Ontological arguments are unique in that they aim to prove God’s existence a priori. In other words, they try to prove God’s existence purely using logic and reason, without any empirical evidence or sense experience.

So, in the same way that you don’t need to do a bunch of experiments of adding 2 things to 2 things and getting 4 things to know that “2+2=4” is true, ontological arguments say we can know “God exists” is true in the same kind of way: Purely by deduction from the idea or definition of God. If these arguments work, this would make “God exists” an analytic truth.

The history of ontological arguments goes back at least as far as St. Anselm of Canterbury in the 11th Century. But in the 18th Century, Immanuel Kant raised a key objection to ontological arguments, that ‘existence’ is not a predicate. This objection gave rise to several ontological arguments in the 20th Century that attempt to avoid Kant’s criticism.

This post looks at a few different versions of the ontological argument and contrasts them against various issues and objections. If you’re looking for a specific argument or objection you can jump straight to it using the links below:

Anselm’s ontological argument

“And indeed, we believe that thou art a being than which nothing greater can be conceived. Or is there no such nature, since the fool hath said in his heart, there is no God? (Psalms 14:1). But, at any rate, this very fool, when he hears of this being of which I speak – a being than which nothing greater can be conceived – understands what he hears, and what he understands is in his understanding; although he does not understand it to exist.
For, it is one thing for an object to be in the understanding, and another to understand that the object exists. When a painter first conceives of what he will afterwards perform, he has it in his understanding, but he does not yet understand it to be, because he has not yet performed it. But after he has made the painting, he both has it in his understanding, and he understands that it exists, because he has made it.
Hence, even the fool is convinced that something exists in the understanding, at least, than which nothing greater can be conceived. For, when he hears of this, he understands it. And whatever is understood, exists in the understanding. And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. For, suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater.
Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.”

– Anselm, Proslogion

The first ontological argument came from St. Anselm of Canterbury, writing in 1078 AD. He defined God as “a being than which nothing greater can be conceived.”

And from this definition of God, he argued that such a being must exist:

  1. God is a being than which nothing greater can be conceived
  2. It is greater to exist in reality than to exist only in the mind
  3. Therefore, God must exist

The reasoning here is that if God only existed in the mind (as an idea), then we could conceive of a greater being – one that exists not just in the mind, but in reality as well. But that would contradict the definition of God as the greatest conceivable being. So, if we accept Anselm’s definition of God, we’re logically committed to saying that such a being exists in reality (because otherwise it wouldn’t be the greatest conceivable).

A similar example to illustrate the point: What’s more powerful?

  • an imaginary dragon
  • or a real dragon?

Clearly, the real dragon. So, if God is supposed to be the most powerful (omnipotent) or greatest being imaginable, then He has to be real. Otherwise, we’re imagining “the greatest conceivable being that isn’t the greatest conceivable being,” which is self-contradictory.

Further detail: If Anselm’s (or any ontological) argument works, then the conclusion that “God exists” would be what philosophers call an analytic truth – something that’s true by definition, like “all triangles have 3 sides” or “all bachelors are unmarried”. If the concept of God is the concept of a being than which nothing greater can be conceived, then existence has to be included in that concept (in the same way that 3-sidedness has to be included in the concept of triangle).

Problem: Gaunilo’s island

Gaunilo of Marmoutiers – a monk and contemporary of Anselm – argued that if Anselm’s argument works, then you could just define a perfect island as “the greatest conceivable island” and prove that this perfect island must also exist:

“For example: it is said that somewhere in the ocean is an island, which, because of the difficulty, or rather the impossibility, of discovering what does not exist, is called the lost island. And they say that this island has an inestimable wealth of all manner of riches and delicacies in greater abundance than is told of the Islands of the Blest; and that having no owner or inhabitant, it is more excellent than all other countries, which are inhabited by mankind, in the abundance with which it is stored.
Now if some one should tell me that there is such an island, I should easily understand his words, in which there is no difficulty. But suppose that he went on to say, as if by a logical inference: “You can no longer doubt that this island which is more excellent than all lands exists somewhere, since you have no doubt that it is in your understanding. And since it is more excellent not to be in the understanding alone, but to exist both in the understanding and in reality, for this reason it must exist. For if it does not exist, any land which really exists will be more excellent than it; and so the island already understood by you to be more excellent will not be more excellent…
…If a man should try to prove to me by such reasoning that this island truly exists, and that its existence should no longer be doubted, either I should believe that he was jesting, or I know not which I ought to regard as the greater fool: myself, supposing that I should allow this proof; or him, if he should suppose that he had established with any certainty the existence of this island. For he ought to show first that the hypothetical excellence of this island exists as a real and indubitable fact, and in no wise as any unreal object, or one whose existence is uncertain, in my understanding.”

