QuestionsDoes God exist?That than which nothing greater can be conceived exists
Does God exist?TheismOntological

That than which nothing greater can be conceived exists

The ontological argument (Anselm)

Anselme de Cantorbéry c. 1033 · c. 1109God is 'that than which nothing greater can be conceived': so he cannot exist in thought alone.
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What it claims

That than which nothing greater can be conceived exists, in the mind and also in reality: God exists.

Why

A being than which nothing greater can be conceived, if it existed only in the mind, could be thought greater by also existing.

The same idea through history
Anselme de Cantorbéry1078Proslogion II: the original version, presented here. Chapter III adds that God cannot even be thought not to exist. The name "ontological argument" comes from Kant (1781), not from Anselm.
René Descartes1641Meditation V: existence belongs to the idea of a perfect being as the valley belongs to the idea of a mountain. Descartes no longer starts from "that than which nothing greater can be conceived" but from the clear idea of a perfect being.
Gottfried Wilhelm Leibniz1714Monadology § 45: the proof works, but on a condition that must first be shown, namely that God is possible (his idea contains no contradiction).
Georg Wilhelm Friedrich Hegel1830After Kant, Hegel still defends the proof: God is not a finite thing like a hundred thalers, his concept includes being.
Kurt Gödel1970Notes from 1970, published in 1987: a version in modal logic, in which God has all "positive" properties.
Alvin Plantinga1974The Nature of Necessity: if it is possible that a maximally great being exists, then it exists. The debate moves to "it is possible".
In short

"That than which nothing greater can be conceived exists" is an argument by Anselme de Cantorbéry (Proslogion, chapters II and III (1077-1078), 1078) on the question "Does God exist?" (answer: theism). Its claim: That than which nothing greater can be conceived exists, in the mind and also in reality: God exists. According to AskPhilosophy's logic check (Z3 solver), the argument is valid only if one grants a premise the author leaves unstated (P4). AskPhilosophy presents 5 objections, 4 of them with a documented reply, and the original text behind each premise, checked word for word.

Proslogion, chapters II and III (1077-1078)
Valid with an implicit premise

Around 1077 Anselm, a monk at the abbey of Bec in Normandy, looks for "a single argument" that would be enough to prove that God exists. He finds it in the mere definition of God: "something than which nothing greater can be conceived". Even someone who says "there is no God" (the "fool" of the Psalm) understands these words. Yet if this being existed only in thought, one could conceive a greater one: the same being, but real. That is a contradiction. So it exists in reality as well. No observation of the world is needed: everything happens in thought. Kant would later call this reasoning the "ontological" proof.

P1God is "something than which nothing greater can be conceived". Even someone who denies that God exists understands what these words mean.
P2What is understood exists at least in the mind. So this being exists at least in the mind, even for the one who denies it.
P3If this being existed only in the mind, it could be conceived as existing in reality as well, which is greater. So something greater than it could be conceived.
P4 · implicit premiseThe idea of "a being than which nothing greater can be conceived" is coherent: such a being is possible, it is not a contradictory idea like "the greatest of all numbers". Only on that condition is "conceiving something greater than it" ruled out.
Therefore that than which nothing greater can be conceived exists, in the mind and also in reality: God exists.

click a premise to reject it

If you accept every premise, logic forces you to accept the conclusion. So the debate is about the premises.
Checked by a logic solver: the premises cannot all be true while the conclusion is false.
Without the implicit premise: Without P4, the computer finds a world where the idea of the greatest conceivable being is incoherent: nothing then prevents one from always conceiving something greater, and this being remains only in the mind, without contradiction. It is like "the greatest whole number": we understand the words, but we can always add 1.
It is a reductio ad absurdum: we suppose that God exists only in the mind, and reach a contradiction (something greater could be conceived than that than which nothing greater can be conceived). It is valid once P4 is added. Anselm does not state it: he assumes that his definition makes sense. The debate is mainly about P2 (do we really understand these words?), P3 (does existing in reality make something "greater"?) and P4 (is such a being even possible?).
Analogy. A painter has a picture in mind before painting it: the picture then exists in his mind, not yet on the canvas (this is Anselm's own example). Now imagine being told about "the most beautiful picture that can be conceived". If it stayed in someone's head, the same picture hanging on the wall would be more beautiful. For a picture this proves nothing. Anselm replies that God is the only case where the reasoning works, because he is the only being defined as "the greatest conceivable" in every respect.

