Anselm’s argument begins with a statement of what God is:
“Now we believe that You are are something than which nothing greater can be thought.”
This definition is not supposed to assume that God actually exists; it is supposed to be rather like a definition of Pegasus as ‘the winged horse of myth.’ We can define Pegasus as the winged horse of myth without assuming that Pegasus exists; all that we are saying is that if Pegasus exists, then it is the winged horse of myth.
Anselm then imagines a character, ‘the Fool’, who denies that God exists. But, Anselm notes, this Fool must surely at least be able to understand the proposed definition of God, just as I can understand the proposed definition of Pegasus, even if I do not believe that Pegasus exists. He says:
“But surely, when this same Fool hears what I am speaking about, namely, ‘something-than-which-nothing-greater-can-be-thought’, he understands what he hears, and what he understands is in his mind, even if he does not understand that it actually exists.”
Similarly, we might say that Pegasus is in my mind, even if I do not think that the winged horse of myth actually exists.
Anselm compares the case to that of a painter executing a painting. A painter might have a certain image in mind before realizing it on the canvas. Before the painting, it is only in his mind; after the painting, it is both in his mind and on the canvas. Just so, Anselm is arguing, the Fool should admit that God - the thing than which no greater can be thought - exists in his mind, but not in reality:
“Even the Fool, then, is forced to agree that something-than-which-nothing-greater-can-be-thought exists in the mind, since he understands this when he hears it, and whatever is understood is in the mind.”
But, Anselm argues, at this point the Fool is in an unstable position, and must admit that God not only exists in his mind, but also exists in reality:
“And surely that-than-which-a-greater-cannot-be-thought cannot exist in the mind alone. For if it exists solely in the mind even, it can be thought to exist in reality also, which is greater. If then that-than-which-a-greater-cannot-be-thought exists in the mind alone, this same that-than-which-a-greater-cannot-be-thought is that-than-which-a-greater-can-be-thought. But this is obviously impossible.”
Anselm is arguing that the Fool has contradictory beliefs. On the one hand, the Fool admits that that-than-which-a-greater-cannot-be-thought exists in the mind. On the other hand, the Fool is claiming that that-than-which-a-greater-cannot-be-thought does not exist in reality. But if that-than-which-a-greater-cannot-be-thought does not exist in reality, then there is something which can be thought of which is greater than that-than-which-a-greater-cannot-be-thought: namely, that thing existing in reality. But this would mean that there is something which can be thought of which is greater than that-than-which-a-greater-cannot-be-thought, which is a contradiction similar to “John is taller than the tallest man in the world” (if he were, he would be the tallest man in the world, and he is not taller than himself).
Anselm’s argument is difficult to follow. And if it is difficult to follow, it is difficult to evaluate. One good way to make arguments easier to follow, and easier to evaluate, is to break them down into a series of claims. We can then evaluate the claims, and the transitions between them, one by one. But to do this, we will first have to understand something about what sort of argument it is.
Suppose that you want to argue for some claim -- say, the claim that I am mortal. The easiest way to do that is to give some premises from which that claim follows. For example:
| 1. | All men are mortal. (Premise) |
| 2. | I am a man. (Premise) |
| C. | I am mortal. (Follows from 1 & 2) |
This argument seems to be valid, since the truth of the premises would guarantee the truth of the conclusion. And it also seems to be sound, since, in addition, the premises seem to be true.
But there is another less direct way to argue for a claim, which is sometimes called reductio ad absurdum, or just reductio. In this sort of argument, we begin by assuming the opposite of the claim we want to prove, and show that from this claim something absurd follows. This shows that the opposite of the claim that we want to argue for is false, and so that the claim we want to argue for is true.
