Ontological argument for the existence of God

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An ontological argument sets out to prove the existence of the God of the monotheistic religions from the nature of concepts alone. It is thus an a priori argument. The term "ontological argument" originates with Immanuel Kant (who rejected the argument form), though it can be traced, in various forms, at least back to the work of Anselm of Canterbury.

The argument typically works via a reductio ad absurdum: it presents a certain concept (for example that of a maximally perfect being — a being that has every possible perfection), supposes that such a being does not exist, and then draws out a contradiction, thus proving that such a being exists. That being is then identified with God. In other words, the concept implies its own instantiation; if one grasps the concept of God, then one is committed to the existence of God. (A separate argument is needed to show that there can be only one instantiation of the concept — only one God.)

The best-known uses of the argument are to be found in the context of the Abrahamic religions, its earliest formulation being found in the Proslogion of the eleventh-century philosopher and theologian Anselm. It was rejected and argued against by the thirteenth-century philosopher and theologian Thomas Aquinas, and was for some time neglected, but the early modern period saw its revival. René Descartes presented what became probably the best-known form of the argument, but versions were devised by prominent philosophers such as Gottfried Leibniz and Baruch Spinoza. In the modern period, attempts have been made to devise updated versions of the argument, most notably by Norman Malcolm, Charles Hartshorne, and Alvin Plantinga.

Anselm's version was criticised by Aquinas and by Anselm's contemporary, Gaunilo. Descartes' version was criticised by many of his contemporaries, including Caterus and Pierre Gassendi, and later by such philosophers as Kant, David Hume, and Gottlob Frege.

The differences between the different versions of the argument are generally a matter of the precise nature of the starting concept.


Mediæval versions

Anselm of Canterbury

Anselm of Canterbury (1033–1109) introduced the ontological argument to the Christian world in Chapter II of his Proslogion.[1] The concept with which he starts is that of a being than which no greater can be conceived. He then refers to the "fool" who "hath said in his heart, there is no God" (Psalms xiv 1), and argues that the fool at least understands the concept of a being than which no greater can be conceived. Now he brings out the contradiction, for the fool must understand the being than which no greater can be conceived as existing only in his understanding — but then he could also conceive of that being as existing reality, and that would be a greater being than the one just in his understanding. How could there be a being greater than a being than which no greater can be conceived? Therefore, a being than which no greater can be conceived must exist both in the understanding and in reality.

In Chapter III of Proslogion, Aquinas goes on to argue that God – the being than which no greater can be conceived – necessarily exists (cannot be conceived not to exist), because a being that cannot be conceived not to exist is greater than one which can be conceived not to exist (a contingent being). Thus, he says, God exists "more truly than all other beings, and hence in a less degree".

In Chapter IV, Anselm asks how, if the denial of the existence of God is a contradiction, people do seem to deny it. He explains it by distinguishing between the mere reciting of words and the genuine holding of a concept. One might say (in speech or thought) "God doesn't exist" (just as one might say "a round square exists"), but one cannot conceive it. Although saying words to oneself might be called conceiving in a weak sense, the stronger sense of conceiving involves the understanding of what is conceived: "In the former sense, then, God can be conceived not to exist; but in the latter, not at all."

Gaunilo's criticisms

The first critic of Anselm's argument was Gaunilo, a monk at Marmoutier and Anselm's contemporary; little is known about him apart from his criticism of the ontological argument: In Behalf of the Fool.

Gaunilo offers two sorts of criticism (to which Anselm replied at length). He starts by arguing that Anselm's approach is misguided, and that it attempts illegitimately to move from conception to reality (that, in a more modern wording, Anselm attempts to define God into existence).

Gaunilo then goes on to offer his best-known criticism, which takes the form of what has become known as an "overload objection". That is, rather than trying to uncover a flaw in the logic of the argument, or challenging one of its premises, he offers an argument by analogy, designed to show that, if the ontological argument were sound, then so would be many other arguments of the same logical form, and this would mean that we were committed to overloading the universe with the existence of a potentially infinite number of things, few of which we should want to accept existed.

