The Ontological Argument for God

Classic Version of the Ontological Argument

The Ontological Argument for God was first advanced by Saint Anselm, who was the Archbishop of Canterbury from 1033 to 1109. in the Proslogium:

[Even a] fool, when he hears of … a being than which nothing greater can be conceived … understands what he hears, and what he understands is in his understanding.… And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. 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.

In standard logical form, this can be written as:

1. God is defined as a being of which none greater can be imagined (that is, the greatest possible being that can be imagined).
2. God exists as an idea in the mind.
3. A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.
4. Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).
5. But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)
6. Therefore, God exists

It didn’t take long for Anselm’s argument to attract criticism. Gaunilo of Marmoutier raised the objection that one could use Anselm’s argument to show the existence of all kinds of non-existent things. Gaunilo substituted “island” for “being” as an example:

Now if some one should tell me that there is … an island [than which none greater can be conceived], 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 understood by you to be more excellent will not be more excellent.”

Gaunilo had the right idea, but chose a poor example, as one can argue that it is impossible to conceive of a perfect island, since the opinions about perfection of an island are subjective (as in the ideal temperature) and even within any one person’s vision of the perfect island, one could propose additional (qualitative or quantitative) features, that might make it even better. Conversely, the Christian God is purported to be all-powerful, all-knowing, all-wise, perfectly just, etc. Some of these traits, such as omnscience, cannot, by definition, be improved upon. It is impossible to conceive of a being knowing more than everything. Other traits, such as “perfectly just” might be arguable on the basis that, like the perfect temperature on an island, it is subjective, because people often disagree on matters of justice. But the simple response to that argument is that human opinions on justice should not be confused with some absolute standard of justice. I think this is a valid position for the purposes of the Ontological Argument, though it has issues in other apologetics arguments, which utilize the circular argument that God’s justice is perfect because he’s God.

So given that Gaunilo’s analogy failed because of the subjective nature of the perfect island, we can easily substitute some other object, which is not subjectively defined. We could postulate a “perfect 1 meter gold sphere”. This hypothetical object would be 100% solid gold, with no impurities, would be EXACTLY 1 meter in diameter, and would be perfectly spherical (to a resolution down to the atomic level). Per Anselm’s logic, the “perfect 1 meter gold sphere” MUST exist in reality, since an imaginary “perfect 1 meter gold sphere” would be inferior to a real one, and hence would be imperfect. And of course, the 1 meter size was an arbitrary choice. We could just as easily postulate a 1 billion km diameter perfect gold sphere. Neither perfect gold spheres nor gods can simply be imagined into existence.

Immanuel Kant (1724-1804) explained the specific logical flaws in both Anselm’s and Descartes’ arguments. Kant attacks Anselm’s premise 3’s claim (that a being that exists as an idea in the mind and in reality is greater than a being that exists only as an idea in the mind). In The Critique of Pure Reason, Kant rejects premise 3 on the ground that existence does not function as a predicate (i.e. as a PROPERTY) of any object:

…It is absurd to introduce—under whatever term disguised—into the conception of a thing, which is to be cogitated solely in reference to its possibility, the conception of its existence. If this is admitted, you will have apparently gained the day, but in reality have enounced nothing but a mere tautology. I ask, is the proposition, this or that thing (which I am admitting to be possible) exists, an analytical E.g., or a synthetical proposition? If the former, there is no addition made to the subject of your thought by the affirmation of its existence; but then the conception in your minds is identical with the thing itself, or you have supposed the existence of a thing to be possible, and then inferred its existence from its internal possibility—which is but a miserable tautology. The word reality in the conception of the thing, and the word existence in the conception of the predicate, will not help you out of the difficulty. For, supposing you were to term all positing of a thing reality, you have thereby posited the thing with all its predicates in the conception of the subject and assumed its actual existence, and this you merely repeat in the predicate. But if you confess, as every reasonable person must, that every existential proposition is synthetical, how can it be maintained that the predicate of existence cannot be denied without contradiction?—a property which is the characteristic of analytical propositions, alone.