– Gaunilo, In Behalf of the Fool

Gaunilo’s point was that if Anselm’s logic worked, then you could use the same reasoning to prove the existence of anything, including this perfect island:

  1. The perfect island is the greatest conceivable island
  2. It’s greater to exist in reality than only in the mind
  3. Therefore, the perfect island must exist

This argument has exactly the same structure as Anselm’s ontological argument for God’s existence, but the conclusion is obviously false. You can’t prove a perfect island exists just by defining it that way because if this logic worked, you could apply it to anything: the perfect dog, the perfect sandwich, the perfect tennis ball. Just define something as “the greatest possible X” and it suddenly has to exist.

Gaunilo’s objection is a classic example of a reductio ad absurdum – a type of argument that shows an argument must be flawed because it leads to absurd or obviously false conclusions.

Potential response:

Modal ontological arguments (e.g. Gödel’s and Plantinga’s versions) potentially avoid Gaunilo’s perfect island objection because existence across all possible worlds – i.e. necessary existence – is arguably not the kind of property that makes something like an island greater or better.

Unlike God, an island is a contingent, physical, thing tied to a particular physical world. The perfect island would be defined by features like beauty, size, or resources – not necessary existence. For the perfect island to have necessary existence and so exist across all possible worlds, it would have to exist in possible worlds where water and land don’t even exist, so the idea doesn’t really make sense.

But even if we did say that ‘existing in all possible worlds’ does make an island greater, this potentially raises another problem: Why stop there? Why not say the island also becomes greater by being omnipotent, or omniscient, or morally perfect? If we keep adding such properties, we don’t end up with a better island – we end up back at God. In other words, once you start stacking on these abstract, maximal properties to make the island ‘greater,’ you’re no longer talking about an island at all. You’re just repackaging the concept of a maximally great being (i.e. God) in island form, which defeats the purpose of the objection.

Descartes’ ontological argument

A few centuries after Anselm, René Descartes offered his own version of the ontological argument in his Meditations on First Philosophy – specifically, the 5th Meditation:

“It is certain that I no less find the idea of God in me, that is to say, the idea of a supremely perfect being…
…when I think about [God’s nature and existence] more attentively, it becomes manifest that existence can no more be separated from the essence of God than the fact that the sum of its three angles is equal to two right-angles can be separated from the essence of a triangle or than the idea of a mountain can be separated from the idea of a valley; so that there is no less contradiction in conceiving a God, that is to say, a supremely perfect being, who lacks existence, that is to say, who lacks some particular perfection, than in conceiving a mountain without a valley…
… For I am not free to conceive a God without existence, that is to say, a supremely perfect being devoid of a supreme perfection, as I am free to imagine a horse with or without wings.”

– Descartes, Meditations on First Philosophy

At its core, this is basically the same argument as Anselm’s, just with slightly different wording. Where Anselm talks about “the greatest conceivable being,” Descartes talks about “a supremely perfect being.” And instead of saying “it’s greater to exist in reality than in the mind,” Descartes says “existence is a perfection.” But the underlying logic is essentially the same: a God who doesn’t exist wouldn’t be as great – or as perfect – as a God who does:

  1. I have the idea of God
  2. The idea of God is the idea of a supremely perfect being
  3. A supremely perfect being does not lack any perfection
  4. Existence is a perfection
  5. Therefore, God exists

Descartes also adds a bit more philosophical depth to the argument by comparing God’s existence to the essential properties of geometric shapes. Just as the concept of a triangle includes interior angles that add up to 180 degrees, the concept of God, he argues, includes existence. In other words, saying “God does not exist” would be impossible – like a triangle with interior angles that aren’t 180 degrees. God not existing might seem like a coherent idea at first glance, but on closer inspection, Descartes thinks it’s logically incoherent.