Gaunilo's analogy uses the notion of a lost island — an island than which no greater can be conceived. He argues that, given that we have the concept of such an island, and given that – on Anselm's assumptions – it is greater to exist in reality than in the understanding alone, then it would be contradictory to say that the lost island doesn't exist.

Anselm's response

Early-modern versions

René Descartes

Descartes' version of the argument is, along with that of Anselm, the best known; the clearest account of it is in his 1641 masterpiece, the Meditationes de Prima Philosophia — the Meditations on First Philosophy, or just Meditations.[2]

Descartes' argument is to be found in Meditations V. He first explains the notion of the essence of a concept, using the example of a triangle.[3] If I have a genuine concept of a triangle (that is, I have the concept of a three-sided plane figure), I can infer many facts about triangles, such as that a triangle's internal angles add up to 180°, that if one of its angles is a right angle, then the square of its hypotenuse is equal to the sum of the squares of its other two sides, and so on. These inferences hold whether or not any triangle exists in the actual world; they hold because to deny any of them would be to contradict myself; for example, something cannot be a three-sided plane figure and not have internal angles that add up to 180°. In other words, the concept of a triangle has an essence, and we can draw inferences about what is essentially true of triangles if we can clearly and distinctly conceive a triangle.

Now, I can clearly and distinctly conceive God as a supremely perfect being — that is, a being that has every perfection. From this concept I can infer various facts about God, just as I could about triangles — facts which hold whether or not God actually exists. I can infer, for example, that God is omniscient, and that he is omnipotent, for it would be to contradict myself if I thought that a being with every perfection lacked a perfection. But existence is a perfection, and I can therefore infer that God has existence.

"Hence it is just as much of a contradiction to think of God (that is, a supremely perfect being) lacking existence (that is, lacking a perfection), as it is to think of a mountain without a valley."[4]

He then considers an objection. Just because I can't think of a mountain without a valley (that is, of an up-slope without a down-slope) doesn't mean that I can infer that any mountain or valley exist; similarly, surely, I can't infer that God exists just from my being unable to think of him as not existing. But that pushes the analogy too far. Of course I can't infer the existence of mountains or valleys from my inability to think of them as being separate — I can only infer their mutual inseparability. In the case of God, what I can infer is, similarly, the mutual inseparability of god and existence — which is precisely to say that God necessarily exists.

"It is not that my thought makes it so, or imposes any necessity on any thing; on the contrary, it is the necessity of the thing itself, namely the existence of God, which determines my thinking in this respect. For I am not free to think of God without existence (that is, a supremely perfect being without a supreme perfection) as I am free to imagine a horse with or without wings."[5]

Descartes goes on to point out that it is normally not possible to argue from concept to existence, because existence and essence are distinct in every case except this one.

Criiticism and defence

Gaunilo's criticisms of Anselm's version can also be raised against Descartes', and many subsequent writers did indeed make very similar points. The main criticisms of Descartes' version fall into four main categories:

  • The claim that his argument begs the question by assuming that God exists.
  • The claim that existence is not a property, so cannot be a perfection.
  • An overload objection that focusses, rather than on perfection as did Gaunilo's, on the relationship between existence and essence.
  • The claim that the argument invalidly moves from one domain of discourse to another.

Baruch Spinoza

Gottfried Leibniz

Modern versions

Norman Malcolm

Charles Hartshorne

Alvin Plantinga

The American philosopher Alvin Plantinga (b. 15 November 1932) presents a version of the ontological argument[6] that brings out its modal nature by drawing on the notion of possible worlds, so we need to start by saying something about them.

Possible worlds

In order to be able to make sense of a lot of involved modal discourse, philosophers have found it useful to appeal to the concept of an infinity of possible worlds, each representing a way that the world might have been or might yet be. These are not the worlds of science fiction or of quantum physics, most importantly because it is by definition not possible to travel between them. They are spatiotemporally and causally isolated from each other. When I have to make a choice between two possibilities, A and B, we can describe the possibilities in terms of two worlds, in one of which I choose A, in the other B. But it is not that my choosing A in this world causes me to choose B in the other — the choice consists in the existence of those two possibilities.

