The Ontological Argument (Anselm, Descartes, Kant, Plantinga)

The argument seems acrobatic at first reading. Many feel that they are being forced into making God exist by a verbal trick. Before examining the objections, a genuine effort at popularization is needed. To understand Anselm's intuition — not to caricature it.

The image of maximal greatness

Let us go back to basics. Every being we encounter in the world can be greater than it is. A mountain can be higher. A scholar, more learned. A saint, more holy. A universe, vaster. For all finite realities, one can always go further. That is precisely what makes them finite and improvable.

Now let us try to think not a great being, but the absolutely great being — one whose greatness cannot be surpassed, or even equalled. If I say "it could be greater still," I am no longer talking about it: I am talking about another being. And if I say "it might not exist," I am talking about one being fewer. Now, a being that exists is manifestly more than the same being that would not exist. So to speak of an absolutely great being that would not exist is to contradict oneself in terms.

That is the heart of the intuition. God, if he is truly God, cannot be a contingent being. He cannot be something that "as luck would have it" exists and "as bad luck would have it" might have been missing. To think a contingent God is to think something other than God. It is to think a super-creature, a "greatest of the gods" in the manner of the pagan pantheons — a being that happens, by accident, to be at the top of the chain, but that might not have been. Now the ontological argument maintains that this is not God: God is the being whose necessity is part of his very identity.

What the argument does not say (three caricatures to set aside)

Before going into detail, three caricatures that have been circulating for a thousand years must be set aside. The argument is delicate: it must be read honestly before being criticized.

The argument does not say: "I imagine Pegasus, therefore Pegasus exists." Pegasus is by nature a finite, composite, localized reality. One can think him greater, more beautiful, or non-existent. Pegasus is essentially contingent. The argument concerns only a single case: that of a being whose concept implies necessity.

The argument does not say either: "I can imagine a God, therefore God exists." To imagine is to form a sensory representation — an image. But God is not an object of imagery. The argument speaks of an understanding of the concept, not of a visual representation.

The argument does not say finally: "the word God contains the word existence, therefore God exists." This is the caricature that Kant will attack. The Anselmian argument says something quite different: "the very concept of the greatest possible being does not tolerate the possibility of non-being."

Why this way is unique in all of philosophy

The ontological argument is the only purely a priori argument in favor of the existence of a real being. All the other theistic arguments — the five ways of Saint Thomas, the Kalam argument, the fine-tuning argument, the moral argument, the argument from desire — start from an observable fact about the world and work back to God as their cause. These are a posteriori arguments (reasoning from effects).

The ontological argument reverses the approach. It claims that God's existence can be deduced from the concept of God alone, independently of any observation. It is this uniqueness that gives it its fascination, and also its difficulty. The philosopher Graham Oppy, the leading contemporary authority on the subject, acknowledges this himself: "ontological arguments are among the most controversial arguments in the whole history of Western philosophy"^[6].

The technical vocabulary: a user's guide

The whole discussion rests on a few technical distinctions. Ignoring them makes one imagine contradictions where there are none.

The last row will be crucial for the modern version. In modal logic S5, if something is possibly necessary, then it is in fact necessary. This seems strange at first sight, but follows from a simple principle: what is necessary is so in all possible worlds; therefore "possibly necessary" means that there is at least one world where this thing is necessary — and since it is then true in all worlds, it is true in ours too.

Three families of ontological arguments

Oppy distinguishes several families of ontological arguments. The three main ones are as follows^[7]:

The Anselmian version is the historical matrix. The modal version is the one most discussed today in analytic philosophy. The Cartesian definitional version is the one most exposed to the Kantian objection. This article will follow chronological order, because each generation has reformulated the argument in response to earlier criticisms.

Saint Anselm of Canterbury (1033-1109) composed the Proslogion at the Abbey of Bec, in Normandy, between 1077 and 1078. The title means Allocution (in the sense of an address to God). It is not a cold treatise: it is a meditation addressed to God, which opens with the verse “The fool said in his heart: there is no God” (Ps 13/14, 1). Anselm seeks an argument that would stand on its own, without needing the long chain of reasoning he had developed in his previous work, the Monologion.

“Lord, you who give faith understanding, grant me to understand, as much as you know to be good for me, that you are as we believe, and that you are what we believe.” — Saint Anselm, Proslogion, ch. I^[8]

This tone is essential. For Anselm, the argument is not a dialectical trap set for atheists: it is a fides quaerens intellectum, a faith that seeks understanding. It is in this climate of prayer that the most famous formula of all medieval Christian metaphysics appears.

Proslogion II: “aliquid quo nihil maius cogitari possit”

Anselm's Latin formula — aliquid quo nihil maius cogitari possit — translates literally as “something than which nothing greater can be thought”. The argument of chapter II consists of a few dense lines. Here is its formal structure, as reconstructed by Graham Oppy^[9] and William Mann^[10]:

1. Even one who denies God understands the expression “that than which nothing greater can be thought”.
2. Whatever is understood exists at least in the understanding.
3. But that than which nothing greater can be thought cannot exist only in the understanding.
4. For a being that would exist also in reality would be greater than a being existing only as an idea.
5. If therefore that than which nothing greater can be thought existed only in the understanding, one could conceive something greater — which is contradictory.
6. Therefore that than which nothing greater can be thought exists both in the understanding and in reality.

