there could be worlds like these:

For simplicity, suppose that W1–3 are all the worlds there are, that only adjacent boxes bear links of direct relative possibility, and that W2 is actual. Say that W1 and W3 are possible relative to W2, but not vice versa. Then both God and Zod exist necessarily (each exists in the only world possible relative to the world in which it exists). And they do not possibly coexist. But both possibly exist, as W1 and W3 are both possible relative to the actual world.

Kant also believed in synthetic necessities. (He discussed these under the rubric of “synthetic a priori” truths. But he also held that whatever is knowable a priori is necessarily true.) But these, he held, all concern how things must appear to our senses, and God, he held, cannot appear to our senses.

Which probably entails that not every prima facie member of the set is actually a member. Being omniscient seems to many a prima facie perfection/positive property. So does being atemporal. Nobody is omniscient who does not know what time it is now. But many think that no atemporal being can know this (e.g., Kretzmann 1966 ). One conclusion from this might be that there are at least two incompatible sets of perfections, differing at least in that one includes atemporality but not omniscience and the other includes omniscience but not atemporality. But if we accept the Gödel/Anderson reasoning, no genuine perfections are incompatible. So on their account, what follows is instead that at most one of atemporality and omniscience is actually a perfection.

Works Cited

Adams, Robert M.   1994 . Leibniz. New York: Oxford University Press.

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Anderson, C. Anthony . 1990 . “ Some Emendations of Gödel's Ontological Proof. ” Faith and Philosophy 7: 292–303.

Anselm . Proslogion [1087] 1965 . Trans. M. J. Charlesworth. Notre Dame, Ind.: University of Notre Dame Press.

Charlesworth, M.  J. 1965 . St. Anselm's Proslogion with a Reply on Behalf of the Fool by Gaunilo and the Author's Reply to Gaunilo. Trans. M. J. Charlesworth. Oxford: Clarendon Press.

Descartes, René . [1641] 1993 . Meditations on First Philosophy. Trans. Donald A. Cress . Indianapolis, Ind.: Hackett.

Findlay, J.  N. 1955 . “Can God's Existence Be Disproved?” In New Essays in Philosophical Theology, ed. Antony Flew and Alasdair MacIntyre , 47–55. New York: Macmillan.

Haldane, Elizabeth , and G. Ross . 1931 . The Philosophical Works of Descartes , vol. 2. New York: Cambridge University Press. (Cited as HR II)

Kant, Immanuel . [1781] 1956 . Critique of Pure Reason. Trans. Norman Kemp Smith. London: Macmillan.

Kretzmann, Norman . 1966 . “ Omniscience and Immutability. ” Journal of Philosophy 63: 409–21. 10.2307/2023849

Lambert, Karel . 1983 . Meinong and the Principle of Independence. New York: Cambridge University Press.

Oppy, Graham . 1995 . Ontological Arguments and Belief in God. New York: Cambridge University Press.

Plantinga, Alvin , ed. 1965 . The Ontological Argument. Garden City, N.Y.: Doubleday.

Van Inwagen, Peter . 1993 . Metaphysics. Boulder, Colo.: Westview Press.

For Further Reading

Adams, Robert . 1971 . “ The Logical Structure of Anselm's Arguments. ” Philosophical Review 80: 647–84.

Alston, William . 1960 . “ The Ontological Argument Revisited. ” Philosophical Review 69: 452–74. 10.2307/2183480

Barnes, Jonathan . 1972 . The Ontological Argument. New York: St. Martin's Press.

Chandler, Hugh . 1993 . “ Some Ontological Arguments. ” Faith and Philosophy 10: 18–32.

Clarke, Bowman , 1971 . “ Modal Disproofs and Proofs for God. ” Southern Journal of Philosophy 9: 247–58.

Coburn, Robert . 1963 . “ Professor Malcolm on God. ” Australasian Journal of Philosophy 41: 143–62. 10.1080/00048406312341151

Davis, Steven . 1976 . “ Does the Ontological Argument Beg the Question ?” International Journal for Philosophy of Religion 7: 433–42. 10.1007/BF00136308

Devine, Philip . 1975 . “ Does St. Anselm Beg the Question ?” Philosophy 50: 271–81. 10.1017/S0031819100025110

Dore, Clement . 1984 . Theism. Dordrecht: D. Reidel .

Dore, Clement . 1984 . “ The Possibility of God. ” Faith and Philosophy 1: 303–15.

Forgie, William , 1972 . “ Frege's Objection to the Ontological Argument. ” Nous 6: 251–65.

Forgie, William . 1976 . “ Is the Cartesian Ontological Argument Defensible ?” New Scholasticism 50: 108–21.

Forgie, William . 1990 . “ The Caterus Objection. ” International Journal for Philosophy of Religion 28: 81–104. 10.1007/BF00131743

Forgie, William . 1991 . “ The Modal Ontological Argument and the Necessary A Posteriori. ” International Journal for Philosophy of Religion 29: 129–41. 10.1007/BF00141327

Gale, Richard , 1986 . “ A Priori Arguments from God's Abstractness. ” Nous 20: 531–43.

Gale, Richard . 1988 . “ Freedom vs. Unsurpassable Greatness. ” International Journal for Philosophy of Religion 23: 65–75. 10.1007/BF00138712

Gale, Richard . 1991 . On the Nature and Existence of God. Cambridge, England: Cambridge University Press.

Gotterbarn, Dale . 1976 . “ Leibniz' Completion of Descartes' Proof. ” Studia Leibnitiana 8: 105–12.

