The necessary being

I mentioned earlier one of the great divides in metaphysical think­ing about God in the Western philosophical tradition, namely the divide between those who think God is a necessary being and those who do not.

The best-known of the a priori arguments for the existence of God—which goes back to the great eleventh-century Christian philosopher St. Anselm, who was archbishop of Canterbury in England—is called the ontological argument. The argument is deceptively simple. In the famous version Anselm gave in his Proslogion, it reads as follows:

So even the foolish person is convinced that that than which nothing greater can be conceived is in his understanding, because what he hears he under­stands, and what is understood is in the understanding. And certainly that than which nothing greater can be conceived cannot exist only in the understanding. For if it actually only existed in the understanding, it could be conceived to exist in reality, which would be greater. If therefore that than which nothing greater can be conceived exists only in the understanding, then that than which nothing greater can be conceived is something than which something greater can be conceived.

(The foolish person Anselm has in mind is the fool in Isaiah 7:9, who has “said in his heart that there is no God.”)

Let me lay this argument out just a little more formally. The idea of God is the idea of the greatest conceivable being. Let us call the greatest conceivable being “Alpha.” Alpha is greater, by this defini­tion, than all other beings. Now we argue, as Anselm does, by reductio.

Then there's another conceivable being exactly like Alpha, except that he exists. Call that being “Beta.”

G: What exists is greater than what doesn't exist.

So: Beta is greater than Alpha.

Alpha is greater than all other beings.

Alpha is greater than Beta.

So: Beta is not greater than Alpha.

Our assumption that Alpha doesn't exist has led to a contradiction.

So: Alpha does exist.

Q.E.D.

If proving the existence of God were this straightforward, there would probably be fewer nonbelievers! So, as you would anticipate, many difficulties can be and have been raised for the ontological argu­ment. One of the most obvious difficulties lies with the assumption that I labeled “G” above: the claim that what exists is greater than what does­n't exist. Is this really a reasonable claim? What does it mean to say that Beta is greater than Alpha because it exists? Before accepting this argu­ment, we should surely want to understand this premise better.

Descartes offered, in the fourth discourse of The Discourse on Method, a different version of the ontological argument, which might help us to understand this premise.

For example, I could see very well that, if one considered a triangle, its three angles had to be equal to two right angles, but I could see nothing of the same sort that assured me that there would be any actual triangle in the world: whereas returning to the examination of the idea that I had of a perfect being, I found that existence was included in that idea in the same way that it is included in the idea of a triangle that its three angles are equal to two right angles or in the idea of a sphere that all its parts are equally distant from its center, or even more obviously so; and that, as a consequence, it is at least as certain that God, who is this so perfect being, is or exists, as any demonstration in geometry can be.

Here the argument is phrased not in terms of greatness but in terms of perfection. The idea is that existence is an aspect of perfection, so that a perfect being must exist. This is also a possible elucidation of Anselm's thought, since by a perfect being we might just mean one than which none greater could be conceived.

Unfortunately, however, Descartes' notion that existence is con­ceptually included in perfection is not really much clearer (despite what he says!) than the idea that what exists is “greater” than what does not. There are two elements to the claim that something is the greatest or the most perfect thing of a certain sort. One is that noth­ing is greater or more perfect than it is; this is the “comparative claim.” And the other is a “uniqueness claim”: there is nothing else that is as great or perfect as it is. If “great” means just large in size, then there's nothing larger than the whole universe: everything else is a part of it and, therefore, smaller. And it's unique.

That the physical universe exists is not quite a necessary truth, however; there could have been nothing at all, apart from whatever abstract objects exist necessarily. But since a possible world is defined by what is true in it, and since the truths about the neces­sary existents are the only things that are true in that possible world, there's only one possible world in which the universe doesn't exist. (Some metaphysicians will think I should say there are two: the uni­verse also doesn't exist in the impossible world, which is the one world where everything is true and everything is false... but, of course, it does exist there as well! Others might think that the impos­sible world, though it turns out to be a useful technical device in modal logic, isn't something that exists in the way that other possi­ble worlds do.) In short, if the ontological proof is taken to show that the universe exists, it doesn't quite do the job of showing that it's a necessary being, though it gets about as close as you can get. But Anselm would have said so if he thought that his proof had the less- than-stunning conclusion that the universe existed!

Descartes' talk of “perfection” implies not just great size, how­ever, but also some more substantial properties, perhaps even moral or aesthetic ones. (And presumably that's what Anselm meant, too.) But then there are reasons to doubt premise G. Suppose we take “perfect” to mean morally or aesthetically as good as can be. (And from now on in this discussion, I'll use “good” as shorthand for “morally or aesthetically good.”) Consider a person in the actual world—call her Jane Actual—and another good person in some other possible world—call her Jane Possible. Suppose that every­thing that Jane Actual does, Jane Possible does also, that they look identical, and that everything that happens to Jane Actual happens to Jane Possible.

Imagine Dorothy Possible, a metaphysician in Jane Possible's world, thinking about this question. In her world, of course, Jane Possible will be better than Jane Actual by this argument, because from where Dorothy Possible sits it is Jane Possible who exists, not Jane Actual! Interpreting G requires that we should be able to com­pare people in different possible worlds and say absolutely which of them is closer to perfection. But if G is right, then in every possible world each person is better than his or her identical cross-world twins in other possible worlds. Judgments of which is better and which is worse cannot be made, then, except relative to a particular world. So if G (understood as making a claim about what is morally best) is right, we can't make the very comparisons G requires.

I should be clear that I've been using “exists” in two senses. In one sense something exists if it exists in a possible world: but, as you know, to say that is just to say that it might have existed. In this sense, golden mountains exist. In another sense, it exists if it exists in the actual world. In this sense, Mount Everest exists. Now, the word “exists” in

G: What exists is greater than what doesn't exist

really means “exists in the actual world.” So the claim is that a thing is better if it exists in the actual world than if it just exists in some other worlds. One way of putting the problem for G is to ask why we should think what is in the actual world is superior in some moral or aesthetic way to other possible worlds.

There seem, at any rate, to be reasons for doubting that the onto­logical argument, at least as I have reconstructed it above, is sound, however we understand G.

Suppose Alpha doesn't exist.

Then there's another conceivable TV soap exactly like Alpha, except that it exists. Call that possible TV soap opera “Beta.”

G: What exists is greater than what doesn't exist.

So: Beta is greater than Alpha.

Alpha is greater than all other soap operas.

Alpha is greater than Beta.

So: Beta is not greater than Alpha.

Our assumption that Alpha doesn't exist has led to a contradiction.

So: Alpha does exist.

Q.E.D.

Somewhere there's a perfect television soap opera, so why can't I find it? An objection pretty much like this was made in St Anselm's own day. An eleventh-century monk named Gaunilo of Marmoutiers, who was a contemporary of Anselm's, argued, by way of a reductio of Anselm's proof that a similar argument showed that there was an ideal island somewhere. Gaunilo concluded:

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.

Since the rest of the argument seems to depend only on definitions, we might be inclined to conclude that it is G that is doing the dam­age here, and then we could say that, whatever Anselm meant by “greater,” G just isn't true.

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