First order logic, set theory and God

[Belacqua]

The objection is that it's sloppy...haven't even gotten into why the notion of parts is antithetical to first causes.  Is the first cause some -part- of the universe?  What would observations of parts of wholes tell us about something that is not supposed to be a part of anything, itself?

Yes, I was thinking about this just now actually. How do the three Ps inevitably lead to God (who is typically supposed to NOT be a part of this natural reality) as a first cause? I'm guessing there's a point behind P2 that I may have missed ... otherwise, the 3 Ps fail as a collective to prove a first cause God must exist.

The point to P2, if I'm reading it right, is that we can't pick an arbitrary point in an essential chain and declare that that's the cause of what follows on. 

When the OP wants to talk about the First Cause, it requires that we follow the essential chain all the way back. 

So let's say we've got all the car parts. And this is a Marvel Universe movie, so the car parts have some kind of flying nanotech, and when Tony Stark pushes a button they fly together and make a car. Someone might then say that the causal chain begins with the parts and ends with the car. 

But P2 won't let us do that, because the parts are caused, in their turn, by several things. 

~ Material cause: steel and nanotech
~ Formal cause: design
~ Efficient cause: Tony Stark
~ Final cause: to whisk Gwyneth Paltrow to safety

But I think P2 demands we go back even further, because Tony Stark depends for his existence on causes. Per accidens, he exists because of his parents, grandparents, etc. Per se, he exists because of organic matter and the laws of biology that allow him to exist. And then we follow back: what caused the laws of biology, etc. 

That's a bit silly, but applied to the real world it's important. 

Someone might say that a quantum flux started the whole universe. They would say that the causal chain begins there and continues through what we have now. But if we agree to P2, we're not allowed to begin at this arbitrary point, where something was already there. There was obviously  something quantum there which could fluctuate. More importantly, there were already laws of nature which meant that when the quantum flux occurred, it resulted in a universe. OK, the quantum flux was caused by a previous quantum flux, and pretty soon it's turtles all the way down. 

dron3 promises that Hatcher's proof avoids this infinite regress dilemma. I am hoping to figure that out soon.

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The point of p2 was to arbitrarily, and incorrectly (again, as rahn commented in that same post) exclude all other causes that could very well be one of the essential whatsits from consideration.

That's not correct. Rahn is not understanding the argument.