Grim, Patrick . 1979 . “ Plantinga's God. ” Sophia 18: 35–42. 10.1007/BF02790688

Grim, Patrick . 1979 . “ Plantinga's God and Other Monstrosities. ” Religious Studies 15: 91–97. 10.1017/S0034412500011112

Grim, Patrick . 1981 . “ Plantinga, Hartshorne and the Ontological Argument. ” Sophia 20: 12–16. 10.1007/BF02789922

Grim, Patrick   1982 . “In Behalf of ‘In Behalf of the Fool.’ ” International Journal for Philosophy of Religion 13: 33–42. 10.1007/BF00148937

Hartshorne, Charles . 1962 . The Logic of Perfection. LaSalle, Ill.: Open Court Press.

Hartshorne, Charles . 1965 . Anselm's Discovery. LaSalle, Ill.: Open Court Press.

Hazen, Alan . 1998 . “ On Gödel's Ontological Proof. ” Australasian Journal of Philosophy 76: 361–77. 10.1080/00048409812348501

Hopkins, Jasper . 1972 . A Companion to the Study of St. Anselm. Minneapolis: University of Minnesota Press.

Hopkins, Jasper . 1976 . “Anselm's Debate with Gaunilo.” In Analecta Anselmiana V, ed. H. Kohlenberger , 25–53. Frankfurt: Minerva GmbH.

Kane, Robert . 1990 . “ The Modal Ontological Argument. ” Mind 93: 336–50.

Kenny, Anthony . 1968 . “Descartes' Ontological Argument.” In Fact and Existence , ed. Joseph Margolis , 18–36. New York: Oxford University Press.

Leftow, Brian . 1988 . “ Anselmian Polytheism. ” International Journal for Philosophy of Religion 23: 77–104. 10.1007/BF00138713

Leftow, Brian . 1990 . “ Individual and Attribute in the Ontological Argument. ” Faith and Philosophy 7: 235–42.

Lewis, David. 1970 . “ Anselm and Actuality. ” Nous 4: 175–88.

Mackie, John . 1982 . The Miracle of Theism. New York: Oxford University Press.

Malcolm, Norman . 1960 . “ Anselm's Ontological Arguments. ” Philosophical Review 69: 41–62. 10.2307/2182266

Mann, William . 1976 . “ The Perfect Island. ” Mind 85: 417–21. 10.1093/mind/LXXXV.339.417

Mann, William . 1991 . “Definite Descriptions and the Ontological Argument.” In Philosophical Applications of Free Logic , ed. Karel Lambert. New York: Oxford University Press.

Mason, P.   1978 . “ The Devil and St. Anselm. ” International Journal for Philosophy of Religion 9: 1–15. 10.1007/BF00138726

Oppenheimer, Paul , and Edward Zalta . 1991 . “On the Logic of the Ontological Argument.” In Philosophical Perspectives V , ed. James Tomberlin , 509–29. Atascadero, Calif.: Ridgeview Press.

Plantinga, Alvin . 1967 . God and Other Minds. Ithaca, N.Y.: Cornell University Press.

Plantinga, Alvin . 1986 . “ Is Theism Really a Miracle ?” Faith and Philosophy 3: 109–34.

Rowe, William . 1976 . “ The Ontological Argument and Question-Begging. ” International Journal for Philosophy of Religion 7: 425–32. 10.1007/BF00136307

Shaffer, Jerome . 1962 . “ Existence, Predication and the Ontological Argument. ” Mind 71: 307–25. 10.1093/mind/LXXI.283.307

Sobel, Jordan . 1987 . “Gödel's Ontological Proof.” In On Being and Saying , ed. Judith Thomson , 241–261. Cambridge, Mass.: MIT Press.

Stone, Jim . 1989 . “ Anselm's Proof. ” Philosophical Studies 57: 79–94. 10.1007/BF00355663

Tooley, Michael . 1981 . “ Plantinga's Defense of the Ontological Argument. ” Mind 90: 422–27. 10.1093/mind/XC.359.422

Van Inwagen, Peter . 1977 . “ Ontological Arguments. ” Nous 11: 375–95.

Wainwright, William . 1978 . “ Unihorses and the Ontological Argument. ” Sophia 17: 27–32. 10.1007/BF02798116

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since 01.01.06

Anselm's "Ontological Argument"

Abstract: Anselms's Ontological Argument is stated, and a few standard objections to his argument are listed.

• The doctrine of realism implies that the extent to which anything is real is dependent upon its degree of universality; hence, God is the most real. Other existent things in the world are emanations from archetypes.
• The general idea of the ontological argument is based on the notion that the concept of God as the greatest being implies that God exists—if not, there could be something greater, namely an existent greatest being—but this being would be God.
• We conceive of God as a being than which no greater can be conceived.
• This being than which no greater can be conceived either exists in the mind alone or both in the mind and in reality.
• Existing both in the mind and in reality is greater than existing solely in the mind.
• This being, existing in the mind alone, can also be conceived to exist in reality.
• This being existing in the mind alone is not therefore the being than which no greater can be conceived. (See statement 1 above.)
• Therefore, this being than which no greater can be conceived exists in reality as well as exists in the mind.
• Anselm's Reply: There is no contradiction in denying the existence of a perfect island, but there is in denying God's existence. (Note: does Anselm relate an intuitive recognition of the distinction between à priori and à posteriori truth?)
• Anselm notes the only way God can be conceived of not to exist is to conceive of the word "God" not existing since this kind of perfection implies existence. (Note: it's difficult to phrase Anslem's objection without circularity— cf, the informal fallacy of petitio principii .
• Anselm's Reply: If one does not understand the definition, then one is a fool. You cannot argue with a fool. (Anselm here can be charged with committing the fallacy of ad hominem ).
• Anselm believes that one must suppose a minimum of intelligence in anyone considering the argument—but, of course, the burden of proof in this regard is on Anselm. Cf , the related ideas of the prinicple of charity and the argumentum ad ignorantiam
• Anselm's Reply:  No, not at all—Anselm believes he is not just comparing ideas. The comparison is between existing in the mind alone and existing in the mind and in reality. Both of these are thought of as they are, not thought of as in the mind. (Note: Yet how can this objection be phrased without the notion of "the thought or idea" of existence…)
• If Anselm is wrong here, it would seem to follow that deductive arguments ( i.e. , à priori arguments) are of no use to proving things about the nature of the world of existent entities. Instead, this kind of rationality only shows the relations of ideas to other ideas.
• Anselm of Canterbury. Wikipedia 's reprint from the scholarly 1911 Encyclopedia Britannica on Anselm's life and works.
• Anselm, "The Ontological Argument" A short selection of Anselm's argument from Proslogium 2 in the online Reading for Philosophical Inquiry on this site.
• Ontological Arguments. A good discussion with extensive links to the history, classification, and classic objections to various versions of the ontological argument by Graham Oppy in the Stanford Encyclopedia of Philosophy.
• The Ontological Argument. Anselm's argument together with Gaunilo's, Aquinas' and Kant's objections are conveniently summarized by Kenneth Einar Himma in the Internet Encyclopedia of Philosophy. This entry is a good place to start for clarification of the above notes to the argument.