Problem: Existence is not a predicate

Probably the most significant issue for ontological argument is Immanuel Kant‘s objection that ‘existence’ is not a predicate:

“‘Being’ is obviously not a real predicate; that is, it is not a concept of something which could be added to the concept of a thing. It is merely the positing of a thing… The proposition ‘God is omnipotent’, contains two concepts, each of which has its object – God and omnipotence. The small word ‘is’ adds no new predicate, but only serves to posit the predicate in its relation to the subject. If, now, we take the subject (God) with all its predicates (among which is omnipotence), and say ‘God is’ or ‘There is a God’, we attach no new predicate to the concept of God, but only posit the subject in itself with all its predicates, and indeed posit it as being an object that stands in relation to my concept… Otherwise stated, the real contains no more than the merely possible. A hundred real thalers do not contain the least coin more than a hundred possible thalers…
…By whatever and by however many predicates we may think a thing – even if we completely determine it – we do not make the least addition to the thing when we further declare that this thing is. Otherwise, it would not be exactly the same thing that exists, but something more than we had thought in the concept; and we could not, therefore, say that the exact object of my concept exists.”

– Kant, Critique of Pure Reason

In grammar, a predicate is the part of a sentence that tells us something about the subject – like a property or quality. For example:

  • “The frog is yellow”
    • yellow is the predicate, describing the frog (subject)
  • “Mount Everest is 8,849m tall”
    • 8,849m tall is the predicate, telling us something about the mountain (subject)

Kant’s point is that actual properties – like being yellow or being tall – add something to our understanding of the idea or concept they describe. If a frog is yellow rather than red, that changes how we picture it – it changes the idea. If a mountain is 1,000m tall instead of 8,849m, that makes a real difference to the concept.

But existence, Kant argues, isn’t like that. Adding ‘existence’ to a concept doesn’t add anything to that concept or change it. For example:

  • imagine a dog,
  • now imagine that same dog, but existing.

You just imagine the same idea twice. But, if you imagine the dog with stripes or wings then the idea changes – because those are real predicates.

kant existence is not a predicate
The idea of a dog (left) and the idea of a dog that exists (right)

Kant illustrates this with a practical example: coins. He uses thalers – an old form of currency – and says that 100 real thalers don’t contain a single coin more than 100 possible thalers. Both concepts are the same: You can’t pay for your shopping with the idea of 100 coins that exist any more than you can pay for your shopping with the idea of 100 imaginary coins because they’re both just ideas or concepts. The idea of something that exists is still ultimately an idea.

So, going back to ontological arguments, Kant says you can’t define a concept into real-world existence by building existence into that concept:

  • Applied to Descartes’ version, Kant would reject the premise that “existence is a perfection” – it’s not a property that makes something better (unlike e.g. power or knowledge)
  • And applied to Anselm’s version, Kant would reject the idea that existence makes a being greater – existence isn’t a greatness or a quality you can compare.

Potential response:

Instead of saying God has the property of ‘existence’, modal ontological arguments (see below e.g. Malcolm’s and Plantinga’s versions) talk about God having the property of necessary existence – which is, arguably, a real predicate.

Malcolm’s ontological argument

Kant’s objection that existence is not a predicate was widely considered to be a devastating problem for traditional ontological arguments like Anselm’s.

But in the 20th century, philosophers tried to revive ontological arguments in ways that avoid Kant’s objection. For example, in 1960, Norman Malcolm argued that the traditional ontological argument had been misunderstood – including by Kant. He said that Anselm’s real point (especially in Proslogion chapter 3) wasn’t that God has the property of existence, but that God has the property of necessary existence.

Contingent existence Necessary existence
Exists but might not have existed Must exist, impossible not to exist
E.g. this website exists but if I didn’t decide to make it then it wouldn’t exist E.g. God is said to exist necessarily, His existence is not caused by or dependent on anything else

If something exists contingently, then its non-existence is logically possible. You, for example, exist contingently – your existence depends on all kinds of things, like your parents meeting. But if something exists necessarily, then it must exist – it’s not possible for it not to exist.

