What do you think of this argument for God?

[SuperSentient]

That is the main problem with it, why assume this "greatest possible being" is necessary? If we do, then it is pushing the concept into existence, which can be done with nearly anything.

However, it does not ride on the idea that anything is possible, but bases itself on whatever is possible.

Then if you don't hold to the idea that "anything is possible" you will have to accept that the actual possibilities of reality may not include the "God" that this argument is trying to define away.

Haha, you got me there, after I typed this:
Accepting that the actual possibilities would not include God would be a contradiction since God in this case by definition is whatever the greatest possible being (remember premise 1) is. Like what I said before, the "greatest possible being" would be the manifestation of all logical possibilities, so it would be nonsense to say that the actual possibilities of reality may not include the manifestation of all logical possibilities. 
The last sentence of the two proves your point, so I have two main options:
1. Retract my claim that the "greatest possible being" is the "manifestation of all logical possibilities"
2. Retract that Premise 5 follows from Premise 4 and then this argument essentially falls apart.

---

It assumes logic exists independent of Humans and their rationality. A contradiction would be impossible to exist, and so does not exist in any possible world. 
All logical possibilities would be manifested in God and all logical impossibilities wouldn't.

Logic may well exist independent of humans, but logic is just a way to go from assumptions to conclusions.

I guess another assumption made would be that all objective logic is absolute.