In my view, as a conservative Christian, there are a number of problems with the Ontological Argument, as follows:
1. It assumes a hierarchical view of God, in which God is viewed as the greatest being in a pyramid of "greatnesses", hence we have the confusing term "maximal greatness".
But, Maximal and greatness are both English language words, right? wouldn´t English speaking people prima facie understand their basic meaning?
This smacks of a view of God consistent with a certain medieval view of the Church and society, but it is, in my view, incoherent.
The MOA is based on modern modal logic, and, Perfect being theology which is one of the mainstream models of God´s attributes, today.
God is the source of all greatness and goodness, and therefore, objectively, is the only being who can be said to be 'great' or 'good'.
There is no explicit contradiction from the argument to this principle.
A hierarchical view of God is elitist and thus oppressive
What ever this is, it is not a critique of the argument.
...and also seems to suggest that beings other than God can possess legitimate greatness independently of the greatness of God.
Talk about vague, what ever legitimate means, to you (can you justify that?), the argument is mute about it.
2. It is presented as an a priori argument, but the terms used are ill defined and vague. What precisely do we understand by 'greatness' and 'possible' as in the phrase "possible worlds"?
There is nothing ill defined about Maximal or greatness, these are common words, used by any competent English speaker, as well as Excellence.
And, possible worlds is a well known concept in modern analytic philosophy, we can not blame arguments for our failing in reading the relevant material.
And how are those definitions justified?
Read the material.
Please, justify this assertion: "An
a priori argument can only work if its terms are justified beyond any reasonable refutation."
Also, please, define the terms "reasonable", "refutation", "work","a-priori", "argument", "terms", and justify them beyond any reasonalbe refutation.
I take the assertion above meant as a universal principle, and, as such, clearly false.
Take Gettier cases as a counterexample of your assertion
They are a-priori arguments against a certain conception of knowledge, yet, with out having anything even remotely close to the term knowledge definition being justified beyond any reasonable refutation, Gettier cases are solidly sucessfull to command the whole of the field of epistemology in heoric efforts to develop a new more complete and correct account of knowledge.
To say that "
a priori argument can only work if its terms are justified beyond any reasonable refutation" commands no epistemic obligation.