Five Ontological Arguments

I find it difficult to critique something if you have not read the argument (assuming, for example, it is in a textual or narrative form) in its designated context. We moderns may struggle with a plethora of classical problems that contained phenomena, terms and language that don’t quite mean the same as they used to. For instance, those who have read the Republic will find it strange that only a third of the book deals with political theory (or “statescraft”) as such (Havelock 1963: 3). Even more strangely, it is Plato’s attack on poetry that consumes almost the entire first half of the book.

Anselm’s ontological argument contains somewhat of the same struggle. If we follow the initial premise of the argument (God is “something than which nothing greater can be thought” is understood) to its conclusion, that this God exists in reality, we tend to see a rather big leap made by Anselm. However, what one has to understand is that Anselm was a Christian as well as a neo-Platonist. Like Plato, he saw that ideas (mental things) had a different kind of reality than nonmental things. Hence, it is vastly different to say that “the best possible” thought of a thing must exist in reality, than to say that ideas correspond to a certain kind of reality than “real” things do (Davies 1998: xii-xiii).

To formulate a scheme of Anselm’s argument from Proslogion II, let us look at the argument in its full narrative form:

… [I]ndeed we believe that thou art a being than which nothing great can be conceived. Or is there no such nature, since the fool hath said in his heart, there is no God? (Ps. 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 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 afterward 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 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 exists both in the understanding and in reality (Deane 1962: 53).

I agree with Alvin Plantinga’s (1990) interpretation of this argument as being a reductio ad absurdum. The argument is as follows:

1. God exists in the understanding but not in reality – assumption for reductio.
2. Existence in reality is greater than existence in the understanding alone – premise.
3. A being having all of God’s properties plus existence in reality can be conceived – premise.
4. A being having all of God’s properties plus existence in reality is greater than God – from (1) and (2)
5. A being greater than God can be conceived (3), (4).
6. It is false that a being greater than God can be conceived – by definition of “God”.
7. Hence it is false that God exists in the understanding but not in reality – (1)-(6), reductio ad absurdum. (Plantinga 1990: 29)

Anselm initially makes the observation that a “being which nothing greater can be conceived” is understood – or, conceived. Even the atheist (“fool”) who says that this being doesn’t exist in reality at least understands what he hears. This suggests that God is conceivable. In other words, there is nothing logically impossible in the supposition that it obtains. However, isn’t existence in reality greater than existence in the understanding?

Some philosophers think that this a rather dubious premise; I don’t think so. At least, I don’t think that this premise goes without argument. Anselm prior in his Monologion, including other Middle Age philosophers in his time, makes the case that things can be organized in terms of a hierarchy, or “great chain of being.” As he writes:

… [I]f someone considers the natures of things, he cannot help realizing that they are not all of equal dignity; rather, some of them are on different and unequal levels. For anyone who doubts that a horse is by its very nature better than wood, and that a human being is more excellent than a horse, should not even be called a human being. Therefore, since it is undeniable that some natures are better than others, reason makes it no less obvious that one of them is so pre-eminent that he has no superior. (Anselm 1995: 14)

Whether rationalist, scholastic, neo-Platonist or what have you, most philosophers would agree that things can be ordered in terms of ontological/normative greatness. I don’t think the premise of the argument fails at this specific point, since I believe it is more plausible than not. Moreover, that even to find something where the thought of a thing is “greater” than its reality (say, the idea of a disease rather than an actual disease) is an equivocation of what Anselm means by “greater.”*

 

Modal Versions of the Argument

There has been a lot of scholarly work on the interpretations of Anselm’s argument. Is Anselm making one argument (unum argument) or perhaps two? Charles Hartshorne (1967) has differentiated between two kinds of arguments in the Proslogion:

Proslogion II: For any x and y, x exists (not merely in the mind) and y does not, implies, x is greater than y.

Proslogion III: For any x and y, x exists noncontingently and y exists contingently implies, x is greater than y.

Charles Hartshorne and Norman Malcolm think that there is a superior argument to be found in Proslogion III, and that modern objections to the OA are often leveled to Proslogion II and not III. A summary of Hartshorne’s argument can be as follows:

1. The existence of a Necessary Being must be either (a) an impossible existence, (b) a possible but not necessary existence, (c) a necessary existence.
2. It cannot be impossible, since it is not a contradiction in terms to affirm “a Necessary Being necessarily exists.”
3. It is a contradiction to affirm that a Necessary Being (one that cannot not exist) is a possible Being (i.e., one that can not exist).
4. Therefore, a Necessary Being necessarily does exist.

Norman Malcolm (1960), also building off of the argument in Proslogion III, can have his structured as follows:

1. If God does not exist, his existence is logically impossible.
2. If God exists, his existence is logically necessary.
3. Hence God’s existence is either logically impossible or logically necessary.
4. If God’s existence is logically impossible, the concept of God is contradictory.
5. The concept of God is not contradictory.
6. Therefore, God’s existence is logically necessary.