What exactly are possible worlds? There are many answers, ranging from the modal realist position that they’re worlds just like ours, existing just like ours, with no ontological difference between then, to the modal fictionalist claim that they’re merely heuristically useful fictions. Plantinga thinks of them as maximal consistent sets of states of affairs or propositions — abstract objects with no spatial or material parts.

The most important use of possible worlds, at least for our purposes, is that they allow us to talk relatively simply and clearly about difficult and involved modal matters. We can start by saying that the statement: "p is possible" can be restated as: "there is a possible world in which p is true", that the statement: "p is logically necessary" can be restated as: "p is true in all possible worlds", and that the statement: "p is logically impossible" can be restated as: "there is no possible world in which p is true".

Plantinga's main argument

We start by making a distinction between what Plantinga calls "maximal greatness" and "maximal excellence". Maximal excellence is the complex property of having all perfections (such omnipotence, omniscience, etc.), while maximal greatness is the property of having the property of maximal excellence at all possible worlds. Another way of putting this is to say that there is the property of being perfect, and the property of being necessarily perfect, but we shall stick with Plantinga's terminology for now.

It is not enough, says Plantinga, to start with the premise that it is possible (conceivable) that there is a maximally excellent being, as writers like Descartes did, because that leaves the argument open to serious criticism. The premise is too weak, and thus cannot get us to the very strong conclusion that there is a god. We need, rather, to start with the premise:

P1: It is possible (conceivable) that there is a maximally great being.

In possible-worlds terms that is:

P2: There is at least one possible world at which there is a maximally great being.

But "maximally great" means "maximally excellent at all possible worlds" — so P2 implies:

P3: There is at least one possible world at which there exists a being that is maximally excellent at all possible worlds.

But all worlds are accessible to all other worlds. That is, if it is true at one world that p is logically necessary, then it is true at all world that p is logically necessary. Or, to put it another way: "Possibly necessarily p" implies (or just means): "Necessarily p". Therefore:

C1: There is a being that is maximally excellent at all possible worlds.

As our world is a possible world, we can conclude that god exists.


There are various places at which Plantinga's argument can be and has been (most notably by J.L. Mackie) criticised. First, we might complain that the principle that "possibly necessarily" just means "necessarily" is by no means universally accepted. It is certainly accepted by most modal logicians for the purposes of talk about logical necessity and possibility, but there are modal logics that might be preferable for talk about, for example, epistemic necessity and possibility, and which deny the principle in question.

Plantinga himself points to what has been taken to be one of the most important objections. He asks first whether his premise is just question begging; that is, whether one would only accept that it was possible that there be a maximally great being if one already believed that there actually was. He denies this, arguing that belief in the mere possibility of such a being is surely innocent of such commitments. He then looks at the possible objection that we form a similar argument by introducing the property of maximal near-greatness. That is, we could start with the premise that it is possible that there exist a being that doesn’t exist at all worlds, but which is the most excellent being at all the worlds at which it does exist. This rules out the existence of a maximally great being. Plantinga concedes that such an argument would be as sound as his own, and that therefore his is not a knock-down ontological argument in the way that Descartes' and Anselm's tried to be, but that it's at least a rational argument, because it is perfectly rational to accept the premise at issue. This is not good enough, however. If there are two contradictory premises, and either is possible, then what grounds do we have for accepting one or the other? We seem to be back at the accusation of begging the question.


  1. All quotations taken from the Deane translation, as reprinted in Plantinga [1965].
  2. All citations will be given using the standard Adam & Tannery reference, followed by a reference to the Cottingham translation in Volume II of the Cottingham, Stoothoff, and Murdoch English edition; e.g., "AT VII 65, CSM II 45".
  3. AT VII 64–65, CSM II 44–45
  4. AT VII 66, CSM II 46
  5. AT VII 67, CSM II 46
  6. Plantinga [1982]