“For I do not seek to understand in order to believe; I believe in order to understand. For I also believe that ‘Unless I believe, I shall not understand.’” St Anselm, Proslogion I , trans. Thomas Williams (Indianapolis, Indiana: Hackett Publishing, 2001) 6.

Relay corrections, suggestions or questions to larchie at lander.edu Please see the disclaimer concerning this page. This page last updated 01/27/24 © 2005 Licensed under the GFDL

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In This Article Expand or collapse the "in this article" section Arguments for the Existence of God

Introduction, general overviews.

• Anthologies
• Assessing Arguments
• Anselm’s Proslogion
• Modal Ontological Arguments
• Gödel’s Ontological Argument
• Aquinas’s Five Ways
• Arguments from Sufficient Reason
• Arguments from Contingency
• Kalām Cosmological Arguments
• Biological Arguments for Design
• Cosmological Fine-Tuning Arguments for Design
• Moral Arguments
• Arguments from Religious Experience
• Arguments from Miracles
• Arguments from Consciousness
• Arguments from Reason
• Aesthetic Arguments
• “Cumulative” Arguments
• Pascal’s Wager

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Arguments for the Existence of God by Graham Oppy LAST REVIEWED: 26 February 2020 LAST MODIFIED: 26 February 2020 DOI: 10.1093/obo/9780195396577-0040

Philosophical discussion of arguments for the existence of God appeared to have become extinct during the heyday of logical positivism and ordinary language philosophy. However, since the mid-1960s, there has been a resurgence of interest in these arguments. Much of the discussion has focused on Kant’s “big three” arguments: ontological arguments, cosmological arguments, and teleological arguments. Discussion of ontological arguments has been primarily concerned with (a) Anselm’s ontological argument; (b) modal ontological arguments, particularly as developed by Alvin Plantinga; and (c) higher-order ontological arguments, particularly Gödel’s ontological argument. Each of these kinds of arguments has found supporters, although few regard these as the strongest arguments that can be given for the existence of God. Discussion of cosmological arguments has been focused on (a) kalām cosmological arguments (defended, in particular, by William Lane Craig); (b) cosmological arguments from sufficient reason (defended, in particular, by Richard Gale and Alexander Pruss); and (c) cosmological arguments from contingency (defended, in particular, by Robert Koons and Timothy O’Connor). Discussion of teleological arguments has, in recent times, been partly driven by the emergence of the intelligent design movement in the United States. On the one hand, there has been a huge revival of enthusiasm for Paley’s biological argument for design. On the other hand, there has also been the development of fine-tuning teleological arguments driven primarily by results from very recent cosmological investigation of our universe. Moreover, new kinds of teleological arguments have also emerged—for example, Alvin Plantinga’s arguments for the incompatibility of metaphysical naturalism with evolutionary theory and Michael Rea’s arguments for the incompatibility of the rejection of intelligent design with materialism, realism about material objects, and realism about other minds. Other (“minor”) arguments for the existence of God that have received serious discussion in recent times include moral arguments, arguments from religious experience, arguments from miracles, arguments from consciousness, arguments from reason, and aesthetic arguments. Of course, there is also a host of “lesser” arguments that are mainly viewed as fodder for undergraduate dissection. Further topics that are germane to any discussion of arguments for the existence of God include (a) the appropriate goals at which these arguments should aim and the standards that they should meet, (b) the prospects for “cumulative” arguments (e.g., of the kind developed by Richard Swinburne), and (c) the prospects for prudential arguments that appeal to our desires rather than to our beliefs (e.g., Pascal’s wager).

There are few works that seek to provide a comprehensive overview of arguments for the existence of God; there are rather more works that seek to give a thorough treatment of arguments for and against the existence of God. Mackie 1982 is the gold standard; its treatment of arguments for the existence of God remained unmatched until the publication of Sobel 2004 . Other worthy treatments of a range of arguments for the existence of God—as parts of treatments of ranges of arguments for and against the existence of God—include Gale 1991 , Martin 1990 , and Oppy 2006 . The works mentioned so far are all products of nonbelief; they all provide critical analyses and negative assessments of the arguments for the existence of God that they consider. Plantinga 1990 is an interesting product of belief that also provides critical analyses and negative assessments of the arguments for the existence of God that it considers, although in the service of a wider argument in favor of the rationality of religious belief; first published in 1967, this work was clearly the gold standard for analysis of arguments for the existence of God prior to Mackie 1982 . Of the general works that provide a more positive assessment of arguments for the existence of God, consideration should certainly be given to Plantinga 2007 and, for those interested in a gentle but enthusiastic introduction, Davies 2004 .

