1.) If we can think of something better than X, then X is not God.
(The can indicates logical possibility for a informed knower. Said another way, our assertion of “greater” is assumed not to result from our ignorance. “Greater” is on any scale of greatness.)
2.) So God is that than which a better cannot be thought. (by contraposition)
“Can” keeps same meaning.
3.) If God had no existence outside our idea, in thinking of an existent God we would think of something better.
The argument assumes an ideal knower, that is, a being who knows his judgments about what can or cannot be the case are not the result of ignorance.