Objections

5

Each objection is a conversation: click to see who replies and where the debate stands.

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Gaunilo, monk of Marmoutier 1078 · attacks premise 2

I do not have this being in my mind the way I have the things I know. I do not know the reality that God is, and I cannot form an idea of it from something similar, since nothing is like it. All I have in mind are words, as with a false or invented thing.

Cantorbéry replies
A
Anselm 1079 · Anselm's reply to Gaunilo
That is false. Every lesser good resembles the greater good, insofar as it is good. By rising from lesser goods to greater ones (what begins and ends, what does not end, what never changes), we can form an idea of that than which nothing greater can be conceived. Not understanding it completely does not prevent understanding it: someone who cannot look straight at the sun still sees daylight.
The debate goes on (our summary) Gaunilo did not reply, at least in no known text. But the question returns with Thomas Aquinas: understanding the words "the greatest being" does not mean knowing what God is (see below).
Where the debate stands (our summary)Anselm replies that we form an idea of the greatest being by rising from lesser goods to greater ones. Gaunilo left no known reply. The basic disagreement remains: is understanding the words of a definition enough to have in mind the being it designates?
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Gaunilo (the lost island) 1078 · attacks premise 3

They say that somewhere in the ocean there is an island, richer than all inhabited lands, called "the lost island" because it cannot be found. I understand these words. If someone concluded that it must exist, since a real island is greater than one that is only thought of, I would take it as a joke. The same reasoning would prove anything perfect: so it is worthless.

Cantorbéry replies
A
Anselm 1079 · Anselm's reply to Gaunilo
If anyone finds a single thing, real or imaginary, other than "that than which nothing greater can be conceived", to which my reasoning applies, I will find him his lost island and give it to him so that he never loses it again. The reasoning holds only for the greatest being of all, not for the richest island.
Alvin Plantinga 1974
Plantinga sharpens Anselm's reply: the perfect island is an incoherent idea. What makes an island better (the number of palm trees, the quantity of coconuts) has no maximum: one can always add more. So there cannot be an island than which nothing greater can be conceived. God's perfections, by contrast, do have a maximum: knowing everything, being able to do everything.
See the rest of the debate (1)
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Graham Oppy, Joshua Rasmussen and Joseph Schmid 2024
It is false that more palm trees always make an island better: too many end up spoiling it. An island's greatness is a balance between several qualities, and we do not know in advance that there is no best possible balance. So the perfect island is no more clearly incoherent than the perfect being.
Where the debate stands (our summary)Anselm rejects the parody: the island is not "that than which nothing greater can be conceived". Plantinga adds that the perfection of an island has no maximum; Oppy and his co-authors reply that an island's greatness can also be a balance that has a maximum. The debate on what truly distinguishes God from the parodies remains open.
Thomas Aquinas 1268 · attacks premise 3

Even if everyone understands that the word "God" means "that than which nothing greater can be conceived", it only follows that this being is in the mind, not in reality. To conclude that it is real, one would first have to grant that such a being really exists, which is exactly what the one who denies God refuses. Thomas does not conclude that God does not exist: since we do not know God's essence, he must be proved from his effects, from the world (Thomas's "five ways").

no reply
No reply possible: objection raised in 1268, after the author's death (1109).
The debate goes on (our summary) Anselm's defenders reply that the argument does not assume in advance that God exists: it reasons by reductio, from the opponent's own supposition ("it exists only in the mind"). Thomas maintains that comparing "in the mind" and "in reality" is only possible for someone who knows what God is, which we do not (same article, main answer).
Where the debate stands (our summary)Thomas disputes the move from idea to reality; Anselm's defenders reply that the argument reasons by reductio from the opponent's own supposition. The basic disagreement: can one compare "in the mind" and "in reality" without knowing what God is? There is no widely accepted answer.
Kant 1781 · attacks premise 3

