Excursus on Natural Theology (Part 24)

April 20, 2016

Premises of the Ontological Argument and its Defense

Last time we introduced the concept of possible worlds in order to help us better understand the ontological argument for God’s existence. I emphasized that possible worlds are not any sort of concrete object – a planet or a universe. The easiest way to think about a possible world is just as a list of statements – a sort of massive conjunction:

W1: p & q & r & s . . .

so that this massive conjunction includes every proposition or its opposite. Thus it yields a maximal description of reality. Nothing is left out. That is what a possible world is. It is just a sort of a maximal description of reality. Reality could have been different ways. So different descriptions will make different possible worlds. For example:

W2: p & not-q & not-r & s . . .

W3: not-p & q & r & not-s . . .

W4: not-p & not-q & not-r & s . . .

So you have various descriptions of the way the world could have been. The description which has only true conjuncts (that is to say the description every conjunct of which is true) will be the description of the actual world. That will be the true description. That will be the actual world.

What the ontological argument wants to show is that if God’s existence is possible – if God exists in one possible world – then he exists in all of them.

Last time someone raised the idea that maybe these other worlds really aren’t possible. Maybe there is only one possible world, and that is the actual world alone. I think that is a mistake. But suppose we, for the sake of argument, agree that there is only the actual world. How would that affect the ontological argument? Would that mean that the ontological argument doesn’t work if there is only one possible world? Well, in fact if you think that there is only one possible world, what that really implies is that the ontological argument goes through with a vengeance! Why is that? Remember the ontological argument wants to prove that if God exists in one possible world then he exists in all of them. If there is only one possible world, it follows immediately that if God’s existence is possible then it’s actual because that is the only world there is – the actual world. So far from invalidating the ontological argument, this view actually makes the ontological argument all that much easier.

The challenge in the ontological argument for the person who thinks that there are lots of possibilities is how do you get from the fact that God exists in one possible but non-actual world (like, say, W5) to existing in the actual world? That is a challenge. How do you get from God’s existing in some possible but non-actual world to the actual world? But if you think there is only one world (there is only the actual world) then that obstacle no longer presents itself, does it? Then the inference is immediate. If God’s existence is possible then God actually exists because there is only one possible world – namely, the actual world. So I think that if you do hold to that view the ontological argument should be very congenial to you and would be one that you would readily support.[1]

When we talk about possible worlds, as I said in response to another person last time, these various conjunctions need to be not only compossible (that is to say, they need to not only be possible together) but each one of them individually needs to be possible as well. For example, take the proposition, “The prime minister is a prime number.” That proposition isn’t even possibly true. The prime minister is a concrete object – a flesh and blood human being. Therefore it is impossible that he could have been a prime number. There is no way that a prime number could be the prime minister. That means that no possible world will include that statement as one of its conjuncts because it is impossible. That will be false in every possible world. It is necessarily false. So a proposition which is necessarily false will be one that is false in every possible world.

By contrast, the proposition, “George McGovern is the President of the United States” is false in the actual world. But there are possible worlds in which it is true. McGovern could have been elected President of the United States. So that is a possible proposition, and it will be a conjunct in some possible worlds. To say that McGovern is the President of the United States in some possible world is simply to say that there is a maximal description of reality that has that relevant proposition as one of its conjuncts. That isn’t the actual world (that would be a non-actual possible world – a possible world which isn’t actual. One in which that conjunct is true).

Leibniz’s insight into the ontological argument is that the argument assumes that the proposition “God exists” or “A greatest conceivable being exists” or “A perfect being exists” is possibly true. That is to say that God exists in some possible world. In some possible world that statement, that conjunct – “God exists” or “A maximally great being exists” or “A perfect being exists” – that proposition is true in some possible world.

If the concept of God is incoherent or impossible then God would be like that prime minister that is a prime number. It would be a metaphysical impossibility. He would not exist in any possible world. The word “God” in that case (if the concept of God is incoherent) would refer to nothing anymore than the words “a square circle” refers to something. In both cases the words “A greatest conceivable being” or “a square circle” would just be an incoherent combination of words. They don’t refer to anything. As Leibniz says, the ontological argument assumes that the concept of God is a coherent concept – it is possible for God to exist.

