It is normal to talk of "inductive logic", as if non-deductive reasoning formed a branch of logic, with discoverable rules. But what if it is not so? What if the rules of inductive reasoning, unlike the rules of deductive logic, are merely "subjectively necessary", to use Kant's phrase? It is perhaps simply the case that our minds are hard-wired to think in certain ways inductively. This hard-wiring is truth-conducive, not for any deep logical reason (as in the case of deductive logic, where the validity of modus ponens, and the truth of excluded middle, etc. are all necessary truths), but simply because God created us with minds hard-wired to reason inductively in ways that match the arrangement of large segments of the world that he has created.
One can say some of this with natural selection in place of God, but natural selection will only yield the result that our minds' functioning matches the structure of the world in those respects that are relevant to the fitness of our evolutionary forebears—it will give us little or no reason to think that things will work out when we do cosmology or quantum mechanics.
If this is right, then we should not be surprised if one particular formalization of inductive logic—say, the Bayes-Kolmogorov probabilistic account—yields doxastic rules that some of our doxastic practices break, and are right to break. (See the previous several days' posts.) For the theistic story gives us reason to think that our inductive reasoning will get us to the truth, but does not give us much reason to think that our inductive reasoning can be formalized. If this is right, then working scientists may very well do better than ideal Bayesian epistemic agents, say, and be unable to explain their successes.
Probably, the epistemology that would go along with a view like that would have to be some sort of proper-function epistemology. But I am happy to leave that to the epistemologists—I am just a probability theorist.