The first premise begs the question, of course.

There's also a difference between conceiving of the greatest possible in vague, abstract terms, and understanding all the properties of such a being. My point was that even atheists can say the words, "the greatest possible being" and understand their English meaning. That's not to say we know everything there is to know about such a possible being, or even that we've analyzed the concept and concluded that it's coherent.

It's like understanding the idea of the largest frying pan. Maybe there's one in the Guinness Book of World Records. Maybe someone could make one just a little larger than that one. Maybe a structural engineer could explain how a frying pan beyond a certain size would be useless or counterproductive, in which case we'd have hit the upper limit.

But even without that analysis, we'd still have a rough idea of what it would mean to have the largest frying pan. It would be the one that's bigger than all the others.

More specifically, the idea of the greatest possible being is about the most real being, the one that underlies everything else. So it's just another way of speaking of God as the First Cause.