In his version of the argument, Alvin Plantinga (whose version we are examining) conceives of God as a being which is maximally excellent in every possible world. What does he mean by that? By maximal excellence, Plantinga takes this to entail such excellent-making properties as being all-knowing, all-powerful, and all-good. A being which has those properties will be more excellent than a being which is limited in knowledge or strength or goodness. So a maximally excellent being will be one that has omnipotence, omniscience, and moral perfection.

A being which has maximal excellence in every possible world has what Plantinga calls maximal greatness. There is a difference between maximal greatness and maximal excellence. Maximal excellence is the property of being all-knowing, all-powerful, all-good. Maximal greatness is the property of having maximal excellence in every possible world.[2]

Now, Plantinga says, the property of maximal greatness is possibly exemplified. That is to say, this is a coherent concept. There is a possible world in which a maximally great being exists. But if a maximally great being exists in every possible world then if it exists in one possible world it exists in all of them, including the actual world. Therefore, God exists.

Although Plantinga thinks that the ontological argument is a sound and non-question begging argument for God’s existence, initially at least he did not regard it as a “successful piece of natural theology.” Why not? Why isn’t this a successful piece of natural theology? He said it is because the key premise, “Possibly maximal greatness is exemplified” can be rationally denied. You can be rational and deny that maximal greatness is possibly exemplified. Or, in other words, you can be rational and deny that it is possible that a maximally great being exists.

But Plantinga later confessed that he had set the bar for “success in natural theology” unreasonably high. This is what he later came to say,

I employed a traditional but wholly improper standard: I took it that these arguments are successful only if they start from propositions that compel assent from every honest and intelligent person and proceed majestically to their conclusion by way of forms of argument that can be rejected only on pain of insincerity or irrationality. Naturally enough, I joined the contemporary chorus in holding that none of the traditional arguments was successful. (I failed to note that no philosophical arguments of any consequence meet that standard; hence the fact that theistic arguments do not is of less significance than I thought.)[3]

So Plantinga says he initially thought to be a successful piece of natural theology these arguments had to compel assent from any rational person. He came to see that if you hold that standard then there are no sound philosophical arguments for anything (or no good philosophical arguments for anything). Plantinga now believes, “The ontological argument provides as good grounds for the existence of God as does any serious philosophical argument for any important philosophical conclusion.”[4] George Mavrodes, who was a professor of philosophy at the University of Western Michigan rightly remarked on Plantinga’s assessment, “But if natural theology can be that good, as good as the best arguments anywhere in serious philosophy, . . . why should we not put forward these powerful arguments as proofs of God?”[5]

We can formulate Plantinga’s version of the ontological argument as follows:

1. It is possible that a maximally great being exists (in other words, maximal greatness is possibly exemplified).

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. If a maximally great being exists in the actual world then a maximally great being exists.

6. Therefore a maximally great being exists.

You might be surprised to learn that premises (2) through (5) of this argument are relatively uncontroversial. The real point of contention is premise (1) – that it is possible that a maximally great being exists.[6] This is the principal question which needs to be settled with regard to Plantinga’s version of the ontological argument. What warrant exists for thinking that this key premise “It is possible that a maximally great being exists” is true?

In dealing with this issue it is very important that we keep firmly in mind the difference between what we could call epistemic possibility and metaphysical possibility. “Epistemic” derives from the Greek word episteme or “knowledge.” Epistemic possibility indicates what is possible with respect to your knowledge. So, in response to the ontological argument’s key premise, one is tempted to say, “Well, it is possible that God exists, and it’s possible that God does not exist.” That is true only with respect to epistemic possibility. What you are saying there is: “For all I know God exists or he doesn’t exist. It is possible with respect to what I know. It is epistemically possible. I don’t know which is right. For all I know, God may or may not exist.”