Malcolm’s idea was that if God exists, He must exist necessarily. And, unlike ordinary existence, Malcolm argued that necessary existence is a meaningful predicate – it does add something to our concept of a thing. And so, he argued, this argument avoids Kant’s objection:

“Previously I rejected existence as a perfection. Anselm is maintaining in the remarks last quoted, not that existence is a perfection, but that the logical impossibility of nonexistence is a perfection. In other words, necessary existence is a perfection. His first ontological proof uses the principle that a thing is greater if it exists than if it does not exist. His second proof employs the different principle that a thing is greater if it necessarily exists than if it does not necessarily exist.”

– Norman Malcolm, Anselm’s Ontological Arguments

So, based on this idea of necessary existence, Malcolm’s argument can be summarised as:

  1. God is a being greater than which cannot be conceived
  2. Either God (as defined) exists or God does not exist
  3. If God does exist, His existence is necessary (because if God didn’t exist necessarily, we could conceive of a greater being, the one that does exist necessarily)
  4. If God does not exist, His existence is impossible (because if God doesn’t exist now but springs into existence tomorrow, then we could conceive of a greater being: The one that always existed)
  5. So God’s existence is either impossible or necessary (because 2+3+4)
  6. God’s existence is only impossible if the concept of God is self-contradictory
  7. The concept of God is not self-contradictory
  8. So God’s existence is not impossible (because 6+7)
  9. So God’s existence is necessary (because 5+8)

Potential responses:

One way you could respond to Malcolm’s argument here is to reject premise 7 and argue that God’s existence is self-contradictory in some way and so God’s existence is impossible (see e.g. the paradox of the stone).

Another potential response is to argue that Malcolm commits what’s known as the modal scope fallacy. If we say Malcolm’s argument essentially boils down to:

  • God’s existence is either impossible or necessary
  • God’s existence is not impossible
  • Therefore, God exists necessarily.

Then the meaning of ‘necessary’ switches between premises and conclusion. Initially, Malcolm talks about necessary existence in the sense of a property that something might have – if it exists. But in his conclusion, he shifts from saying that God would have this property to claiming that it’s a necessary truth that God exists. But this is a different claim.

We might agree that if God exists, then God would exist necessarily – He would have the property of necessary existence. But this doesn’t mean the same thing as saying that God does actually exist necessarily – that “God exists” is a necessary truth.

Gödel’s ontological argument

Another modern (post-Kant) ontological argument comes from the 20th-century mathematician and logician Kurt Gödel. Like Malcolm, Gödel’s goal was to show that God must exist necessarily, not just contingently. And Gödel thought this could be proven logically, with the right definitions and axioms.

Gödel’s version is quite technical, involving symbolic logic, but the basic idea can be summarised in plain language like this:

  1. God is defined as a maximally great being – one that possesses all positive properties (such as omniscience, omnipotence, moral perfection, etc.)
    • (Gödel doesn’t define ‘positive property’ precisely, but treats it as intuitively meaningful. A property is positive if it is good, desirable, or contributes to greatness)
  2. Necessary existence is one of these positive properties
  3. If it is possible that a maximally great being exists, then such a being exists in some possible world
  4. If a maximally great being exists in some possible world, it must exist in all possible worlds (because a maximally great being would exist necessarily, not contingently)
  5. Therefore, if it’s possible that God exists, then God exists necessarily
  6. It is possible that God exists
  7. Therefore, God exists necessarily

Gödel’s ontological argument relies on modal logic – which basically means reasoning about possibility and necessity across possible worlds (like parallel universes where things could have been different). For example, there’s a possible world where you don’t exist, or where Leeds is the capital of England instead of London.

In short, Gödel’s argument says: if it’s logically possible for a maximally great being to exist, then it must exist in all possible worlds – including our world. And so, God exists.