“And certainly that than which a greater cannot be thought cannot be in the understanding alone. For if, at the very least, it is in the understanding alone, it can be thought to exist also in reality, which is greater. If therefore that than which a greater cannot be thought is in the understanding alone, that than which a greater cannot be thought is that than which a greater can be thought. Which certainly cannot be. There exists therefore, without any doubt, both in the understanding and in reality, something than which a greater cannot be thought.” — Saint Anselm, Proslogion, ch. II, 1077-1078^[11]

The movement is very swift. The argument does not say “I imagine God, therefore God exists”. It says: “if I truly think the maximal being, I cannot think that it lacks the very quality that would make it be rather than not be.” Anselm's strength is to require of the reader nothing more than agreement on the definition; everything else follows by deduction.

Proslogion III: God cannot even be thought not to exist

Chapter III considerably strengthens the argument by introducing necessity. Anselm no longer content to assert that God exists: he maintains that God cannot even be thought not to exist. It is this passage — long commented on less than chapter II — that will be the starting point of the entire modern modal version of the twentieth century.

“It exists so truly, that one cannot even think that it does not exist. For one can think that there exists something that cannot be thought not to exist, and which thereby is greater than what can be thought not to exist. Hence, if that than which nothing greater can be thought can be thought not to exist, then that than which nothing greater can be thought is not that than which nothing greater can be thought: which is contradictory. There exists therefore so truly something than which nothing greater can be thought, that one cannot even think it not to exist. And this, Lord, our God, is you.” — Saint Anselm, Proslogion, ch. III^[12]

The contribution of chapter III is decisive. A contingent being, which may or may not be, is by nature less great than a necessary being, which cannot not be. Anselm therefore concludes that God is absolutely necessary being, the being whose non-being is metaphysically impossible. This is exactly what the contemporary modal version will defend.

Proslogion IV: how can the fool say what cannot be thought?

Chapter IV resolves an apparent objection. If God cannot be thought not to exist, how does the atheist manage to say in his heart: “there is no God”? Anselm answers with a very fine distinction between understanding a word and understanding a thing:

1. One can understand the word “God” without grasping what it actually signifies — like a man who says “diamond” without knowing what a diamond is.
2. One can, on the contrary, understand the thing itself, and then one can no longer think of it as not existing.

“A thing, indeed, can be thought when one thinks its word; it is thought in another sense when one understands what it is in itself. In the first sense, then, one can think that God does not exist; in the second, in no way.” — Saint Anselm, Proslogion, ch. IV^[13]

This distinction is central. It protects the argument against the easy retort: “I have the word ‘God’ in mind, so I can think it non-existent”. Anselm answers that one who thinks God as non-existent is not thinking God — he is thinking the word, or a false idea, or a caricature. This is exactly what Malcolm and Plantinga will take up, nine centuries later and in other forms.

Anselm's argument did not remain isolated. Reused, transformed, attacked, and defended, it has run through the whole of modern philosophy. Four reformulations mark the history of thought.

Bonaventure and Duns Scot: The Franciscan Tradition in the Middle Ages

Before the moderns, Anselm's argument was taken up by the great Franciscans of the 13th century. Saint Bonaventure (1221–1274), in his Itinerarium mentis in Deum (1259), holds that the knowledge of God as the "most perfect being" is innate in man and that it entails His reality. John Duns Scotus (1266–1308), in the Lectura and the Ordinatio, transforms the argument into a proof based on the non-contradictory possibility of a first efficient cause — a direct anticipation of the modern modal strategy^[14].

This Franciscan tradition was never condemned by the Church. It forms the scholastic counterpart to the Thomistic position, and it survives down to Plantinga, who explicitly claims this Augustinian-Anselmian lineage.

Descartes: Existence Belongs to the Essence of God

René Descartes (1596–1650) takes up the argument in the fifth Meditation on First Philosophy (1641). His version differs from Anselm's: he no longer reasons from the "greatest" but from the idea of a "supremely perfect being." His intuition is mathematical: existence belongs to God as the property of having three angles equal to two right angles belongs to the triangle.

"When I conceive a supremely perfect being, and when I wish to examine whether it belongs to His nature to exist, I always find that, and from whichever side I turn my thought, I cannot think of a supremely perfect being lacking existence (that is, lacking some perfection), any more than I can think of a horse with wings or without wings." — René Descartes, Meditations on First Philosophy, V, 1641^[15]

The Cartesian structure is therefore:

1. I have the clear and distinct idea of a supremely perfect being.
2. Existence is a perfection.
3. A supremely perfect being cannot lack any perfection.
4. Therefore, existence belongs to the essence of God.

This version has one brilliant merit: it is lucid. It also has one decisive weakness: it treats existence as one perfection among others, on a par with power, knowledge, or goodness. This is what Kant will attack head-on, and the Kantian critique will bear far more on Descartes than on Anselm.

Leibniz: One Must First Prove That God Is Possible

Gottfried Wilhelm Leibniz (1646–1716) accepts the Cartesian structure but sees a decisive gap in it. The argument assumes that the idea of a supremely perfect being is coherent — that is, that the divine perfections do not contradict one another. As long as this coherence is not demonstrated, the argument remains suspended^[16].

"It must be proved with the rigor of geometrical demonstrations that such a [supremely perfect] being is possible." — Gottfried Wilhelm Leibniz, Quod Ens Perfectissimum Existit, November 1676^[17]

Leibniz therefore attempts to fill this gap. He argues that perfections are simple (not decomposable) and positive (containing no internal negation). Now, two simple and positive properties cannot contradict one another: only an opposition between an affirmation and a negation produces a contradiction. Therefore, all the divine perfections can coexist in one and the same being.

This Leibnizian precaution is essential. It shifts the ground of the debate. The question is no longer "can I conceive of God?" but "is such a being metaphysically possible?" The entire contemporary modal version of the argument will turn precisely on this question, three centuries later.

Spinoza and Hegel: The Drift Toward Pantheism

Baruch Spinoza (1632–1677), in the Ethics published posthumously in 1677, offers a radicalized version: God is defined as the substance whose essence involves existence. But Spinoza identifies this substance with Nature, which takes him outside classical theism and leads him to pantheism — a position incompatible with the Catholic faith.

G. W. F. Hegel (1770–1831), in his Lectures on the Proofs of the Existence of God (published posthumously in 1831), sharply criticizes the Kantian refutation. For Hegel, Kant treats God as a finite object among others (like the one hundred thalers of his famous example). But God, in Hegelian speculative thought, is the Absolute Spirit, the totality of being. To compare Him with a finite object is a category mistake^[18]. The Hegelian position, however, lies outside the frameworks of classical Christian philosophy: it confuses God with the absolute of history, which cannot be reconciled with divine transcendence.

For the Catholic reading, these two reformulations are both useful and dangerous. They restore metaphysical dignity to the question, but they slide toward pantheism. This is why the Catholic center of gravity remains Anselmian or Thomistic, never Spinozist or Hegelian.

The ontological argument gave rise, from the 11th to the 19th century, to five major classical objections. Each attacks a specific point. Each calls for a specific answer. We present them here in their strongest version, without caricature or dilution.

Gaunilo of Marmoutiers: the parody of the lost island (1078)

Anselm's first critic is a Benedictine monk from the abbey of Marmoutiers, near Tours: Gaunilo. In his Liber pro insipiente (In Behalf of the Fool), he offers a parody that has remained famous. Suppose someone speaks to me of a lost island, superior to all other lands in fertility and beauty, "such that nothing more excellent can be conceived." I understand this description. But I cannot conclude that this island actually exists somewhere in the ocean.

"They say that somewhere in the ocean is an island, which, because of the difficulty, or rather the impossibility, of finding what does not exist, is called the Lost Island. They say that this island is furnished with such an abundance of all manner of riches and delights in every way surpassing those of all other lands inhabited by men, that, having no owner or inhabitant, it excels in riches all the other lands that men inhabit. (...) If anyone were to tell me that there is such an island, I could understand him without difficulty, and if he were to add that it truly exists, I should not find this hard to understand either, but only that I should be doubtful as to whether he really knew it. (...) If someone told me: "You can no longer doubt the real existence of this island, since you do not doubt that it is in your understanding," I would think he was joking, or I would not know which of the two I should judge the more foolish." — Gaunilo of Marmoutiers, Liber pro insipiente, § 6, c. 1078^[19]

The objection is scathing. If Anselm's argument makes God exist by definition, one could make any object exist by definition, provided one declares it "the greatest of its kind." This parody is, even today, the first that comes to the mind of any sceptical reader. It must therefore be taken seriously.

Saint Thomas Aquinas: self-evident in itself, not for us (c. 1268)

Saint Thomas Aquinas (1225–1274) rejects the Anselmian argument as a demonstration accessible to man. In the Summa Theologiae (Prima Pars, q. 2, a. 1), he raises the question: Is God's existence self-evident? His answer is subtle, and constitutes the classic Catholic reading of the ontological argument.

"The proposition "God exists" is self-evident in itself, for the predicate is the same as the subject: for God is His own existence (...). But since we do not know the essence of God, the proposition is not self-evident to us; it needs to be demonstrated by things that are more known to us, namely by His effects." — Saint Thomas Aquinas, Summa Theologiae, I, q. 2, a. 1, respondeo^[20]

Thomas thus distinguishes two orders:

The Thomistic objection is thus epistemological. It does not say that the argument is false in itself; it says that it would work if we had an intuitive grasp of the divine essence. But this grasp is precisely denied us in the present condition. Saint Thomas therefore rejects the argument as a demonstrative starting point, without thereby denying that in God Himself, essence and existence are identical. The contemporary Thomist philosopher Edward Feser notes that this objection "aims precisely at the crux of the problem"^[21].

David Hume: no existence can be demonstrated a priori (1779)

David Hume (1711–1776), the Scottish empiricist, rejects outright any claim to demonstrate existence a priori. In the Dialogues Concerning Natural Religion (posthumous publication, 1779), he has Cleanthes say:

"Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently, there is no being, whose existence is demonstrable." — David Hume, Dialogues concerning Natural Religion, IX, 1779^[22]

For Hume, the only mode of demonstration is conceptual analysis, and conceptual analysis never bears on existence — which does not belong to the content of a concept. The Humean objection directly foreshadows Kant. Its strength lies in the fact that it applies to all ontological arguments indiscriminately.

Kant: "existence is not a real predicate" (1781)

The most famous objection is that of Immanuel Kant (1724–1804) in the Critique of Pure Reason (1781, 2nd edition 1787). Kant does not discuss Anselm directly (he often confuses him with Descartes): he attacks the general form of the argument as reformulated by Descartes and Leibniz. It is he, moreover, who coins the expression "ontological argument."

His thesis can be summed up in one sentence that has become canonical:

"Being is obviously not a real predicate, that is, a concept of something that could be added to the concept of a thing. It is merely the positing of a thing, or of certain determinations in themselves." — Immanuel Kant, Critique of Pure Reason, A598/B626, 1781/1787^[23]

The idea is this. When I say "the triangle has three angles", I add a property to the concept of triangle — I determine it further. But when I say "the triangle exists", I add nothing to its content: I merely assert that an object corresponds to the concept. Existence is not a quality comparable to the others — it is the positing of the object in reality.

To make the point concrete, Kant takes the classic example of the hundred thalers (the Prussian currency unit):

"A hundred real thalers contain nothing more than a hundred possible thalers. For while the former signify the concept, the latter the object and the positing of this object in itself, then, if the former contained more than the latter, my concept would not express the whole object, and would not therefore be the adequate concept of it." — Immanuel Kant, Critique of Pure Reason, A599/B627^[24]

The concept of a hundred thalers is the same, whether they exist or not. What changes when they exist is not their conceptual content: it is that they are posited in reality. Kant concludes that the ontological argument commits a category mistake: it treats existence as a property, whereas it is something entirely different. This objection is so powerful that, for nearly two centuries, the ontological argument was held to be dead by most academic philosophers.

Frege and Russell: existence is a higher-order predicate

In the 19th and 20th centuries, modern logic refines and formalises the Kantian objection. Gottlob Frege (1848–1925) shows in The Foundations of Arithmetic (1884) that existence is a second-order predicate: it does not bear on objects, but on concepts. Saying "horses exist" is not the same as attributing a property to horses; it is saying that the concept "horse" is non-empty^[25].

Bertrand Russell (1872-1970) systematises this point in his famous theory of descriptions. "The present King of France is bald" is not a simple attribution of a property: it is a disguised existential claim. Modern logic thus shows that existence cannot be made to depend on a purely analytic reasoning about concepts. Russell himself would recount that he once believed, for a lightning-flash moment, that the argument was sound — an anecdote that shows the very real fascination it exerts even on the most sceptical minds:

« Good God in boots! — the ontological argument is valid! » — Bertrand Russell, Autobiography, vol. 1, p. 84^[26]

But the flash passes: Russell goes on to reject the argument for the rest of his life.

Each of the five classical objections called for a precise response. The aim is not to pulverise them — they all have real force — but to show that they do not touch the most rigorous version of the argument. This section is the pivot of the article: it is here that the solidity or otherwise of the Anselmian argument is decided.

Response to Gaunilo: the island is not a valid parallel

Anselm replies personally to Gaunilo in a Responsio editoris (Reply of the Author) that circulates immediately alongside the Proslogion. His central argument is simple: the island parody does not work, because an island is by nature finite, composite, localised and improvable, whereas God is by nature absolute being, incomposite, infinite.

« That than which nothing greater can be thought cannot be thought not to exist, because it alone exists in such a way that it has in itself the fullness of being; everything else, which consequently has a part of what it is outside itself, can be thought not to exist. (...) If anyone can conceive thus, either to think it to exist or to think it not to exist, let him find me this island, and I will give him what he has lost, without fear of losing it. » — Saint Anselm, Responsio editoris, chap. 3, c. 1078^[27]

The Anselmian argument is not a recipe one applies to just any object. It holds only for a being whose greatness includes necessity — that is, for a metaphysically maximal being. An island, even "the most perfect possible", remains by nature a contingent object: one can always imagine it being greater, better placed, better populated, more alive. The very concept of a "maximal island" is unstable, because it concerns a finite reality.

The modern response reformulates the same intuition in other words. The parody works only on condition of introducing necessity into the parodied concept. But then the parody ceases to be a parody: "an island that exists necessarily" is an incoherent concept (islands, by definition, are localised contingent realities), whereas "a maximal being that exists necessarily" is precisely what theists call God. The asymmetry is ontological, not merely rhetorical.

Response to Thomas Aquinas: an argument of clarification, not a direct proof

The Thomist position is not a radical refusal of the argument. Saint Thomas explicitly acknowledges that the proposition "God exists" is self-evident. He refuses only that it should be evident to us. This position therefore leaves room for the ontological argument, but as metaphysical illumination rather than as a demonstration of God's existence.

