- God exists in the understanding but not in reality.
- Existence in reality is greater than existence in the understanding alone. (premise)
- God’s existence in reality is conceivable. (premise)
- If God did exist in reality, then He would be greater than He is. [from (1) and (2)]
- It is conceivable that there is a being greater than God is. [(3) and (4)]
- It is conceivable that there be a being greater than the being than which nothing greater can be conceived. [(5) by the definition of "God"]
- Therefore, it is false that God exists in the understanding but not in reality. (by contradiction)
pp. 87-88. Plantinga, Alvin. God, Freedom, and Evil. Grand Rapids, MI: Eerdmans Publishing Company, 1978.
Anselm makes the implicit assumption that his definition of greatness is transitive, without demonstrating this to be true. Without transitivity, a set does not necessarily possess a greatest element. Consider, for example, a chess club consisting of three players: A, B, and C; for which A consistently defeats B, B consistently defeats C, and C consistently defeats A. There is in this case no greatest chess player.
Anselm also assumes that his set under consideration (all entities existent or conceivable) contains its upper bound, without demonstrating this to be true. Without an upper bound, one can always produce an element greater than any other element. Consider, for example, the set of natural numbers: 1, 2, 3, . . ., with the traditional greater-than metric. This set has no greatest element, because it does not contain its upper bound, which is infinity.
Reality as Greater than Thought
Anselm makes the assumption that an entity that exists in reality is implicitly greater than one that exists in thought. Though a plausible assumption, I believe Anselm should spend more time defending it. Consider, for example, the proposition that the greatest entity is a thought about a thought. (Or a thought about a meta-thought, . . . and once again we see the problem of upper bounds.) This, too, is a valid assumption, one that is also quite tempting to assert.
Anselm also fails to adequately define a metric for the differentiation between reality and thought. While he assumes a God in reality is greater than a God in the imagination, would a worm in reality also be greater than a God in the imagination?
Attributes of God
Anselm assumes, without any prior explanation, that the greatest entity must necessarily have those properties which he attributes to God, such as omnipotence and omniscience. This is an entirely arbitrary assumption.
By changing these assumed properties, one can manipulate this argument to say the exact opposite. Consider this reasoning:
- Clearly the greatest conceivable evil should be that which can triumph over the greatest conceivable good.
- Follow the steps of Anselm’s argument to prove the existence of a being so evil that it can utterly destroy God.
Or consider the following “proof”:
- The maximally great square is necessarily round, since roundness is an attribute of perfection.
- Follow the steps of Anselm’s argument to prove the material existence of a maximally great square which is round.
Infinite versus Greatest
Anselm also assumes that, for each of the properties he attributes to God, the notion of greatest automatically entails total. His proof claims to demonstrate that God exists, possessing the greatest power, knowledge, etc.; but then he jumps to the conclusion that God possesses exhaustive power, knowledge, etc.
Anselm’s argument assumes without prior cause that the greatest entity is itself invariant with respect to time, and is never superceded by some other greatest entity over time.
I believe that Anselm has at most succeeded in proving that the universe (as a whole greater than any portion thereof) exists.
I believe that his primary mistake is in trying to subject God to physical reality, rather than realizing that reality and logic are themselves reliant upon God for their existence. He assumes that God exists in reality, whereas reality, in a sense, exists in God. Thus, his argument fails in that it is circular; by assuming God’s existence, he has claimed to prove it. Sadly, though the God of his assumption is the glorious and transcendent God that is the author of reality, the God of his proof is a lesser God, subject to and entirely contained within material reality.