Define God as that than which nothing greater can be conceived.
A formulation of Anselm’s argument is as follows:
Call “that than which nothing greater can be conceived” G.
- If G fails to exist in reality, then there exists an x in the understanding such that x is conceivable and x is greater than G.
- Suppose toward a contradiction that G fails to exist in reality.
- By 2, there exists an x in the understanding such that x is conceivable and x is greater than G, which is a contradiction.
- Hence, G exists in reality.
The argument relies on there being two kinds of existence: existence in the understanding and existence in reality. That there should be two kinds of existence is dubious and needs external justification.
Zalta analyzes Premise 1 of the argument:
Suppose the antecedent of Premise 1 is true. There are two cases where this happens:
(a) If G fails to denote, then Premise 1 is false by rules for definite descriptions.
(b) If G denotes, but G does not exist in reality, then the consequent of Premise 1 is false since it contradicts that G denotes.
In the case that the antecedent is false:
(c) If G denotes and G exists in reality, then Premise 1 is true, but it begs the question.
There is an alternative formulation of the argument, more faithful to the text:
- G exists in the understanding.
- If G fails to exist in reality, then there exists an x in the understanding such that x is conceivable and x is greater than G.
- Suppose toward a contradiction that G fails to exist in reality.
- By 2, there exists an x in the understanding such that x is conceivable and x is greater than G, which is a contradiction.
- Hence, G exists in reality.
References
- Paul Oppenheimer, Edward Zalta, A Computationally-Discovered Simplification of the Ontological Argument. https://mally.stanford.edu/papers/ontological-computational.pdf
God Anselm of Canterbury Ontological Argument Definite Descriptions Edward Zalta