The Anselmian argument functions then less as a first proof than as a clarification of the concept of God. It does not say: "here is how to know that God exists". It says: "if you are truly speaking of God, you are speaking of a being that cannot be contingent". This does not convert an atheist out of nothing; but it prevents any serious theist from treating God as a "super-object" set alongside the other beings of the world.

Étienne Gilson, a major twentieth-century Catholic medievalist, puts it thus: the Anselmian demonstration "is assuredly the triumph of a pure dialectic operating upon a definition", but its strength comes "from a correct intuition of what is unique in the notion of being taken in the absolute sense"^[28]. Thomism and Anselmism do not contradict each other head-on: they complement each other, provided one does not confuse the orders of discovery (a posteriori) and the orders of analysis (a priori).

Response to Hume: metaphysical necessity is not logical non-contradiction

Hume held that whatever is conceived as existing can be conceived as not existing, and that no existence is demonstrable. But this thesis conflates two different notions: logical possibility (the absence of internal contradiction) and metaphysical possibility (coherence in the order of being).

That I can imagine a world without God does not prove that such a world is metaphysically possible. I can imagine a world in which water would not be H₂O — that is logically non-contradictory. But it is not metaphysically possible: if water is H₂O, it is so in every possible world, because that is its essence. Likewise, if God is the necessary being, I may utter the words "a world without God", but I am not thereby formulating a coherent metaphysical possibility. The contemporary modal argument will rest precisely on this distinction^[29].

Response to Kant: the necessity of existing is not an ordinary predicate

The Kantian objection strikes hard at the Cartesian version, which treats existence as a perfection set alongside the others. It strikes less at the properly Anselmian version, and it strikes the contemporary modal version even less.

The decisive point is this. Kant is right to say that "to exist" is not an internal quality of a concept. But the solid version of the argument does not speak merely of "existing". It speaks of the necessity of existing — that is, of a modal property, which characterises the mode of existence of a being.

Norman Malcolm was the first, in 1960, to show clearly that the Kantian objection does not reach the version of Proslogion III, which rests on necessity and not on bare existence^[30]. The contemporary modal argument (Plantinga, Hartshorne) takes up this point: the necessity of existing is a modal property that can be attributed to or withheld from a being; it is not the bare existence of which Kant speaks.

Concretely: the difference between "God exists" and "God exists necessarily" is the same as that between "the Eiffel Tower exists" and "the Eiffel Tower could not fail to exist". The second proposition makes a claim far stronger than the first, and that claim concerns the manner of existing, not merely the fact of existing. Now it is precisely this necessary manner that belongs to God — and that belongs to no other being.

Response to Frege and Russell: modern logic does not settle the debate

The logical objection of Frege and Russell reduces existence to an existential quantifier — "there exists an x such that...". But this reduction is itself a philosophical thesis, not a neutral fact. Several contemporary logicians and metaphysicians (Crocco, Sobel, Anderson, Hájek) have shown that modal logic can perfectly well treat the necessity of existing as a property of an object, without conflating the orders. C. Anthony Anderson's modal system Q3, for example, reformulates the Gödelian argument within a logically coherent framework^[31].

Modern logic has therefore not refuted the ontological argument. It has simply refined its language and shifted the ground: the question is no longer whether existence is a predicate, but whether the metaphysical necessity of a being is coherent. The contemporary objections all bear on this point, and we shall examine them in the sections that follow.

In the twentieth century, the ontological argument changes face. It abandons the scholastic vocabulary of "greatness" and becomes a modal argument, formulated in the logic of possible worlds. This renaissance is the work mainly of three philosophers: Norman Malcolm, Charles Hartshorne, and above all Alvin Plantinga. To this is added, in parallel, the most formal logical work ever done on the question: the Gödelian proof.

Malcolm (1960): rediscovering Proslogion III

In a famous article in the Philosophical Review, Norman Malcolm (1911-1990) argues that Anselm actually formulated two arguments, and that the Kantian critique touches only the first one (chapter II). The second argument (chapter III) rests not on existence as perfection, but on necessity as perfection.

Its modern formulation is as follows^[32]:

1. If God exists, his existence is necessary.
2. If God does not exist, his existence is impossible.
3. Therefore God's existence is either necessary or impossible.
4. If God's existence is merely possible but not necessary, we have a contradiction (1).
5. If God's existence is not impossible (nothing contradictory in his concept), then it is possible.
6. Therefore God's existence, if it is not impossible, is necessary.

The decisive point is premise 5: the coherence of the concept of God suffices, in modal logic, to entail his necessary existence. The whole issue is thus shifted onto coherence — onto the positive possibility of a necessary being.

Hartshorne: perfection cannot be contingent

Charles Hartshorne (1897-2000), an American neo-classical philosopher, formalises the same reasoning in modal logic as early as Man's Vision of God (Willett, Clark & Co., 1941), and then above all in Anselm's Discovery (Open Court, 1965)^[33]. For Hartshorne, the conclusion is non-trivial: if God is the necessary being, his existence is either necessary or impossible — there is no intermediate option.

"Anselm discovered the only valid argument: perfection cannot be a contingent fact." — Charles Hartshorne, Anselm's Discovery, 1965^[34]

The whole issue therefore hinges on the possibility of God. Hartshorne argues that it falls to the opponent to prove that the concept of God is incoherent. As long as he has not made that demonstration, coherence works in favour of theism, and the modal argument delivers its conclusion.