Davies, Brian. An Introduction to the Philosophy of Religion . Oxford: Oxford University Press, 2004.

Wide-ranging introduction to philosophy of religion that includes a discussion of ontological arguments, cosmological arguments, teleological arguments, arguments from religious experience, arguments from miracles, and moral arguments. Good coverage of a range of arguments for the existence of God.

Gale, Richard. On the Nature and Existence of God . Cambridge, UK: Cambridge University Press, 1991.

Entertaining and energetic discussion of ontological arguments, cosmological arguments, arguments from religious experience, and pragmatic arguments (e.g., Pascal’s wager).

Mackie, John. The Miracle of Theism: Arguments for and against the Existence of God . New York: Oxford University Press, 1982.

Superb presentation of cumulative case argument for atheism. Considers ontological arguments, cosmological arguments, teleological arguments, moral arguments, arguments from consciousness, arguments from religious experience, arguments from miracles, and Pascal’s wager. Benchmark text for critical discussion of arguments for the existence of God.

Martin, Michael. Atheism: A Philosophical Justification . Philadelphia: Temple University Press, 1990.

Comprehensive cumulative case for atheism. Considers ontological arguments, cosmological arguments, teleological arguments, arguments from miracles, arguments from religious experience, Pascal’s wager, and minor evidential arguments. Worthy contribution to the literature on arguments for the existence of God.

Oppy, Graham. Arguing about Gods . Cambridge, UK: Cambridge University Press, 2006.

DOI: 10.1017/CBO9780511498978

Detailed discussion of cosmological arguments, teleological arguments, Pascal’s wager, and a range of other arguments. Discussion of ontological arguments that supplements Oppy 1995 (cited under Ontological Arguments ). Also includes some discussion of methodology: the mechanics of assessment of arguments for the existence of God.

Plantinga, Alvin. God and Other Minds: A Study of the Rational Justification of Belief in God . Ithaca, NY: Cornell University Press, 1990.

Groundbreaking discussion of cosmological arguments, ontological arguments, and teleological arguments. Instrumental in setting new standards of rigor and precision for the analysis of arguments for the existence of God. First published in 1967.

Plantinga, Alvin. “Appendix: Two Dozen (or so) Theistic Arguments.” In Alvin Plantinga . Edited by Deane-Peter Baker, 203–228. Cambridge, UK: Cambridge University Press, 2007.

DOI: 10.1017/CBO9780511611247

A collection of sketches or pointers to what Plantinga claims would be good arguments for the existence of God. Divided into (a) metaphysical arguments (aboutness, collections, numbers, counterfactuals, physical constants, complexity, contingency), (b) epistemological arguments (positive epistemic status, proper function, simplicity, induction, rejection of global skepticism, reference, intuition), (c) moral arguments, and (d) other arguments (colors and flavors, love, Mozart, play and enjoyment, providence, miracles).

Sobel, Jordan. Logic and Theism: Arguments for and against Beliefs in God . Cambridge, UK: Cambridge University Press, 2004.

Brilliant discussion of major arguments about the existence of God. Contains very detailed analyses of ontological arguments, cosmological arguments, teleological arguments, and arguments from miracles. Brought new rigor and technical precision to the discussion of these arguments for the existence of God.

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6.3 Cosmology and the Existence of God

Learning objectives.

By the end of this section, you will be able to:

• Describe teleological and moral arguments for the existence of God.
• Outline Hindu cosmology and arguments for and against the divine.
• Explain Anselm’s ontological argument for the existence of God.
• Articulate the distinction between the logical and evidential problems of evil.

Another major question in metaphysics relates to cosmology. Cosmology is the study of how reality is ordered. How can we account for the ordering, built upon many different elements such as causation, contingency, motion, and change, that we experience within our reality? The primary focus of cosmological arguments will be on proving a logically necessary first cause to explain the order observed. As discussed in earlier sections, for millennia, peoples have equated the idea of a first mover or cause with the divine that exists in another realm. This section will discuss a variety of arguments for the existence of God as well as how philosophers have reconciled God's existence with the presence of evil in the world.

Teleological Arguments for God

Teleological arguments examine the inherent design within reality and attempt to infer the existence of an entity responsible for the design observed. Teleological arguments consider the level of design found in living organisms, the order displayed on a cosmological scale, and even how the presence of order in general is significant.

Aquinas’s Design Argument

Thomas Aquinas’s Five Ways is known as a teleological argument for the existence of God from the presence of design in experience. Here is one possible formulation of Aquinas’s design argument:

• Things that lack knowledge tend to act toward an end/goal.
• It is obvious that it is not by chance.
• Things that lack knowledge act toward an end by design.
• If a thing is being directed toward an end, it requires direction by some being endowed with intelligence (e.g. the arrow being directed by the archer).
• Therefore, some intelligent being exists that directs all natural things toward their end. This being is known as God.

Design Arguments in Biology

Though Aquinas died long ago, his arguments still live on in today’s discourse, exciting passionate argument. Such is the case with design arguments in biology. William Paley (1743–1805) proposed a teleological argument, sometimes called the design argument, that there exists so much intricate detail, design, and purpose in the world that we must suppose a creator. The sophistication and incredible detail we observe in nature could not have occurred by chance.

