An Intuitionist's Response to St. Anselm's Ontological Argument (and Gödel's)

The ontological argument for God’s existence would seem to be a slam dunk for the rational theist. It is a straightforward proof by contradiction with extremely minimal axiomata. I will represent Gyula Klima’s formulation here. Take as our universe of discourse all things that can be conceived—or, in other words, all consistent, admissible concepts.

1. God is that thought object greater than which nothing can be conceived.
2. Any thought object which can be thought to exist in reality is greater than a thought object which is otherwise identical but is not thought to exist in reality.
3. Suppose that God can only be thought to exist in the mind.
4. Then there is a greater thought object, namely this God but thought to exist in reality.