I should have a reasonable hope of putting an end for ever to this sophistical mode of argumentation, by a strict definition of the conception of existence, did not my own experience teach me that the illusion arising from our confounding a logical with a real predicate (a predicate which aids in the determination of a thing) resists almost all the endeavours of explanation and illustration. A logical predicate may be what you please, even the subject may be predicated of itself; for logic pays no regard to the content of a judgement. But the determination of a conception is a predicate, which adds to and enlarges the conception. It must not, therefore, be contained in the conception. 

Being is evidently not a real predicate, that is, a conception of something which is added to the conception of some other thing. It is merely the positing of a thing, or of certain determinations in it. Logically, it is merely the copula of a judgement. The proposition, God is omnipotent, contains two conceptions, which have a certain object or content; the word is, is no additional predicate—it merely indicates the relation of the predicate to the subject. Now, if I take the subject (God) with all its predicates (omnipotence being one), and say: God is, or, There is a God, I add no new predicate to the conception of God, I merely posit or affirm the existence of the subject with all its predicates—I posit the object in relation to my conception. The content of both is the same; and there is no addition made to the conception, which expresses merely the possibility of the object, by my cogitating the object—in the expression, it is—as absolutely given or existing. Thus the real contains no more than the possible.

A hundred real dollars contain no more than a hundred possible dollars. For, as the latter indicate the conception, and the former the object, on the supposition that the content of the former was greater than that of the latter, my conception would not be an expression of the whole object, and would consequently be an inadequate conception of it. But in reckoning my wealth there may be said to be more in a hundred real dollars than in a hundred possible dollars—that is, in the mere conception of them. For the real object—the dollars—is not analytically contained in my conception, but forms a synthetical addition to my conception (which is merely a determination of my mental state), although this objective reality—this existence—apart from my conceptions, does not in the least degree increase the aforesaid hundred dollars.

By whatever and by whatever number of predicates—even to the complete determination of it—I may cogitate a thing, I do not in the least augment the object of my conception by the addition of the statement: This thing exists. Otherwise, not exactly the same, but something more than what was cogitated in my conception, would exist, and I could not affirm that the exact object of my conception had real existence. If I cogitate a thing as containing all modes of reality except one, the mode of reality which is absent is not added to the conception of the thing by the affirmation that the thing exists; on the contrary, the thing exists—if it exist at all—with the same defect as that cogitated in its conception; otherwise not that which was cogitated, but something different, exists. Now, if I cogitate a being as the highest reality, without defect or imperfection, the question still remains—whether this being exists or not? For, although no element is wanting in the possible real content of my conception, there is a defect in its relation to my mental state, that is, I am ignorant whether the cognition of the object indicated by the conception is possible á posteriori. And here the cause of the present difficulty becomes apparent. If the question regarded an object of sense merely, it would be impossible for me to confound the conception with the existence of a thing. For the conception merely enables me to cogitate an object as according with the general conditions of experience; while the existence of the object permits me to cogitate it as contained in the sphere of actual experience. At the same time, this connection with the world of experience does not in the least augment the conception, although a possible perception has been added to the experience of the mind. But if we cogitate existence by the pure category alone, it is not to be wondered at, that we should find ourselves unable to present any criterion sufficient to distinguish it from mere possibility. 

Whatever be the content of our conception of an object, it is necessary to go beyond it, if we wish to predicate existence of the object. In the case of sensuous objects, this is attained by their connection according to empirical laws with some one of my perceptions; but there is no means of cognizing the existence of objects of pure thought, because it must be cognized completely á priori. But all our knowledge of existence (be it immediately by perception, or by inferences connecting some object with a perception) belongs entirely to the sphere of experience—which is in perfect unity with itself; and although an existence out of this sphere cannot be absolutely declared to be impossible, it is a hypothesis the truth of which we have no means of ascertaining. 

The notion of a Supreme Being is in many respects a highly useful idea; but for the very reason that it is an idea, it is incapable of enlarging our cognition with regard to the existence of things. It is not even sufficient to instruct us as to the possibility of a being which we do not know to exist. The analytical criterion of possibility, which consists in the absence of contradiction in propositions, cannot be denied it. But the connection of real properties in a thing is a synthesis of the possibility of which an á priori judgement cannot be formed, because these realities are not presented to us specifically; and even if this were to happen, a judgement would still be impossible, because the criterion of the possibility of synthetical cognitions must be sought for in the world of experience, to which the object of an idea cannot belong. And thus the celebrated Leibnitz has utterly failed in his attempt to establish upon á priori grounds the possibility of this sublime ideal being. 

