St. Anselm’s Ontological Proof for the Existence of God

1.	God is that-than-which-nothing-greater-can-be-thought. (definition)

2.	That-than-which-nothing-greater-can-be-thought exists in the imagination. (premise)

3.	What exists in reality is greater than what exists in the imagination.

4.	For all things that exist in the imagination, either they exist only in the imagination, or they exist in the imagination and in reality. (implied premise)

5.	If that-than-which-nothing-greater-can-be-thought exists only in the imagination, then there is something greater than that-than-which-nothing-greater-can-be-thought. (instantiation of premise 3)

6.	There can’t be something greater than that-than-which-nothing-greater-can-be-thought. (principle of non-contradiction)

Thus,

7.	It is not the case that that-than-which-nothing-greater-can-be-thought exists only in the imagination. (modus tollens 5,6))

Therefore,

8.	That-than-which-nothing-greater-can-be-thought exists in the imagination and in reality. (disjunctive syllogism 4,7)

Therefore,

9. God exists in reality as well as in the imagination. (Definition 1,8)