Paley employs an analogy between design as found within a watch and design as found within the universe to advance his position. Suppose you were walking down a beach and you happened to find a watch. Maybe you were feeling inquisitive, and you opened the watch (it was an old-fashioned pocket watch). You would see all the gears and coils and springs. Maybe you would wind up the watch and observe the design of the watch at work. Considering the way that all the mechanical parts worked together toward the end/goal of telling time, you would be reluctant to say that the watch was not created by a designer.

Now consider another object—say, the complexity of the inner workings of the human eye. If we can suppose a watchmaker for the watch (due to the design of the watch), we must be able to suppose a designer for the eye. For that matter, we must suppose a designer for all the things we observe in nature that exhibit order. Considering the complexity and grandeur of design found in the world around us, the designer must be a Divine designer. That is, there must be a God.

Often, the design argument is formulated as an induction:

• In all things we have experienced that exhibit design, we have experienced a designer of that artifact.
• The universe exhibits order and design.
• Given #1, the universe must have a designer.
• The designer of the universe is God.

Think Like a Philosopher

Read “ The Fine-Tuning Argument for the Existence of God ” by Thomas Metcalf.

Evaluate the arguments and counterarguments presented in this short article. Which are the most cogent, and why?

Moral Arguments for God

Another type of argument for the existence of God is built upon metaethics and normative ethics. Consider subjective and objective values. Subjective values are those beliefs that guide and drive behaviors deemed permissible as determined by either an individual or an individual’s culture. Objective values govern morally permissible and desired outcomes that apply to all moral agents. Moral arguments for the existence of God depend upon the existence of objective values.

If there are objective values, then the question of “Whence do these values come?” must be raised. One possible answer used to explain the presence of objective values is that the basis of the values is found in God. Here is one premise/conclusion form of the argument:

• If objective values exist, there must be a source for their objective validity.
• The source of all value (including the validity held by objective values) is God.
• Objective values do exist.
• Therefore, God exists.

This argument, however, raises questions. Does moral permissibility (i.e., right and wrong) depend upon God? Are ethics an expression of the divine, or are ethics better understood separate from divine authority? To explore this topic further, students will find a helpful overview and updated references in the Stanford Encyclopedia article, " Moral Arguments for the Existence of God ."

Write Like a Philosopher

Watch “ God & Morality: Part 2 ” by Steven Darwall.

Darwall’s argument for the autonomy of ethics may be restated as follows:

• God knows morality best (1:44).
• God knows what is best for us (2:12).
• God has authority over us (2:48).

How does Darwall refute the conclusion? What is the evidence offered, and at what point within the argument is the evidence introduced? What does his approach suggest about refutational strategies? Can you refute Darwall’s argument?

As you write, begin by defining the conclusion. Remember that in philosophy, conclusions are not resting points but mere starting points. Next, present the evidence, both stated and unstated, and explain how it supports the conclusion.

The Ontological Argument for God

An ontological argument for God was proposed by the Italian philosopher, monk, and Archbishop of Canterbury Anselm (1033–1109). Anselm lived in a time where belief in a deity was often assumed. He, as a person and as a prior of an abbey, had experienced and witnessed doubt. To assuage this doubt, Anselm endeavored to prove the existence of God in such an irrefutable way that even the staunchest of nonbelievers would be forced, by reason, to admit the existence of a God.

Anselm’s proof is a priori and does not appeal to empirical or sense data as its basis. Much like a proof in geometry, Anselm is working from a set of “givens” to a set of demonstrable concepts. Anselm begins by defining the most central term in his argument—God. For the purpose of this argument, Anselm suggests, let “God” = “a being than which nothing greater can be conceived.” He makes two key points:

• When we speak of God (whether we are asserting God is or God is not), we are contemplating an entity who can be defined as “a being than which nothing greater can be conceived.”
• When we speak of God (either as believer or nonbeliever), we have an intramental understanding of that concept—in other words, the idea is within our understanding.

Anselm continues by examining the difference between that which exists in the mind and that which exists both in the mind and outside of the mind. The question is: Is it greater to exist in the mind alone or in the mind and in reality (or outside of the mind)? Anselm asks you to consider the painter—for example, define which is greater: the reality of a painting as it exists in the mind of an artist or that same painting existing in the mind of that same artist and as a physical piece of art. Anselm contends that the painting, existing both within the mind of the artist and as a real piece of art, is greater than the mere intramental conception of the work.

At this point, a third key point is established:

Have you figured out where Anselm is going with this argument?

• If God is a being than which nothing greater can be conceived (established in #1 above);
• And since it is greater to exist in the mind and in reality than in the mind alone (established in #3 above);
• Then God must exist both in the mind (established in #2 above) and in reality;
• In short, God must be. God is not merely an intramental concept but an extra-mental reality as well.

Hindu Cosmology

One of the primary arguments for the existence of God as found within Hindu traditions is based on cosmological conditions necessary to explain the reality of karma. As explained in the introduction to philosophy chapter and earlier in this chapter, karma may be thought of as the causal law that links causes to effects. Assuming the doctrine of interdependence, karma asserts that if we act in such a way to cause harm to others, we increase the amount of negativity in nature. We therefore hurt ourself by harming others. As the self moves through rebirth ( samsara ), the karmic debt incurred is retained. Note that positive actions also are retained. The goal is liberation of the soul from the cycle of rebirth.

Maintenance of the Law of Karma

While one can understand karmic causality without an appeal to divinity, how the causal karmic chain is so well-ordered and capable of realizing just results is not as easily explainable without an appeal to divinity. One possible presentation of the argument for the existence of God from karma could therefore read as follows:

• If karma is, there must be some force/entity that accounts for the appropriateness (justice) of the karmic debt or karmic reward earned.
• The source responsible for the appropriateness (justice) of the debt or reward earned must be a conscious agent capable of lending order to all karmic interactions (past, present, and future).
• Karmic appropriateness (justice) does exist.
• Therefore, a conscious agent capable of lending order to all karmic interactions (past, present, and future) must exist.

