In the ontological argument, Anselm assumes that "A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind". Isn't this a very big assumption? He hasn't even defined properly what greatness is. He should 1st define what greatness is and then logically prove that assumption from his definition. If someone claims that "A being that exists as an idea in the mind and in reality, other things being equal, has the same greatness as a being that exists only as an idea in the mind", how will the defenders of ontological argument argue against it?
I haven't read about Gödel's ontological proof and other more rigorous ontological arguments. Do they have similar axioms/assumptions which are not reasonable?
Even if we assume the ontological argument; does it say anything about God except the fact that it is maximally great? Can ontological arguments tell anything about the number of maximally great beings?
For example, I can claim that the universe and laws of physics are the maximally great beings and the universe and laws of physics are gods and therefore they necessarily exist.