First order logic, set theory and God

[The Grand Nudger]

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. 

By assertion, Bel.  

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.

The inability to demonstrate that any candidate per se cause does not itself resolve into yet another per se cause without resorting to a circular argument or an axiomatic argument (since we're ruling out regressive arguments).

Cutting through all of this, we do not reject regressive cause because it cannot be, but because regressive cause is not amenable to our system of rational inference - that system being built on finite observations.  If regressive cause is the true state of affairs....it simply can't provide us with the terminus of conclusion we so desperately seek.  It's a limitation of logical systems with respect to their intended purpose, not a limitation of reality.

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Just read the rest of the OP and, surprise to say, it isn't that complicated.

These cause arguments never are.