Here is a good example of a reductio, from Jim Pryor’s notes on ‘Philosophical Terms and Methods’ (http://jimpryor.dyndns.org/teaching/vocab/index.html). Suppose that a scientist produces a computer program which he claims to be mathematically guaranteed to win every game it plays, no matter whom the opponent. Suppose that you want to show that the mathematician’s claim is false: that is, the claim that you want to argue for is that the mathematician’s program is not mathematically guaranteed to win every game that it plays. One good way to argue for this claim would be to reduce its opposite to absurdity, as follows:
| 1. | The mathematician’s computer program guarantees victory in every game of chess, no matter whom the opponent. (Premise to be reduced to absurdity) |
| 2. | If the mathematician’s program is put on Computer 1, then Computer 1 will win every game of chess it plays. (Follows from 1) |
| 3. | If the mathematician’s program is put on Computer 2, then Computer 2 will win every game of chess it plays. (Follows from 2) |
| 4. | The mathematician’s program could be put on both Computer 1 and Computer 2. (Premise) |
| 5. | Computer 1 and Computer 2 could be matched against each other in a game of chess. (Premise) |
| C. | There could be a game of chess in which both players win. |
Here we can see right away that the conclusion of this argument is false: the rules of chess are such that it can never be the case that both players win. We know further that the conclusions of sound arguments are always true; so we know that this argument is not sound, and must either be invalid, or have a false premise. It appears to be valid, so one of the premises must be false. There are only three independent premises: 1, 4, and 5. One of these three must be false; but 4 and 5 each seem uncontroversial. So 1 must be false: it is not the case that the mathematician’s computer program guarantees victory in every game of chess. And this is the result that we were trying to establish.
This example nicely illustrates that it is sometimes much easier to argue for a claim via a reductio than by direct argument.
One good way to understand Anselm’s argument is as a reductio ad absurdum, where the claim to be reduced to absurdity is the Fool’s claim that God exists in the mind, but not in reality.
Here is one way to present Anselm’s argument as a reductio:
| 1. | God is that than which nothing greater can be conceived. (Definition) |
| 2. | God exists in the mind, but not in reality. (Premise to be reduced to absurdity) |
| 3. | Existence in reality is greater than existence in the understanding alone. (Premise) |
| 4. | It is conceivable that God exists in reality. (Premise) |
| 5. | It is conceivable that there is a being greater than God. (Follows from 2, 3, and 4) |
| C. | It is conceivable that there is a being greater than that than which nothing greater can be conceived. (Follows from 1 and 5) |
The problem is that (C) is clearly false. So there must be a problem in the argument which led to it, since sound arguments cannot have false conclusions. Anselm’s idea is that the problem with the argument which leads to (C) is that (2) is false: God exists in reality, as well as in the mind.
If one wants to deny that God exists, one has to do one of two things: argue that the conclusion (C) is not in fact false, or show that there is some problem other than (2) with the argument which leads to (C). Since the first option is not very promising, let’s explore the second.
There are two things that might be wrong with the argument: it might be invalid, or one of its premises might be false. (These are, remember, the two ways that an argument can be unsound.)
First, consider the possibility that the argument is invalid. If it is, then one of its two logical steps must be invalid. The step from (1) and (5) to (C) is clearly valid. So the only possibility is that the step from (2), (3), and (4) to (5) is invalid. To test this possibility, let’s consider an analogous logical inference:
| 2*. | Bob is 5’10” tall, but not 6’ tall. |
| 3*. | Being 6’ tall is being taller than being 5’10” tall. |
| 4*. | It is conceivable that Bob be 6’ tall. |
| 5*. | It is conceivable that Bob be taller than he is. (Follows from 2*, 3*, and 4*) |
Is this argument valid? Is it of the same form as the argument from (2), (3), and (4) of the original argument to (5) of the original argument? Is (5*) true or false? Is it ambiguous?
Suppose that the argument is valid; we can still ask whether it is sound. If you want to find a false premise, you can’t choose either (5) or (6); they follow from other premises. It also looks unpromising to challenge (1), since this is just a definition. This means that if one wants to challenge the soundness of the argument without questioning its validity, one has to deny either (2), (3), or (4).
Can (2) be challenged? Is it plausible to deny (3)? How about (4)?
(If you are interested, you can find more discussion of Anselm’s argument and its descendants in Alvin Plantinga, God, Freedom, and Evil, and in the entry on ‘Ontological arguments’ in the online Stanford Encyclopedia of Philosophy.)