Physical World as Manifestation of Divine Consciousness

The cosmology built upon the religious doctrines allows for an argument within Hindu thought that joins a version of the moral argument and the design argument. Unless a divine designer were assumed, the moral and cosmological fabric assumed within the perspective could not be asserted.

Hindu Arguments Against the Existence of God

One of the primary arguments against the existence of God is found in the Mīmāmsā tradition. This ancient school suggests that the Vedas were eternal but without authors. The cosmological and teleological evidence as examined above was deemed inconclusive. The focus of this tradition and its several subtraditions was on living properly.

Problem of Evil

The problem of evil poses a philosophical challenge to the traditional arguments (in particular the design argument) because it implies that the design of the cosmos and the designer of the cosmos are flawed. How can we assert the existence of a caring and benevolent God when there exists so much evil in the world? The glib answer to this question is to say that human moral agents, not God, are the cause of evil. Some philosophers reframe the problem of evil as the problem of suffering to place the stress of the question on the reality of suffering versus moral agency.

The Logical Problem of Evil

David Hume raised arguments not only against the traditional arguments for the existence of God but against most of the foundational ideas of philosophy. Hume, the great skeptic, starts by proposing that if God knows about the suffering and would stop it but cannot stop it, God is not omnipotent. If God is able to stop the suffering and would want to but does not know about it, then God is not omniscient. If God knows about the suffering and is able to stop it but does not wish to assuage the pain, God is not omnibenevolent. At the very least, Hume argues, the existence of evil does not justify a belief in a caring Creator.

The Evidential Problem of Evil

The evidential problem considers the reality of suffering and the probability that if an omnibenevolent divine being existed, then the divine being would not allow such extreme suffering. One of the most formidable presentations of the argument was formulated by William Rowe :

There exist instances of intense suffering which an omnipotent, omniscient being could have prevented without thereby losing some greater good or permitting some evil equally bad or worse. An omniscient, wholly good being would prevent the occurrence of any intense suffering it could, unless it could not do so without thereby losing some greater good or permitting some evil equally bad or worse. (Therefore) there does not exist an omnipotent, omniscient, wholly good being. (Rowe 1979, 336)

Western Theistic Responses to the Problem of Evil

Many theists (those who assert the existence of god/s) have argued against both the logical and evidential formulations of the problem of evil. One of the earliest Christian defenses was authored by Saint Augustine. Based upon a highly Neo-Platonic methodology and ontology, Augustine argued that as God was omnibenevolent (all good), God would not introduce evil into our existence. Evil, observed Augustine, was not real. It was a privation or negation of the good. Evil therefore did not argue against the reality or being of God but was a reflection for the necessity of God. Here we see the application of a set of working principles and the stressing of a priori resulting in what could be labeled ( prima facie ) a counterintuitive result.

An African Perspective on the Problem of Evil

In the above sections, the problem of evil was centered in a conception of a god as all-powerful, all-loving, and all-knowing. Evil, from this perspective, reflects a god doing evil (we might say reflecting the moral agency of a god) and thus results in the aforementioned problem—how could a “good” god do evil or perhaps allow evil to happen? The rich diversity of African thought helps us examine evil and agency from different starting points. What if, for example, the lifting of the agency (the doing of evil) was removed entirely from the supernatural? In much of Western thought, God was understood as the creator. Given the philosophical role and responsibilities that follow from the assignment of “the entity that made all things,” reconciling evil and creation and God as good becomes a problem. But if we were to remove the concept of God from the creator role, the agency of evil (and reconciling evil with the creator) is no longer present.

Within the Yoruba-African perspective, the agency of evil is not put upon human agency, as might be expected in the West, but upon “spiritual beings other than God” (Dasaolu and Oyelakun 2015). These multiple spiritual beings, known as “Ajogun,” are “scattered around the cosmos” and have specific types of wrongdoing associated specifically with each being (Dasaolu and Oyelakun 2015). Moving the framework (or cosmology) upon which goodness and evil is understood results in a significant philosophical shift. The meaning of evil, instead of being packed with religious or supernatural connotations, has a more down-to-earth sense. Evil is not so much sin as a destruction of life. It is not an offense against an eternal Creator, but an action conducted by one human moral agent that harms another human moral agent.

Unlike Augustine’s attempt to explain evil as the negation of good (as not real), the Yoruban metaphysics asserts the necessity of evil. Our ability to contrast good and evil are required logically so that we can make sense of both concepts.

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1000-Word Philosophy: An Introductory Anthology

Philosophy, One Thousand Words at a Time

The Ontological Argument for the Existence of God

Author: Andrew Chapman Category: Philosophy of Religion Word Count: 1000

1. God’s Greatness

The Abrahamic conception of God is that he’s awesome —all-powerful, all-knowing, all-good, creator of the universe, self-existent, and a host of other properties that make him not just very, very great, but the greatest that there is or could possibly be.

“This is all fine and good,” say non-theists, “but this is a description of a being whose existence we don’t affirm.” However, a famous and powerful argument for God’s existence known as the Ontological Argument purports to be able to show that God’s being the greatest possible being entails God’s existence: the mere definition of God proves his existence.

This essay introduces this argument. 

2. Anselm’s Ontological Argument

There are different versions of the Ontological Argument, but we will focus on one of the earliest, set forth by St. Anselm (1033-1109). 1

As we’ve already noted, God is the being than which no greater can be conceived . This is Anselm’s somewhat unwieldy description of God, which we can abbreviate as BNGC . By definition, BNGC is the greatest conceivable being. If you think you’re conceiving of God and you can possibly conceive of a greater being, then you weren’t initially conceiving of God. Simple enough.