The celebrated ontological or Cartesian argument for the existence of a Supreme Being is therefore insufficient; and we may as well hope to increase our stock of knowledge by the aid of mere ideas, as the merchant to augment his wealth by the addition of noughts to his cash account.

Descartes’ Argument

René Descartes (1596-1650) had proposed a simpler version of the ontological argument:

1. Whatever I clearly and distinctly perceive to be contained in the idea of something is true of that thing.
2. I clearly and distinctly perceive that necessary existence is contained in the idea of God.
3. Therefore, God exists.

Descartes’ formulation clearly suffers from the same flaw as Anselm’s, in declaring existence to be a predicate in his conception of God.

Plantinga’s Argument

Alvin Plantinga reformulated the Ontological Argument, adding semantic devices that are designed to obscure the logical flaws. His version is as follows:.:

1. A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
2. A being has maximal greatness if it has maximal excellence in every possible world.
3. It is possible that there is a being that has maximal greatness. (Premise)
4. Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
5. Therefore, it is necessarily true that an omniscient, omnipotent and perfectly good being exists (axiom S5).
6. Therefore, an omniscient, omnipotent and perfectly good being exists.

• Point 1 is a simple definition.
• Point 2 makes essentially the same error as both Anselm and Descartes, by equating “Maximal Greatness” of a “maximally excellent” but otherwise hypothetical being as one that actually exists in every possible world. And this definition is already begging the question, by setting the criterion that a god can only be maximally great, if it is impossible for it to not exist.
• Point 3 is identified as a Premise, and completes the act of begging the question. To rephrase it, he’s saying that it’s possible that a god exists in every possible world. Left unstated is the possibility that this being exists in no possible world, or only in some possible worlds. So points 2 and 3 stack the deck for the conclusion. He’s saying that it’s possible that every imaginable world has a god. That statement is obviously false, as we KNOW that we can imagine a world without god. Since this premise is false, his Ontological argument fails.

Gödel’s Argument

Kurt Gödel developed an updated form of Anselm’s original argument, using modal logic, shown here in its original mathematical notation.

Wikipedia provides a translation of this to standard English:

As noted, Gödel developed this as an update to Anselm’s argument, and he has not solved the key problem. Axiom 5 (“A5”) declares that necessary existence is a positive property. This is equivalent to Anselm’s claim that the greatest possible being that one can imagine (and who actually exists) is superior to the EXACT same being who does not exist. This notion was refuted earlier in the discussion of Anselm’s argument.

Craig’s Argument

William Lane Craig has an alternative form of Plantinga’s ontological argument:

1. It is possible that a maximally great being (God) exists.
2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
3. If a maximally great being exists in some possible world, then it exists in every possible world.
4. If a maximally great being exists in every possible world, then it exists in the actual world.
5. Therefore, a maximally great being exists in the actual world.
6. Therefore, a maximally great being exists.
7. Therefore, God exists.

Craig provides some definitions of his terminology in his post: https://www.reasonablefaith.org/writings/question-answer/misunderstanding-the-ontological-argument/

Craig defines the “possible worlds” term as follows: “To say that some entity exists in a possible world is just to say that such an entity possibly exists. It isn’t meant that the entity actually exists somewhere. Look again at my explanation: “To say that God exists in some possible world is just to say that there is a possible description of reality which includes the statement ‘God exists’ as part of that description.””

Note that Craig is using the “Maximally Great” terminology, which he defines as ” A maximally great being is one that has, among other properties, necessary existence. So if it exists in one world, it exists in all of them!”

So in premises 1 and 2, he inherently includes the criterion of existence in every possible world. But by starting out with that terminology, Craig’s first statement is already guilty of begging the question. He’s declaring that it’s possible that a god necessarily exists in every possible world (which he expressed later in step 3). Those statements are clearly false. We can obviously conceive of worlds in which no god exists, so it’s a gross error to state that it’s possible that every imaginable world has a god. Every statement after his first point is therefore moot. Craig’s argument is sophistry of the worst sort.

While all of these formulations of the Ontological argument are fatally flawed, the most recent forms seem to have gone out of their way to hide the flaws through use of deceptive semantics within their premises. I doubt this was unintentional.