"Existing" is not a quality that is added to a thing and makes it greater. A hundred real thalers contain nothing more than a hundred possible ones. Saying that a real being is "greater" than the same being merely thought of treats existence as one more perfection: that is the mistake of every ontological proof.

a defender replies
No reply possible: objection raised in 1781, after the author's death (1109).
Norman Malcolm defender of the argument · 1960
Malcolm defends the chapter III argument. Kant is right against chapter II: mere existence is not a perfection. But chapter III says something else: God cannot even be thought not to exist. Necessary existence is a real perfection: a being that cannot fail to exist is greater than one that could disappear. This version escapes Kant's objection.
The debate goes on (our summary) The debate then took a modal form (Hartshorne, Plantinga): if a necessary being is merely possible, it exists. The discussion then turns on the premise "it is possible", see the modal ontological argument.
Kant 1781 · Kant's anticipated reply (on the absolutely necessary being)
Kant had already examined the "absolutely necessary being". If I say "God is not", I remove the subject with all its qualities, necessity included: nothing is left that could contradict anything. So existence, even necessary existence, cannot be drawn from a mere concept.
Where the debate stands (our summary)Malcolm grants Kant that simple existence is not a perfection, but maintains that necessary existence is one; Kant had already held that removing the subject removes its necessity too, without contradiction. The debate moved to the modal version, where everything depends on the premise "such a being is possible".
Leibniz (the missing premise) 1714 · attacks premise 4

The proof holds only if God is possible: only the necessary being has the privilege that it must exist if it is possible. So one must first show that its idea is not contradictory. Leibniz said this about Descartes, but it applies to Anselm. He himself thinks he can fill the gap: what has no limits and no negation cannot contain a contradiction.

a defender replies
No reply possible: objection raised in 1714, after the author's death (1109).
Kurt Gödel defender of the argument · 1970
Summary of the structure of his proof: Gödel tries to fill this gap. He posits that "positive" properties are compatible with one another and defines God as the being that has them all. He deduces that God is possible, then, by modal logic, that he necessarily exists.
J
Jordan Howard Sobel 1987
Gödel's axioms entail a "modal collapse": everything that is true becomes necessary. The proof of God's possibility therefore proves too much, and at least one axiom is false. The rest of the debate (Anderson's corrections, the list of positive properties) is treated in the modal argument.
see the argument
The debate goes on (our summary) Critics reply that the absence of a visible contradiction does not prove there is none: knowing everything, being able to do everything and being perfectly good might clash (the paradox of the stone too heavy to lift, for instance). And one can say with equal right that it is possible that this being does not exist. This is still the heart of the debate on the modal version.
Where the debate stands (our summary)All sides acknowledge that the proof requires God to be possible. Gödel tries to show it through the compatibility of positive properties; Sobel's objection targets his axioms. There is no agreement on an independent proof of this possibility, which remains the heart of the debate.
What today's voices say
Criticize it
Alex O'ConnorHe says scholars almost all reject Anselm's ontological argument.
Matt DillahuntyAgainst the idea that understanding the word God proves God, he says having a concept is not the same as the thing being real.
Philip GoffHe says there are no a priori arguments for any kind of god and that the ontological arguments do not work.
In the same family · Ontological
Existence is not a predicateImmanuel Kant
Does God exist?Agnosticism 2
The ontological proofRené Descartes
Does God exist?Theism 3
God is not a hundred thalers: Hegel defends the ontological proof against KantGeorg Wilhelm Friedrich Hegel
Does God exist?Theism 3
If it is possible, it exists: the modal ontological argumentAlvin Plantinga · 1974 · debate over 3 levels
Does God exist?Theism 4