But if God is a maximally great being then his existence, if it is metaphysically possible, it will be metaphysically necessary. This type of possibility has to do with what is actualizable or what is real independently of what you think about it. In God’s case his existence is going to be either necessary or impossible. It can’t be merely contingent. It will not be true to say it is possible that God exists or it is possible that he doesn’t. That would be to say that God exists in some possible worlds but he doesn’t exist in other possible worlds. That would be metaphysically incorrect. The concept of a maximally great being is such that it either exists in all possible worlds or it exists in none of them. But you can’t say it exists in some of them and does not exist in others of them.

Let me give an illustration of this difference between epistemic possibility and metaphysical possibility that will help to make the point clear.

There is a mathematical proposition known as Goldbach’s Conjecture that remains unproven in mathematics today. Goldbach’s Conjecture says that every even number greater than 2 can be expressed as the sum of two prime numbers. So take any even number greater than 2 – that will be equal to the sum of two prime numbers. Although Goldbach’s Conjecture has been tested to enormous lengths, no mathematician has ever been able to prove it or disprove it. We don’t know whether Goldbach’s Conjecture is true or not. So in this epistemic sense one can say (epistemically) Goldbach’s Conjecture could be true or it could be false. We just don’t know which. But as a piece of mathematics, Goldbach’s Conjecture is either necessarily true or necessarily false. It is either necessary that Goldbach’s Conjecture is true or it is impossible that it is true. It cannot possibly be true and possibly be false in this metaphysical sense. It is either impossible or necessary. One or the other. But it cannot be both possibly true and possibly false. It is necessarily true or necessarily false.

In the same way, although the key premise of the ontological argument could be epistemically uncertain – we don’t know whether it is possible that a maximally great being exists or not. Nevertheless, the epistemic entertainability of the key premise or of the denial of the key premise doesn’t guarantee that it is metaphysically possible.[7]

The question we are asking here is: is it metaphysically possible that a maximally great being exists? Not is it epistemically possible, which I think it certainly is. But is it metaphysically possible?

Think about it – the concept of a maximally great being seems intuitively-speaking a coherent idea and therefore possibly instantiated. The idea of a being which is all-knowing, all-powerful, all-good in every possible world seems to be a perfectly coherent idea and therefore possibly instantiated. In order for the ontological argument to fail the concept of a maximally great being would have to be logically incoherent. It would need to be like the concept of a married bachelor. The concept of a married bachelor when you think about it is not a strictly or explicitly self-contradictory concept as would be, say, the concept of a married unmarried man. That would be strictly contradictory. But nevertheless once you understand the concept or the meaning of what a bachelor is you can see that it is impossible that there could be something corresponding to that concept – that that concept could be possibly exemplified or that property possibly instantiated. By contrast to that, the concept of a maximally great being doesn’t seem at all incoherent. Quite the contrary, it seems perfectly coherent to talk about a being which is maximally excellent in every possible world. That would go some distance, I think, to warrant the first premise that it is possible that a maximally great being exists.

Some of you might be thinking, “But doesn’t this lead to a kind of ontological overkill?” One of the most important strategies that detractors of the ontological argument adopt is to provide parodies of the ontological argument that would lead to all sorts of absurdities that nobody would think exists. These go back to Anselm’s fellow monk Guanilo. You remember Anselm was asking the question, “Why does the Scripture say ‘the fool hath said in his heart there is no God?’” Why does the Scripture call the atheist a fool? Anselm’s answer to that was because once you properly understand the concept or the word “God” you can see that God must exist. Therefore the fool is saying something incoherent in saying God does not exist. Guanilo, his fellow monk, wrote a treatise called On Behalf of the Fool in which he criticized Anselm’s argument. The way he did so was to construct parodies of the argument where you would try to construct parallel ontological arguments for absurd conclusions. For example, it has been suggested that you could prove that a most-perfect island exists in this way by saying a most-perfect island must have all of these properties in every possible world, and that is possible, therefore a most-perfect island actually exists. Or a necessarily existent lion – a lion that has the property of necessary existence would exist in every possible world and therefore there must be a necessarily existent lion. Those seem to be coherent concepts, and yet they would lead to the postulation of entities which nobody would accept. In my debates on the existence of God, some of my opponents have suggested, for example, the idea of a necessarily existent pizza or a most-perfect pizza would be one that exists in every possible world. Therefore if the ontological argument is sound we should believe in the existence of the most-perfect pizza or necessarily existent pizza.