Plantinga (1974): maximal excellence and maximal greatness

It is Alvin Plantinga (1932-) who gives the modal argument its most discussed form today. In The Nature of Necessity (Oxford University Press, 1974), chapter 10, and then in the popularised version God, Freedom, and Evil (Eerdmans, 1974), he introduces two crucial technical notions.

"Let us say that a being has maximal excellence in a possible world W if and only if, in W, it is omniscient, omnipotent and morally perfect. Let us say that a being has maximal greatness if it has maximal excellence in every possible world." — Alvin Plantinga, The Nature of Necessity, Oxford University Press, 1974^[35]

The Plantingian argument then takes the following form:

1. It is possible that a maximally great being exists.
2. If a maximally great being exists in a possible world, it exists in all possible worlds (by the definition of maximal greatness).
3. If something exists in all possible worlds, then it exists necessarily.
4. Therefore, if such a being is possible, it exists necessarily.
5. Therefore it exists in the actual world.

Step (2) to (3) rests on the modal system S5, which formalises the following intuitive idea: what is necessarily true is so necessarily, that is, in all possible worlds. If something is possibly necessary, there exists at least one world where that thing is necessarily true; and since necessity extends to all worlds, it extends to ours too. This step is mathematically valid in S5 — there is no trick.

Matthieu Lavagna, in Soyez rationnel, devenez catholique ! (Cerf, 2024), points out that it is precisely this kind of Anglo-Saxon analytic rigour that enabled philosophical theism to be reborn in the twentieth century, emerging from the vagueness of "continental philosophy" and imposing modal precision^[36].

Plantinga, cautious: a rationally defensible argument

Plantinga himself does not claim that his argument proves the existence of God in a way that is compelling for every opponent. He presents it as a rationally defensible argument, showing that belief in God is not absurd — but without claiming to force the atheist into conversion.

"Perhaps one cannot say that they prove or establish their conclusion. But since it is rational to accept their central premise, they show that it is rational to accept that conclusion." — Alvin Plantinga, The Nature of Necessity, p. 221^[37]

This modesty is essential for properly situating the argument. Plantinga acknowledges that the possibility premise — "it is possible that a maximally great being exists" — is precisely what the informed atheist will be able to refuse. But he argues that one can, by other routes (cosmological arguments, fine-tuning, religious experience), give this possibility sufficient plausibility to set the argument going. This is why the argument works best within a cumulative case, as we shall see.

Gödel: the most formal version (1970, published 1995)

Kurt Gödel (1906-1978), one of the greatest logicians of the twentieth century, left behind at his death a manuscript formalising an axiomatic version of the ontological argument. The text, transcribed by Dana Scott on 18 February 1970, was published posthumously in the Collected Works (Oxford University Press, 1995)^[38].

The Gödelian version rests on the notion of a positive property. It can be summed up in five axioms and two definitions:

From these axioms, Gödel formally demonstrates that the necessary existence of a divine being is a theorem of higher-order modal logic. The proof was formally verified in 2013 by Christoph Benzmüller and Bruno Woltzenlogel-Paleo using the automated theorem provers Coq and Isabelle/HOL^[39].

"Gödel's ontological argument has been fully computer-verified: the logical derivation is valid. The philosophical question therefore shifts entirely to the truth of the axioms." — Christoph Benzmüller & Bruno Woltzenlogel-Paleo, arXiv:1308.4526, August 2013^[40]

Formal verification does not, however, say that the axioms are true — only that if one accepts the five axioms, then the conclusion follows necessarily. The entire philosophical debate centres on the relevance of the axioms, particularly A3 (the existence of a "divine" property) and A5 (necessary existence as a positive property).

The modal version did not put an end to the debate. Three main objections are discussed today by analytic philosophers. They are, in turn, the most rigorous ones ever raised against the argument. They must be presented in their strongest form before replying to them.

The symmetry problem: the Reverse Modal Ontological Argument

The most powerful objection against the Plantingan version is the symmetry problem. If I can lay down as a premise "it is possible that a maximally great being exists", why could my opponent not symmetrically lay down "it is possible that a maximally great being does not exist"?

In modal logic S5, these two premises cannot both be true. If God, defined as a necessary being, is merely possible of existing, he is necessary. But if his non-existence is possible, he is not necessary — hence impossible. The logic is relentless: one must choose.

Graham Oppy puts the impasse as follows^[41]:

"In the absence of an independent argument in favour of the positive possibility premise rather than the negative premise, the modal ontological argument remains dialectically inert for anyone who does not already believe in God's existence." — Graham Oppy, Ontological Arguments, Stanford Encyclopedia of Philosophy^[42]

The objection is powerful. Without a symmetry breaker, the argument appears to collapse dialectically. This is precisely why Plantinga himself presents his argument as rationally defensible, and not as binding for every interlocutor.

Is the possibility premise grantable?

More radically, some philosophers (Jordan Howard Sobel, J. L. Mackie, Graham Oppy himself) simply refuse the premise "a maximally great being is possible". For them, the very concept of this being has not been shown to be coherent — it has not been demonstrated that its attributes (omniscience, omnipotence, moral perfection, necessity) are mutually compatible.

