The Ontological Argument for the Existence of God

[Mudhammam]

I have never seen this argument before, so I'm interested in some discussion of it. A philosopher by the name of Alvin Plantinga states it this way:

The Ontological Argument

1. It is possible that a maximally great being exists.
   
2. If it is possible that a maximally great being exists, then a maximally great being exists is some possible world.
   
3. If a maximally great being exists in some possible world, then it exists in every possible world.
   
4. If a maximally great being exists in every possible world, then it exists in the actual world.
   
5. If a maximally great being exists in the actual world, then a maximally great being exists.
   
6. Therefore, a maximally great being exists.
   

Thoughts?

a) What does it mean to be "maximally great"? b) What does it mean to "exist"? (the thought of a "maximally great" circle exists... both in my intellect and in my imagination... but what does that mean? Does that satisfy the criteria of whatever it might mean for a "maximally great being" to "exist"?)