Question

As I understand it, the ontological proof goes like this: we define / conceive of a reality than which no greater can be conceived, and we call that God.
Now we ask whether this reality also exists in actuality (and not only in our minds). If the answer is yes, then God exists. If the answer is no—meaning that there does not actually exist a reality than which none is greater—we run into a contradiction, since we are able to conceive of a greater reality, namely the actual existence of such a reality (for actual existence is greater than the idea of a reality than which none is greater). Therefore, it must be that there exists a reality than which no greater can be conceived.
In this argument, we define God as: (a) a great being, and (b) the greatest one possible (none greater can be conceived).
1. What is missing here is an explanation of in what sense this reality is great—physically? morally? Seemingly, “great” has no meaning unless we say in what way it is great. I am inclined to assume that the meaning here is capability, and then the argument is that there exists a reality that is greatest in capability, and nothing is greater than it in capability.
2. My problem with the proof is this: since we are dealing with a relative concept of greatness, all it proves is that there exists a reality that is the greatest (= none is greater than it), and that seems obvious, because any discussion revolving around a relative concept like greatness already assumes that there are several degrees of greatness (after all, “great” has no meaning without “small”). So all that is proved is that if we are talking about a being to which greatness applies (in whatever sense), then necessarily among the beings to which greatness applies there is one that is the greatest (because, as stated, this is a relative concept that presupposes the existence of several degrees of greatness).
There is no proof here that it is omnipotent, or morally perfect, or possesses any absolute excellence at all—only a proof that in any discussion about beings to which greatness in some sense applies, there exists a greatest being (just as there exists a smallest being). And this could also exist within our physical reality (a person who has the greatest ability). How does this prove the existence of an omnipotent spiritual being or any exalted being whatsoever?