Malcolm summarizes his argument:

If God, a being a greater than which cannot be conceived, does not exist then He cannot come into existence. For if He did He would either have been caused to come into existence or have happened to come into existence, and in either case He would be a limited being, which by our conception of Him He is not. Since He cannot come into existence, if He does not exist His existence is impossible. If He does exist He cannot have come into existence (for the reasons given), nor can He cease to exist, for nothing could cause Him to cease to exist nor could it just happen that he ceased to exist. So if God exists His existence is necessary. Thus God’s existence is either impossible or necessary. It can be the former only if the concept of such a being is self-contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists (Malcolm 1960: 49-50).

Alvin Plantinga (1974) has formulated his famous modal ontological argument in terms of “possible world semantics,” and moreover working off of the concept of a maximally great being. His argument can be structured as follows:

1. It is possible that there be a being that has maximal greatness.
2. So there is a possible being that in some world W has maximal greatness.
3.  A Being has maximal greatness in a given world only if it has maximal excellence in every world.
4. A being has maximal excellence in a given world only if it has omniscience, omnipotence, and moral perfection.
5. There is a possible world in which maximal greatness is instantiated. And the analogues of (3) and (4) spell out what is involved in maximal greatness:
6. Necessarily, a being is maximally great only if it has maximal excellence in every world
7. Necessarily, a being has maximal excellence in every world only if it has omniscience, omnipotence, and moral perfection in every world.
8. Therefore, there actually exists a being that is omnipotent, omniscient, and morally perfect, and who exists in every possible world.

Let’s suppose G stands for the following proposition:

G: An entity exists that is maximally excellent.

By “maximally excellent,” Plantinga simply means to say an entity possesses maximal greatness if and only if it is necessarily existent and necessarily maximally excellent, properties of which entail that this entity is omniscient, omnipotent, and morally perfect. Hence, for us to say that there is a maximally great entity is to say that this entity necessarily exists. In the formal notation of modal logic the proposition “□G” signifies that G is necessarily true. The first premise of the argument says that “it is possible that there is a being that has maximal greatness,” which in formal notation would be “◊□G”. The conclusion thence follows, □G.

Why is this? According to what is known as the S5 version of modal logic, there is a notion known as “universal accessibility,” and as Vern Poythress explains, “… every possible world that is accessible at all, or from which our world is accessible, is accessible directly. But the postulate of S5 cannot exclude a model where there are other universes of worlds, all of which are inaccessible to our local group of possible worlds and from which there is no access to our local group” (Poythress 2013: 665). The reason for the conclusion is this:

Assume the premise, namely, ◊□G. Let the initial world be E. By definition of the symbol ◊ in the model, there exists a possible world W in which □G. By definition the symbol □, G is true in all possible worlds (in the subset of mutually accessible worlds). Therefore, back in E, G is true. Moreover, G is true in all the other worlds accessible from E. Hence □G in E. (ibid.)

Our last and final argument comes from David Lewis (1970) who formulated his argument on the notion of an understandable being:

1. For any understandable being x, there is a world w such that x exists in w.
2. For any understandable being x, and for any worlds w and v, if x exists in w but not in v, then the greatness of x in w exceeds the greatness of x in v.
3. There is an understandable being x, such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world.
4. There is a being x existing in the actual world such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world.

 

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Works Cited:

Davies, Brian, Evans, G. R. Anselm of Canterbury: The Major Works. 1998. Oxford, NY: Oxford University Press.

Deane, S. W. St. Anselm’s Basic Writings. 2nd ed. 1962. La Salle, IL: Open Court Publishing Co.

Havelock, Eric A. Preface to Plato. 1963. London, England: Harvard University Press.

Malcolm, Norman. “Anselm’s Ontological Arguments,” in The Philosophical Review. 1960. LXIX.

Plantinga, Alvin. God and Other Minds. 2nd edn. 1990. Ithaca, NY: Cornell University Press.

Poythress, Vern. Logic: A God-Centered Approach to the Foundation of Western Thought. 2013. Crossway, p. 665

Williams, Thomas. Monologion and Proslogion. 1995. Indianapolis/Cambridge: Hackett Publishing.

 

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Notations:

* On this point, see Peter Kreeft and Ronald Tacelli’s Handbook of Catholic Apologetics (San Francisco, CA: 2009), 75. To quote in full:

The first premise of this argument is often misunderstood. People sometimes say: “Isn’t an imaginary disease better, and in that sense greater, than a real one?” Well, it is certainly better – and so a greater thing – for you that the disease is not real. But that strengthens Anselm’s side of the argument. Real bacteria are greater than imaginary ones, just because they have something imaginary ones lack: real being. They have an independence, and therefore an ability to harm, that nothing can have whose existence is wholly dependence on your thought. It is this greater level of independence that makes them greater as beings.