Underexplored Epistemological Resources for the Cosmological Argument (and Other Arguments in Natural Theology)

Cosmological arguments standardly include a causal or explanatory premise, and proponents of cosmological arguments have argued that such premises are supported in virtue of being analytic or synthetic a priori truths, or via induction, or via claiming that they are presuppositions of reason. However, these bases are often criticized: they don't seem to be analytic or synthetic a priori truths; the sample size of evidence isn't sufficiently large or representative to support them via induction; they aren’t presuppositions of reason. 

But there are at least three more avenues of support for such premises that seem worthy of further exploration. The first has recently been explicitly appealed to, but so far as I know, the second has not:

(i) Reflective equilibrium: we have the data of our intuitions or reflective judgements about whether this or that particular case has, doesn't have, or must have a cause or sufficient reason for its existence or occurrence. We also have general causal or explanatory principles. And the goal is to eliminate the tension between the two by revising our judgements and our principles so that they are no longer in tension, but in harmony -- the cases reflect the principles, and the principles explain the cases. Perhaps it's worth exploring whether this can be done in a way that supports a version of  PSR or causal causal principle(s) sufficiently robust to play a legitimate role in a cosmological argument. Timothy O'Connor is one of the few exceptions who appeals to reflective equilibrium in his defense of the cosmological argument.

(ii) Phenomenal conservatism: the way things seem serves as at least prima facie pro tanto evidence for how things are. Therefore, if it seems to one that some causal or explanatory principle involved in a cosmological argument is true, then one could thereby receive (perhaps) sufficient support for the premise to accept it. I think William Lane Craig should take this route in his defense of the causal premise in his kalam cosmological argument, as well as his defense of a version of PSR in his Leibnizian cosmological argument (as opposed to his current "more plausible than their denials" approach, which Morriston and others rightly point out as inadequate).

 (iii) Inference to the best explanation: Perhaps the best explanation of the data of all the cases of caused or explained phenomena is some version of PSR (and not some weaker principle that doesn't require an inference to a necessary being as explanatory ultimate).

I of course don't mean to imply that the use of such epistemological resources is restricted to the cosmological argument. So, for example, they can be used to support arguments for atheism (Cf. Trent Dougherty's recent (devil's advocate) defense of the problem of evil in F&P, which employs something like phenomenal conservatism in support of a key premise).