What might the defender of the ontological argument say in response to these parodies? Quite a bit, I think. I think that the proponent of the ontological argument can plausibly claim that the concept of God differs from these supposedly parallel concepts like a most-perfect island or a necessarily existent lion or necessarily existent pizza.[8]

1. The properties that go to make up maximal excellence that Plantinga talks about have intrinsic maximum values. For example, omniscience is the property of knowing only and all truth. You can’t get any more knowing than that if you know all the truths there are. So there is an intrinsic inherent ceiling on this property of omniscience. Similarly for the other properties like moral perfection and omnipotence. But that is not the case with things like islands. Islands don’t have sort of intrinsic maximal properties. As Plantinga says, there could always be more palm trees and native dancing girls to improve the island. It really is an incoherent concept to talk about a most-perfect island in a way that isn’t incoherent to talk about a maximally great being.

2. It is far from clear that there really are objective excellent-making properties of things like islands. Are there really objective properties that go to make up the excellence of islands? It seems not. That is a very subjective thing dependent upon your personal preference. Do you prefer a desert island or one that is crowded with the finest resort hotels? It depends on your tastes which one of these you think is the better island. Right? So there really aren’t these sort of objective excellent-making properties that go into islands in the way that omniscience, omnipotence, and goodness seem to be objective great-making properties.

With respect to the parody of the island, there are two problems – the lack of intrinsic maximum values and the lack of the objectivity of there even being excellent-making properties of islands. As for the idea of something like a necessarily existent lion or a necessarily existent pizza, this also (when you think about it), I think, is incoherent. For as a necessary being, such an animal would have to exist in every possible world that we can conceive. But any animal which would exist in a possible world in which the universe is comprised of a single infinitely dense space-time singularity just is not a lion. That is not what you mean by a lion. Similarly, it is not a pizza either. By contrast, a maximally excellent being could be immaterial and therefore transcend the physical limitations of space and time and so could be necessarily existent. It could exist in a possible world in which the universe is a space-time singularity. Lest you think that a pizza, say, could be immaterial – that wouldn’t be very satisfying, would it? It wouldn’t satisfy your appetite. A pizza is something that you can eat, and you can’t eat an immaterial object. Again, the idea of a necessarily existent pizza or necessarily existent lion upon closer reflection really does turn out to be incoherent and therefore doesn’t exist in other possible worlds.

Perhaps the greatest challenge to the appeal to our intuitions to justify premise (1) (and by appeal to intuition, what I mean is that it just seems clear that it is possible that maximal greatness is exemplified. This looks coherent to us. This looks like a coherent idea, and therefore one that is possibly exemplified.) The greatest challenge to that appeal, I think, would be to say that it is intuitively coherent in exactly the same way to conceive of what we might call a quasi-maximally great being. That is to say, a being which is in every other respect maximally excellent except that in one of those excellent-making properties it is a little deficient.[9] For example, imagine a being which is morally perfect, omnipotent, but it is not quite omniscient because it doesn’t know future contingents. It is the God of open theism who knows all past and present propositions but he doesn’t know the truth value of future tense propositions about contingent events. Why is the premise of the ontological argument more plausible than a parallel argument that says it is possible that a quasi-maximally great being exists? If we are warranted in thinking that a maximally great being exists, wouldn’t we be equally warranted in thinking that it is possible that a quasi-maximally great being exists? If you think that then you’ve got to think that such a being does exist. It wouldn’t deny the existence of God per se but it would mean that in addition to the maximally great being you are going to populate your world with all sorts of quasi-maximally great beings. That would surely be implausible and undesirable.