J. N. Findlay's objection (1948) constitutes the radical version of this criticism. Findlay argued, on the contrary, that a being worthy of worship must be necessary; but that necessity itself is, by the positivist standards of the time, an unintelligible notion. His paradoxical conclusion: God therefore cannot exist^[43]. This objection, ironically, served as the starting point for modal reformulations — Hartshorne and Malcolm refuted it by revaluing the notion of metaphysical necessity. The objection meant to bury the argument gave it new life.

The compatibility of the divine attributes

C. D. Broad (1887-1971) raised an even more precise objection: the traditional divine attributes might be mutually incompatible. How can perfect omniscience be reconciled with the free will of creatures? How can omnipotence be reconciled with the impossibility of doing evil? How can immutability be reconciled with knowledge of temporal events?

These objections have given rise to a vast contemporary literature (Swinburne, Geach, Plantinga, Stump, Helm, Leftow). Most conclude that the divine attributes are compatible given certain classical distinctions: omnipotence extends only to what is metaphysically possible; omniscience is compatible with freedom through Molina's middle knowledge, or through divine eternity as held by Boethius; immutability does not exclude knowledge of temporal events but their knowledge outside time. But these answers go beyond the purely ontological framework: they belong to complete natural theology.

Why the symmetry does not really hold

The deepest answer to the symmetry problem is this: the two premises "God is possible" and "the non-existence of God is possible" are not epistemically symmetric. Asserting the non-existence as possible presupposes that the concept of God has been shown to be incoherent. Yet that demonstration is precisely what no opponent has managed to supply in a thousand years of criticizing the argument.

The Catholic philosopher Alexander Pruss proposes several symmetry-breakers in favour of positive possibility^[44]:

None of these symmetry-breakers is unanswerable on its own. But they are enough to prevent the symmetry from playing in the atheist's favour — who must, for his part, positively demonstrate the incoherence of the concept of God. Pruss and Joshua Rasmussen develop this strategy in Necessary Existence (Oxford University Press, 2018), a work that has become the contemporary reference on the question^[45].

Independent reasons to think God possible

Plantinga himself acknowledges that his argument works best within a cumulative case. If other arguments (cosmological, contingency, order, moral) have already made the existence of a necessary, intelligent, good being plausible, then the premise "it is possible that a maximally great being exists" becomes far more than possible: it becomes probable. And in the modal logic S5, probable tends toward necessary.

This is what is known as a cumulative argument or a convergence argument. The ontological argument taken on its own converts no one. Taken together with the other paths, it plays a decisive role: it shows that the God to which the other paths lead is not a contingent object, but the necessary being in the strong sense. Matthieu Lavagna, following Frédéric Guillaud, adds a complementary argument: if a single necessary being suffices to account for the world, the principle of economy (Occam's razor) suggests that there is only one — and the analysis of the perfections required for this single being precisely overlaps with what the monotheistic religions call God^[46].

Acknowledged limits and the exact place of the argument

The ontological argument thus has a real place, but a precise one. It is not an entry point for a hostile atheist: it already presupposes a mind willing to examine seriously the coherence of the idea of God. It is not a coercive proof: it presupposes that positive possibility is granted. It is not a standalone proof: it works best within a cumulative case.

But within these limits, it plays a unique role. It purifies the intellect. It compels us to think of God not as one more "object" in the universe, but as the being by which every being holds together. It rules out the polytheist conception, and it also rules out the deist conception of a "contingent watchmaker" God. On both these fronts, the argument does irreplaceable metaphysical work.

The Catholic Church has never condemned nor canonised the ontological argument. Several great Catholic doctors (Anselm, Bonaventure, Duns Scotus, Descartes, Leibniz, Hartshorne, Plantinga — Catholic in thought if not in communion) have upheld it in various forms. Several others (Thomas Aquinas, Cajetan, Báñez, Gilson, Sertillanges, Garrigou-Lagrange) have rejected it as insufficient. The majority position is intermediate: the argument is permitted, but not central.

The classical Thomist position

Saint Thomas Aquinas does not deny the intrinsic validity of the Anselmian argument. He denies that it is practicable for us, for want of access to the divine essence in the present condition. It is an epistemological critique, not a metaphysical refutation. The great Thomists of the twentieth century (Maritain, Gilson, Garrigou-Lagrange, Sertillanges) held to this position: the argument is a legitimate metaphysical clarification, but it cannot replace the a posteriori ways that constitute the normal path of human reason toward God.

Étienne Gilson, in his classic 1934 study, concludes that the Anselmian argument is not reducible to a dialectical trick:

"The demonstration is certainly the triumph of a pure dialectic operating on a definition; but its strength comes from a correct intuition of what is unique in the notion of being taken in the absolute sense." — Étienne Gilson, Sens et nature de l'argument de saint Anselme, AHDLMA, 1934^[47]

This formulation is exemplary of the mature Thomist position: the argument is neither an intellectual fraud nor a demonstrative proof. It is a powerful metaphysical intuition concerning the specificity of absolute being.

