Hello Tarski,
Do you have an independent reason to think that our anthropocentric notions of greater and better are objective?
No (not entirely), but if your concession for the sake of argument is taken seriously then yes. If you for the sake of argument concede the ontological argument is valid you have given reason to accept a correlation of our anthropocentric thoughts and reality. I am not alone in that conclusion here is Bertrand Russell:
The real question is: Is there anything we can think of which, by the mere fact that we can think of it, is shown to exist outside our thought? Every philosopher would like to say yes, because a philosopher's job is to find out things about the world by thinking rather than observing. If yes is the right answer, there is a bridge from pure thought to things; if not, not.
I do not concede that (for example Godel's) ontological argument makes it clear in what sense God is supposed to exist: abstract, platonic, physical etc.
It might not but Anselm's ends in a compassionate God after you have accepted existence. Godel's does create a necessary being, I don't know why that is trivial to you - because as I said that expands the cosmological argument it invokes intent and creator. Not trivial things.
Now Anselm's argument is worse and was not even on my mind. It is just too informal and dependent on imprecise anthropocentric notions to do the heavy lifting needed for a concept such as God.
Guilty of following your OP and thinking of my favorite.
Objections more telling than mine are easy to find. Seek and ye shall find.
Look, you posted the OP, "Consider your favorite ontological proof for the existence of God. Now assume for the sake of argument that it proves that some being "God" exists." Then you listed things we wouldn't know even if that was conceded. I answered you would easily know that "God" is a necessary being, that allows for other knowledge - I gave the cosmological argument for example. Now you tell me objections to the proof itself exist and I should seek them out? - well those were the very objections you shelved for the sake of argument?
A rock and the number Pi exist in two totally different senses. How many senses are there in total? Which one do we end up with?
Being was part of the defintion - concrete existence. Anselms Proslogion II answers these - and it is only valid if existence is proved which you conceded for the sake of argument.
But really now, are you really convinced by this stuff???
Convinced of what stuff? That if the ontological argument can indeed prove a concrete existent being maximally or the greatest to be conceived that we wouldn't be at ground zero as you seem to imply? Yes. Or, of the ontological argument from the very beginning (without your concession)? - not so much. But, I do believe in a verisimilitude and correspondence with personal knowledge and reality.
regards, mikwut
All communication relies, to a noticeable extent on evoking knowledge that we cannot tell, all our knowledge of mental processes, like feelings or conscious intellectual activities, is based on a knowledge which we cannot tell.
-Michael Polanyi
"Why are you afraid, have you still no faith?" Mark 4:40