Now, certainly you can conceive of God. To conceive of something is just to think about it clearly and distinctly; you’ve been doing that since the beginning of this essay. So we know, at least, that God can exist in conception , i.e., can be conceived. Even atheists admit this. What the atheist is denying, and what the agnostic is refusing to affirm or deny, is that God exists in reality . So we have an intuitive distinction between a thing that exists merely in conception and a thing that exists in reality as well as in conception .

Now here’s the argument: Assume that the atheist is right, that God doesn’t exist in reality, but merely in conception. But then there would be another possible being, a God who exists not merely in conception but also in reality as well, who is greater than BNGC. 2 That is, there would be a possible being who is greater than the being than which no greater can be conceived. But no being can be greater than the being than which no greater can be conceived—that’s a flat-out contradiction! So our original assumption, that God doesn’t exist in reality, but merely in conception, must be false, since any assumption that entails a contradiction must be false. Therefore, God must exist both in conception and in reality. Therefore: God exists. 3

The Ontological Argument is remarkable in that it reasons from premises containing only definitions and logical laws to perhaps the grandest philosophical conclusion there is. We can know that God exists merely by reflecting on the concept of God .

Many people, however, have been uncomfortable with the purported fact that we can prove the Almighty’s existence so apparently simply. Numerous critics, theist and non- alike, have criticized different aspects of the Ontological Argument. Let’s look at just two of the most influential criticisms: those provided by Gaunilo of Marmoutiers (994-1083) and Immanuel Kant (1724-1804).

3. Gaunilo’s Criticism

Gaunilo was a monk and a contemporary of Anselm’s. In his “Reply on Behalf of the Fool,” 4 Gaunilo has us imagine another really awesome thing: the island than which no greater can be conceived —let’s call it INGC . This island has all the amazing-making properties you can think of: pristine white-sand beaches for lounging, warm water for swimming, and not a tourist in sight. But certainly such an island’s existing only in conception would entail a contradiction, since then there would be a possible thing greater than the INGC, namely, the existing INGC. Therefore, the INGC exists. And, of course, since we have picked island arbitrarily, we can run the same argument for any object: a building, a mousetrap, a horse, whatever you please. 5

What Gaunilo has shown, then, is that, using Anselm’s form of reasoning , we can prove the existence of all sorts of bizarre entities, entities that clearly don’t exist. Accordingly, concludes Gaunilo, there must be something fatally wrong with Anselm’s reasoning. 6

4. Kant’s Criticism

Which do you prefer, coffee or existing coffee ? Notice that this is different from the question of whether you prefer coffee or no coffee at all . No coffee isn’t coffee while both coffee and existing coffee are coffee just the same! If it seems like we’re verging on Lewis Carroll-style nonsense here, you’re right, and this is exactly Kant’s criticism of the Ontological Argument.

According to Kant in his Critique of Pure Reason , what’s gone wrong with Anselm’s argument lies in the distinction between a thing that exists merely in conception and a thing that exists in reality as well as in conception . According to Anselm, there are two different sorts of things : those that exist merely in conception and those that exist in reality as well as in conception. But an existing thing and its non-existing counterpart aren’t two different sorts of thing —one merely exists and the other doesn’t. While it is certainly true that some things exist and others do not, existing does not make a thing a different kind of thing from its non-existing colleague.

The upshot of this, says Kant, is that existence is a very special type of property, one not suited for the type of argument Anselm is running. Since there is no difference between the group of objects falling into the class God and those falling into the class existing God , an existing God can be no better and no worse than a mere God. There’s simply no relevant difference in kind between a God who exists and a God who doesn’t.

5. Conclusion

Of course, Gaunilo and Kant have not had the last word in this debate. Powerful arguments have been mounted in response to Gaunilo’s and Kant’s criticisms of the Ontological Argument. Additionally, increasingly complex versions of the Ontological Argument have been developed and debated. One thing that’s certain is that the Ontological Argument, whether sound or unsound, is a fascinating and powerful attempt at a proof for the existence of God.

1  Two other famous formulations of the argument are Descartes’s formulation from the conception of existence as a perfection  (see  Descartes’ Meditations 4-6 by Marc Bobro) and Alvin Plantinga’s so-called Modal Ontological Argument (see Modal Ontological Arguments for the Existence of God by Thomas Metcalf). 

2  Which is greater, a God who exists merely in conception or a God who exists in reality as well as in conception? Think of all the things a God who exists in reality as well as in conception can do that a God who exists merely in conception cannot do: He can create worlds. He can listen to prayers. He can be the ultimate source and ideal form of goodness. He can reward virtuousness and punish vice… Those all seem like great things, and a God who exists merely in conception can do none of them.

3  You may remember this type of argument or proof from your geometry courses where it was called an indirect proof . Philosophers and logicians call this a reductio ad absurdum , or a reduction to absurdity. The strategy, as you have seen, is to assume the opposite of what you are trying to prove, show how that assumption entails either a contradiction or some other form of absurdity, and then to reject the original assumption.

4  “The fool has said in his heart, ‘There is no God.’” (Psalm 14:1)

5  It’s important to note that we’re not merely talking here about the greatest actually existing island, mousetrap, horse…, but the greatest possible island, mousetrap, horse… It is plausible that for any type of existing object, one of the ones that exists is the best one (in terms of whatever makes that sort of thing a good one of what it is). But it is another thing altogether to talk about the greatest possible or greatest conceivable such object.

