First order logic, set theory and God

[Belacqua]

That's the hook of -every- argument from cause.  Assert a rule or set of rules for no purpose other than to assert some x to break them.

Certainly not. 

The Aristotelian/Thomist causal arguments have nothing breaking any rules. The argument is that everything that has a cause is caused by something other than itself. Nothing in the chain breaks this rule. 

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

Back to what, and how do you know when to stop?  

In causal arguments, you stop when you get to something that hasn't been caused. 

If it seems like turtles all the way down.., why not go with that...why not accept some form of infinitism?  That's one way out of manchhausens trilemma.   Otherwise, what are we doing?   Saying, "it seems like that..but...no..not that, anything but that".

It might be an infinite regress. dron3 promises that Hatcher's argument avoids such a regress, but I haven't figured out how it does that yet, if it really does. 

Aquinas said he could not demonstrate that a per accidens series was not infinite in regress, but he did think he could show that a per se series must culminate in a first mover. So if you'd like an answer to your question you could work on those arguments. If it turns out that they're wrong, you'd at least be able to say why.