Ontology, at least in its classic sense, is the branch of philosophy that deals with being or existence, however exactly that is to be understood. And at the center of the ontological argument is the concept of existence. Anselm argues, in effect, that the existence of God is built into the very concept of God. He proceeds by a form of argument called reductio ad absurdum -- reduction to absurdity. He attempts to show that the position of the fool -- the non-believer who has said in his heart "There is no God" -- is incoherent and leads to absurdity.
First. let's take a look at this form of argument in general. Suppose you think there is a largest prime number. I can prove that you are wrong by reductio. I assume that there is a largest prime -- call it p. My assumption, however, is merely for the sake of letting it self-destruct. I will show that the assumption is inconsistent. That means it would require one and the same thing to be both true and false.
Let's follow the reasoning. To make it work, we will need a premise that you already know from high school algebra. Every whole number is either prime or else can be written as a product of prime factors. For example: 1078 is not prime. But 1078 = 2x7x7x11, and each of these factors is prime. We will take the prime factor theorem for granted. (If anyone is truly curious, let me know and I'll provide a proof.)
Now back to our reductio. We supposed that there is some largest prime number p. Consider this number:
p! = 1x2x3x4x5x6x...xp
and then add 1 to it:
p! + 1
Is p! + 1 prime? If it is, then it is larger than p, and so we have our absurdity: we assumed p was the largest prime, but we have a larger prime. namely p! + 1. On the other hand, suppose P! + 1 is not prime. Then it has prime factor. Which is the smallest of them?
It can't be 2. (p! + 1)/2 has a remainder of 1. So does (p! + 1)/3, (p! + 1)/4, and all the way up to (p! + !)/p. So the smallest prime factor of (p! + 1) must be larger that p itself. The assumption that p is the largest prime number leads to the conclusion that p isn't the largest prime number.
How does Anselm's reductio work? A fully satisfactory answer to this question isn't exactly simple, and not just because Anselm's prose is difficult. But the idea appears to be this: The argument depends on a definition of sorts. Anselm says of God:
Now you might protest that you don't use the word "God" in this way. But that doesn't really matter. If Anselm can show that such a being exists, then he has shown something remarkable whatever you call the being. Furthermore, it isn't clear why anyone should resist calling such a being God.
But now another worry may occur to you: conceivable by whom?
The answer is: conceivable by anyone, no matter how imaginative or brilliant. In fact, what Anselm really seems to be after is the greatest possible being, though he proceeds in terms of what we can or do conceive. Here, in fact, a possible difference between the phrase "greatest conceivable being" and "being than which none greater can be thought" can help straighten out the confusion. Suppose my powers of conception are limited. The greatest being I can conceive of would not be a being than which none greater could be thought. On the other hand, no one could conceive of something greater than the greatest possible being.
In fact, the issues here are a bit tricky. Some philosophers think that Anselm's argument could work with no reference to our understanding. Others disagree. But let us proceed.
The atheist, Anselm points out, can understand the phrase "being than which none greater can be thought." Therefore, God is in the atheist's understanding. But just because something "exists in the understanding," we would not normally conclude that it also exists in reality. As Anselm himself points out, a painter may have the completed work of art in his mind, but that doesn't make it a real painting.
What Anselm tries to show next is that in this case, having an idea in the understanding requires one to admit that the thing exists in reality as well. For suppose that God exists only in the understanding. Then we can conceive of a greater being: one who exists in reality as well. And that would mean that this God who exists only in the understanding is not the greatest conceivable being.
But now we have a contradiction.
Compare: a Euclidean triangle has various features. One is a matter of definition: a triangle has three angles (and three sides). To say "I saw a triangle that didn't have three angles" would be to contradict oneself. Other contradictions are less obvious but equally real. A (Euclidean) triangle has an angle sum of 180 degrees. Anyone who says that some Euclidean triangles have an angle sum other than 180 degrees has said something contradictory, even though this is not simply obvious.
Now come to the case of God. The GCB would have to be wise, because a wise being is greater than a being who is not wise. And the GCB would have to be just, because justice is better than injustice. What Anselm is claiming is that the GCB must also exist, because a being that exists in reality is greater than one that exists merely in the understanding. So:
That, in essence, is Anselm's proof. However, he goes a bit further and the further bit is very important for all that follows. He writes:
But this creates a puzzle. Anselm begins his proof with a quote from the Psalmist: " The fool hath said in his heart 'There is no God'." How could the fool (or anyone else) think such a thing?
Anselm explains this by way of a distinction. In one sense, to think something is simply to think the corresponding words. In another sense, to think it is to understand what it means. The fool can't think God's existence in the second sense; no one can. But he could do so in the first sense. Compare: I can say "There is a largest prime number." But if I really understand the words "There is a largest prime number" I will recognize that they must be false. So the fool says what he says only because he is using the words without thinking about their meaning. The point of Anselm's proof is to lead the fool (and us) through that meaning to the understanding that God must exist.
This is Anselm's argument. In the next set of notes, we will consider the earliest criticisms of it.
© Copyright Allen Stairs 1998. All Rights reserved.
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