Kalam

[emjay]

If God is the uncaused cause, as neo-Thomists and others assert, then his existence has no reason.  His existence is simply a brute fact. 

And if God's existence has no basis in reason, then there is also no reason to assert he is the solitary uncaused cause.  He may very well be one of many uncaused causes.

That's fair, but theists will make a distinction here between an arbitrary and non-arbitrary brute fact. In the case of the latter, they tend to label that as metaphysically necessary instead. When it comes to the First Cause as postulated by Thomists, it would be hard to argue for it being an arbitrary brute fact, considering its voidness of any distinctions and it being strictly absolutely simple. Whereas with a universe like the one we inhabit, it would be hard to argue for it perse being a non-arbitrary brute fact. And if we can have any trust in our intuitions whatsoever, then it would be more preferable rationally to go with a non-arbitrary brute fact (or metaphysically necessary) over an arbitrary brute fact. As such, Thomists (and theists in general) probably have the upper hand here when it comes to the matter of brute facts, unless you're willing to go for a radical atheistic worldview that may avoid the problem of arbitrary brute facts.

The First Cause concept is sort of a hard thing to counter, partly because of how intuitive it is. Nevertheless, there are some relatively strong arguments against it, such as that which invokes existential inertia (something exists at time t because it existed prior to t and there is nothing else at t to prevent its existence).

I haven't been interested in debate much these days with theists, but if I ever did want to argue with a Thomist, I'd challenge them instead on something else related to their theology, namely how they could reconcile a triune God of distinct Persons with the absolutely simple/indivisible First Cause, in addition to other Christian beliefs held by Thomists borne out of revelation instead of logic. I think this is where the many weaknesses of their worldview lie.

Interesting. I've been thinking about that a lot lately; the difference between their brute facts and our brute facts, or put another way their fundamental stuff and ours, and yours is as eloquent an answer to that question as I've ever seen, ie arbitrary vs non-arbitrary. But it still leaves the (rhetorical) question for me... is that enough...   does that excuse it from having to explain its own existence so to speak? And my answer so far being, I don't know. Ie it being logically deduced may make it less arbitrary with regard to us (ie the universe... 'creation'), but it doesn't make it any less arbitrary the other way round, regarding its own eternal existence as something-not-nothing.