If the key premise of the ontological argument is possible or is true, isn’t it also true that it is possible that a quasi-maximally great being exists? I am not so sure. I think not because maximal greatness, I want to argue, is logically incompatible with quasi-maximal greatness. Think about it. A maximally great being is by definition an omnipotent being. It is all-powerful. That is part of what goes to make up maximal greatness. So no concrete object could exist independently of its creative power. As an omnipotent being, a maximally great being would have to have the power to freely refrain from creating anything at all. Therefore, there must be possible worlds in which nothing but the maximally great being exists. But that entails that if maximal greatness is possibly exemplified then quasi-maximal greatness is not. There might be quasi-excellent beings in many worlds – worlds in which the maximally great being has chosen to create quasi-excellent beings. Maybe they would be like angels that would be supernatural, superhuman, but not like God. But those beings would lack necessary existence. They would be created by the maximally great being, and therefore they would not be quasi-maximally great. They could be quasi-excellent but they wouldn’t be quasi-maximally great because they wouldn’t exist in every possible world. So if maximal greatness is possibly exemplified, which I think is intuitive, that means that quasi-maximal greatness actually turns out to be impossible because a quasi-maximally great being would be a being that has necessary existence and therefore would exist in every possible world. He would be outside the omnipotent power of the maximally great being.

So our intuition that a maximally great being is possible is not undermined by the claim that a quasi-maximally great being is also intuitively possible because the latter intuition – the intuition that quasi-maximal greatness is exemplified – depends upon the assumption that a maximally great being cannot possibly exist. And that would beg the question. So long as maximal greatness is possible then it would follow that quasi-maximal greatness is not.

Still, skeptics might insist that we don’t have any way of knowing a priori or in advance whether it is maximal greatness or quasi-maximal greatness which is possibly exemplified. The argument that I’ve just given shows that it can’t be both. You can’t have both a maximally great being and a quasi-maximally great being. They would be incompatible with each other because one would escape the omnipotence of the other. So you can’t have both. But the skeptic might say we don’t know if either one is possible. Our intuitions about modality are unreliable guides.[10]

I do think we can say here that the intuition that a maximally great being exists trumps any intuition that we might have that quasi-maximal greatness is possibly exemplified. You only arrive at the idea of quasi-maximal greatness by subtracting something from the concept of maximal greatness. In a sense it is parasitic on the concept of maximal greatness. If quasi-maximal greatness seems possible, all the more so maximal greatness would seem possible. That would give reason then for thinking that priority should be given to maximal greatness and not quasi-maximal greatness.

But could we say anything more in defense of the ontological argument’s key premise? Can we say something more than just modal intuitions – that it seems intuitive that this is a coherent concept? Plantinga, I think, provides a clue when he says that if we carefully ponder the key premise and the alleged objection to it, if we “consider its connections with other propositions we accept or reject and still find it compelling, we are within our rights in accepting it.” That is a far different story than the sort of a priori speculation that the skeptic denounces. Even if you cannot determine a priori (that is to say, in advance) whether or not maximal greatness is possibly exemplified, what Plantinga is suggesting is that we could come to believe that it is possible that a maximally great being exists on the basis of a posteriori considerations. That is to say on the basis of evidence and argument independent of our modal intuitions. What I want to do next time is to look at some of those considerations that might lend support to our modal intuitions that maximal greatness is indeed a coherent concept. If that is the case then the basis for affirming premise (1) will not simply be our modal intuitions that this is a coherent concept or idea, but that we also have some extra additional reasons for thinking that premise (1) is true.[11]



[1] 5:05

[2] 10:16

[3] Alvin Plantinga, Warranted Christian Belief (New York: Oxford University Press, 2000) p. 69.

[4] Alvin Plantinga, “Reason and Belief in God,” typescript dated October 1981, pp. 18-19. This paragraph was inadvertently omitted in the published version of the essay, with the result that Mavrode’s reference to it has no referent. Fortunately, a nearly identical paragraph appears in Alvin Plantinga, “Self-Profile,” in Alvin Plantinga, ed. James E. Tomberlin and Peter van Inwagen, Profiles 5 (Dordrecht: D. Reidel, 1985), p. 71.

[5] George Mavrodes, “Jerusalem and Athens Revisited,” in Faith and Rationality, ed. A. Plantinga and N. Wolterstorff (Notre Dame, Ind.: University of Notre Dame Press, 1983), pp. 205-6.

[6] 15:06

[7] 20:00

[8] 25:12

[9] 30:00

[10] 35:00

[11] Total Running Time: 38:45 (Copyright © 2016 William Lane Craig)