First order logic, set theory and God

[GrandizerII]

So ... now that I've fully read the OP, I went through the first two to three pages of this thread, and it turns out that first Jorm and then Khem/Gae already pointed out the one problem that stands out with the argument: that the first cause need not be a supernatural God, even if the OP decides to call it "God" anyway.

So Belaqua, you were being unfair in saying that no one effectively addressed the argument earlier.

Really, that was all that was needed to be pointed out. I admit on the basis of my full reading of the OP, my initial counterargument was overkill.

Early on, dron3 made it clear that the argument only addresses a first cause. To show that this cause is anything like a Muslim or Christian God demands lots of other arguments. 

I pointed that out too, as I recall. 

As to whether the first cause can be a part of nature, or has to be somehow outside of nature, that's a part of the argument. That's what all the talk about a whole system vs. a part of that system is about. If a natural object exists, then nature exists. But if nature already exists, then it can't be caused by nature. That's a pretty basic part of the premises.

The argument doesn't rule out a first cause that is eventually part of nature.

In fact, the OP explicitly stated that the first cause G is a component of the whole reality V, which contains all the other components G causes.