Plantinga’s ontological argument

“A similar but simpler version of the argument could go as follows. Let us say that unsurpassable greatness is equivalent to maximal excellence in every possible world. Then
(42) There is a possible world in which unsurpassable greatness is exemplified.
(43) The proposition a thing has unsurpassable greatness if and only if it has maximal excellence in every possible world is necessarily true.
(44) The proposition whatever has maximal excellence is omnipotent, omniscient, and morally perfect is necessarily true.
(45) Possesses unsurpassable greatness is instantiated in every world.
But if so, it is instantiated in this world; hence there actually exists a being who is omnipotent, omniscient, and morally perfect and who exists and has these properties in every world [i.e. God exists in this world and every possible world].”

– Alvin Plantinga, The Nature of Necessity

Alvin Plantinga defines God as a “maximally great being” – meaning specifically a being that is:

  • omnipotent
  • omniscient
  • omnibenevolent
  • and exists necessarily in every possible world.

This is maybe a bit more precise than e.g. Anselm’s and Malcolm’s definition of “a being than which nothing greater can be conceived”.

Like Godel’s argument, Plantinga’s version is based on modal logic – again, reasoning about possibility and necessity across different possible worlds (like parallel universes where things could have been different).

And so, with that definition in mind – a maximally great being that exists in all possible worlds – Plantinga’s ontological argument can be summarised like this:

  1. It’s possible that a maximally great being exists.
  2. If a maximally great being exists in any possible world, then it exists in every possible world (because otherwise it wouldn’t be maximally great).
  3. Therefore, a maximally great being exists in every possible world.
  4. Therefore, a maximally great being exists in our actual world.
  5. Therefore, God exists.

To many, Plantinga’s version is considered the strongest ontological argument. The logic is valid – if the premises are true, the conclusion must also be true. And so, if we accept the possibility of such a being, modal logic dictates that such a being does actually exist.

Problem: The impossibility of a necessary being

However, the possibility of a necessary being is something David Hume challenges:

“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… It is pretended that [God] is a necessarily existent Being; and this necessity of his existence is attempted to be explained by asserting, that, if we knew his whole essence or nature, we should perceive it to be as impossible for him not to exist as for twice two not to be four. But it is evident, that this can never happen, while our faculties remain the same as at present. It will still be possible for us, at any time, to conceive the non-existence of what we formerly conceived to exist… The words, therefore, necessary existence, have no meaning; or, which is the same thing, none that is consistent.”

– Hume, Dialogues Concerning Natural Religion

Because ontological arguments work by proving God’s existence from the definition of God, then “God exists” would be an analytic truth – like “all bachelors are unmarried” – if these arguments succeed. In other words, if ontological arguments work, “God does not exist” would be a contradictory idea, like a “married bachelor” or “4-sided triangle”.

But Hume argues that contradictions are inconceivable. You can’t even bring the idea of a 4-sided triangle to mind, for example, because the contradictory and impossible nature of a 4-sided triangle makes the very idea inconceivable to the mind.

However, says Hume, the idea of God not existing doesn’t seem to work the same way: We can imagine God not existing. God’s non-existence seems just as logically coherent as God’s existence – we can conceive of either without contradiction, so both appear logically possible.

So, to summarise Hume’s objection here:

  1. If ontological arguments work, then God’s non-existence would be contradictory and thus inconceivable
  2. But God’s non-existence is conceivable – anything we can conceive of as existing, we can also conceive as not existing
  3. So ontological arguments can’t prove God’s existence.

In short, Hume says the conceivability of God’s non-existence shows that it’s impossible for “God exists” to be a necessary/analytic truth.

Potential response:

Descartes, in his ontological argument above, argued that “God does not exist” is inconceivable:

“when I think about it more attentively, it becomes manifest that existence can no more be separated from the essence of God than the fact that the sum of its three angles is equal to two right-angles can be separated from the essence of a triangle.”

– Descartes, Meditations on First Philosophy

So, in the same way that it might initially seem conceivable that the angles of a triangle could be something other than 180 degrees, closer inspection – a proper understanding – reveals that such an idea is, in fact, inconceivable. And similarly, Descartes would probably say that closer inspection and a proper understanding of the concept of God would reveal God’s non-existence is equally inconceivable as a triangle whose interior angles don’t add up to 180 degrees.

References/further reading:

See also: