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).
One way to present Anselm’s argument in a more formal way is as a form of argument known as reductio ad absurdum (i.e., ‘reduction to absurdity’). The idea is that we can argue for some claim by showing that its negation involves an absurdity -- often, a contradiction.
Here is one way to present Anselm’s argument as of this form:
| 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) |
| 6. | 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 (6) 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 point is that the problem with the argument which leads to (6) 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 (6) is not in fact false, or show that there is some problem other than (2) with the arguments which leads to (6). 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 so, then one of its two logical steps must be invalid. The step from (1) and (5) to (6) 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?
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)?
(For more discussion of this version of the argument, see Alvin Plantinga, God, Freedom, and Evil.)