First order logic, set theory and God

[Paleophyte]

Space-time is logically necessary for everything else.

Yes, I think so too. If by "anything" you mean "anything that relies for its existence on space-time." We don't want to beg the question by beginning with the axiom that there is nothing else. 

Can you think of anything that can possibly exist without space-time? Do we even have an epistemological framework or did that go crunch along with the very logic we're trying to employ?

The first cause arguments work on whether we have to stop with the brute fact "space-time just exists, period, no further cause is required." Or whether it makes sense to argue that space-time, too, is caused. 

That appears paradoxical:

- Space-time requires a cause.
- Causality requires both space and time.

It's like asking for a chocolate chip cookie when neither chocolate nor cookie dough exist.

The Argument(s) from First Cause are lovely examples of why you can't apply "common sense" to the least common event in the history of history and expect the answers to make sense.

When you say "event," are you referring to the Big Bang?

More specifically the beginning of space-time that is the vital part of the Big Bang. Consider two scenarios:

A Big Bang in which there is no mass or energy. This is going to be more of a Dull Fizzle as space-time majestically unfolds to reveal a shit ton of darkness but it's conceivable.

By contrast, a Big Bang in which there is no space or time never bangs. The mass and energy don't even bother sitting there looking embarrassed. They simply don't exist with space-time.

All of this is ignoring brane cosmology, but that's so a far above my pay grade that I won't even pretend to understand it.