Vatican I: knowledge of God from creatures

The First Vatican Council (1869–1870), in its dogmatic constitution Dei Filius of 24 April 1870, teaches that God can be known with certainty by the natural light of human reason from created things:

"This same Holy Mother Church holds and teaches that God, the beginning and end of all things, can be known with certainty by the natural light of human reason from the created things." — First Vatican Council, dogmatic constitution Dei Filius, chap. 2, 24 April 1870, DS 3004^[48]

This formulation clearly favours a posteriori arguments — that is, the ways leading from the world. It does not condemn the ontological argument, but it does not make it the normal mode of natural knowledge of God. The Catechism of the Catholic Church (§§ 31–38), promulgated in 1992 by Saint John Paul II through the apostolic constitution Fidei Depositum, takes up this way: it is from the world (movement, becoming, contingency, order, beauty, moral conscience) that human reason can ascend to God^[49].

"The world: starting from the movement and becoming, the contingency, the order and beauty of the world, one can know God as the origin and end of the universe." — Catechism of the Catholic Church, § 32^[50]

The Church therefore favours, in her public teaching, the a posteriori ways. But she leaves to theological freedom the development of the ontological argument as a complementary metaphysical clarification. This is precisely the status that the best contemporary Catholic interpreters recognise in it.

Ignispedia's editorial position

The ontological argument is therefore not the central argument of Catholic apologetics. But it is useful and legitimate for those who know how to use it in its proper place. Its role is threefold:

1. To purify the concept of God: to prevent it from being imagined as a super-creature, an "object" among others in the inventory of the world.
2. To complete the cumulative case: to show that the God to whom the other paths lead is not contingent, but necessary.
3. To prepare negative theology: to suggest that everything one says of God remains analogical and limited — God is not a greater being within the same series as the others; he is of another order.

Mature Catholic apologetics therefore combines several avenues: the classic a posteriori route (the Thomistic Five Ways, contingency, fine-tuning, the moral argument, the argument from conscience); the historical route (the resurrection of Jesus); and the ontological route as a final metaphysical clarification. None of these avenues is sufficient on its own. Together, they form a body of cumulative proofs that Catholic thought recognises as convincing.

Suppose the argument is sound. Its conclusion is not merely "something exists". It is far more precise. It concludes to a being whose every one of the following properties is derived from the very definition.

This list is not free-form apologetics: it follows directly from the reasoning. Necessity is part of the definition. Uniqueness follows from the absence of any possible difference between two maxima (an argument Lavagna states with particular clarity in the line of Swinburne and Guillaud)^[51]. Perfection is the central idea. Transcendence, simplicity, intelligence and goodness are contained in maximal excellence. If the argument succeeds, it delivers a complete philosophical monotheism.

But it does not directly deliver the Trinity, the Incarnation, the Eucharist, or the authority of the Church. The argument belongs to natural theology. To move on to Christianity, further steps are needed: messianic prophecies, public miracles, the resurrection of Jesus, the reliability of the Gospels, apostolic continuity. The ontological argument prepares the conviction that there exists one necessary God; it does not dispense anyone from examining the historical traces through which this God has revealed himself in human history.

The ontological argument is one of the most debated lines of reasoning in the whole of the philosophy of religion. Anselm, Bonaventure, Duns Scotus, Descartes, Leibniz, Hegel, Malcolm, Hartshorne, Plantinga and Gödel have defended it in various forms; Gaunilo, Thomas Aquinas, Hume, Kant, Frege, Russell, Sobel, Oppy and Mackie have criticised it. Its longevity proves that it reduces neither to a verbal trick nor to an easy demonstrative proof.

Its strength lies in a deep intuition, first formulated by Anselm and rediscovered eight centuries later by modal logicians: God, if he is truly God, is not a being who exists "by luck" and "by misfortune" might have been missing. He is the necessary being, "He who cannot not be". Its weakness lies in the difficulty of getting someone who doubts a priori to accept, from the concept alone, the positive possibility of such a being.

For Catholic apologetics, it is therefore better to present the argument as a piece of high metaphysics, not as a magical formula that would convert all by itself. It complements the arguments from the world, especially contingency and fine-tuning. It does not replace salvation history; it prepares the intellect to understand that God is not merely "greater" than everything, but that he is He who cannot not be.

This is exactly what was said, at the burning bush, by the very name revealed to Moses:

"I am who am. (...) This is what you shall say to the children of Israel: I-Am has sent me to you." — Exodus 3, 14^[52]

Anselm's argument, in its purest formulation, is the philosophical translation of this divine name. It does not demonstrate it for one who refuses to listen; but it illuminates its depth for one who seeks to understand. Perhaps that is all one should ask of a metaphysical argument: not to convince by force, but to open the intellect to what surpasses it.

• Does God exist? — a synthesis of the rational paths to God.
• The argument from contingency — why the contingent world calls for a necessary being.
• The Kalam cosmological argument — the question of the beginning of the universe.
• Cosmological fine-tuning — the mathematical order of the physical constants.
• The moral argument — the objective foundation of the good.
• The argument from consciousness — the inner voice as a trace of God.
• The resurrection of Jesus — the historical path to the Christian God.