6  Notice that Gaunilo’s argument is also a reductio ad absurdum:  Assume that Anselm’s reasoning is valid and an absurdity results. Therefore, Anselm’s reasoning must be flawed.

Anselm, St.,  Proslogion , in  St. Anselm’s Proslogion , M. Charlesworth (ed.), Oxford: OUP, 1965.

Descartes, R., Discourse on Method and The Meditations , translated with an introduction by F. Sutcliffe, Harmondsworth: Penguin, 1968.

Gaunilo, “On Behalf of the Fool”, in St. Anselm’s Proslogion, M. Charlesworth (ed.), Oxford: OUP, 1965.

Kant, Immanuel.  Critique of Pure Reason . Trans. Paul Guyer and Allen W. Wood. Cambridge: Cambridge UP, 1998.

Oppy, Graham. “Ontological Arguments.”  Stanford Encyclopedia of Philosophy . Stanford University, 08 Feb. 1996. Web. 27 June 2014.  

Related Essays

The Concept of God: Divine Attributes  by Bailie Peterson

Descartes’ Meditations 4-6  by Marc Bobro

Modal Ontological Arguments for the Existence of God by Thomas Metcalf 

Possibility and Necessity: An Introduction to Modality  by Andre Leo Rusavuk

Modal Epistemology: Knowledge of Possibility & Necessity  by Bob Fischer

About the Author

Andrew Chapman is a lecturer in philosophy at the University of Colorado, Boulder. He holds a PhD in philosophy from the University of Colorado, Boulder, an MA in philosophy from Northern Illinois University and a BA in philosophy and a BM in bassoon and sound recording technology from Ithaca College. He specializes in epistemology, metaethics, and the history of philosophy (especially Kant and the 20th Century Anglophone and Phenomenological traditions). When not philosophizing, Andrew is skiing, hiking, listening to great music, or playing the bassoon. www.colorado.edu/philosophy/people/andrew-d-chapman  

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Graham Oppy, editor: Ontological arguments

Cambridge University Press, Cambridge, 2018, x and 284 pp, $34.99 (paper)

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• Volume 86 , pages 91–96, ( 2019 )

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The Many - Faced Argument (ed. Hick and McGill, Macmillan 1967). A very large volume, edited by Miroslaw Szatkowski, appeared in 2013 ( Ontological Proofs Today, Ontos Verlag). That includes much advanced work, but is expensive and much less accessible than the volume under review.

See especially p. 57.

“The Ontological Argument as Cartesian Therapy,” Canadian Journal of Philosophy 35(4), pp. 521–562.

“Ontological Arguments” in Stanford Encyclopedia of Philosophy ; https://plato.stanford.edu/entries/ontological-arguments/ , accessed May 22, 2019.

Lewis, David, "Anselm and Actuality," Nous volume 4, number 2 (1970), pp. 175–188.

The Nature of Necessity (Oxford: Oxford University Press, 1974), p. 221.

See his “Three Versions of the Ontological Argument” in Ontological Proofs Today, Miroslaw Szatkowski (editor), Ontos Verlag 2012, pp. 143–162.

NB: Descartes gives such a restriction, but this involves “clear and distinct perception” by the meditator.

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What Is the Ontological Argument for God’s Existence?

A ttempting to offer a philosophical explanation or justification for the existence of God is one of the most sustained philosophical exercises. The ontological argument is one of the most famous such attempts, as well as the most distinctive. But what is the ontological argument for God’s existence, and how good an argument is it, really? We take a closer look.

An a Priori Argument

The ontological argument for God’s existence is an argument which is not based on any observation about the physical structure of the universe and God’s place in it . Indeed, it is an argument which does not rely on any kind of observation, whatsoever. Rather, it is an argument which justifies God’s existence in a purely rational way. It is an a priori rather than a posteriori argument. An a priori argument is one which uses deductive reasoning only. No new observations are required to make this argument – it can be made by virtue of what we already know, or what is latent within what we already know. Not all deductive arguments are simple. Indeed, many forms of deductive reasoning require us to understand formal systems which are used to represent deductive arguments. 

St Anselm’s Version of the Ontological Argument

However, the ontological argument is mercifully simple (at least to relate). The first statement of this argument is that of St Anselm . During his long career as a leading churchman (he was the Archbishop of Canterbury, which was and remains the highest post in the English Church), Anselm was also a scholar and intellectual. We can quote him directly to give a sense of how simple the argument was even in his initial version of it:

“[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… [and so] … 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.”

Let’s try to clarify the steps of this argument. The argument resolves itself in the conclusion that there is no doubt that there exists the greatest possible being, but how defensible are the premises from which this conclusion can be drawn?  

Objections Against the Ontological Argument

First, there is an assertion that God is the greatest thing which could possibly exist (“than which nothing greater can be conceived”). The plausibility of this argument to an atheist is, clearly, very limited . Indeed, this constitutes one of the first criticisms of the ontological argument – that it is an argument which can only be used to persuade those who already adhere to some theistic worldview. Of course, Anselm lived at a time when belief in God was utterly ubiquitous, and the purpose of creating an argument for God’s existence was not to show that God exists as such, but rather to give the best possible justifications for his existence.

For Christians like Anselm, as for many believers of various faiths, it is intrinsic to the nature of God that He is the greatest possible thing – the most powerful, knowledgeable, good and so forth. Second, there is the assertion that for something to be the best thing, it should also exist. Another popular line of criticism focuses on this part of the argument. Immanuel Kant famously held that ‘existence is not a predicate’. A predicate can be seen simply as a descriptive quality a thing might have. Kant ’s point was that being the greatest conceivable thing is a matter of having the best version of any given predicate, but that to exist is not a quality of the same kind.