I am not decided on the issue. What I will do here is attempt to work out a consistent and non-absurd scenario in which moderate empiricism is true and we come to know it. After developing an account, I will see if it holds water. I'll be happy to receive improvement suggestions. Note that I am at best familiar with the discussion.
I. Suppose moderate empiricism is true. Here is a relaxed, impressionistic attempt at formulating it: Our only source of justification for matters of fact (and not of definition) comes from repeated interaction with reality. I suggest that a creature inhabiting this scenario could conceivably learn about its brain, its reasoning capabilities, and features of the world it inhabits in general. Then it could infer moderate empiricism as the best explanation for what it has learned.
Of course, the creature could only do that if it knew (or was epistemically justified in believing) that its explanatory judgments are reliable, i.e., that the theories they judge to be great explanations are very often true. How could this occur?
If there couldn't be any simple set of experiments to confirm them, then the creature could learn of the reliability of its own explanations by observing that they very often lead to predictive theories.
Quine proposed something similar to account for how we are justified in believing certain fundamental statements in mathematics, logic, epistemology, and metaphysics, but not justified a priori. His point is that these statements are central to the way we reason when interacting with reality, and that since we interact successfully with reality, it must be because they reflect something of reality. The argument given for the creature's explanatory practices above follows a similar trail.
Finally, the creature's modes of explanation could conceivably lead it to discover moderate empiricism. It is difficult to work out how, since it would require spelling out what kind of evidence would call for moderate empiricism as the best explanation. However, all I needed to show is that basic tools of reasoning could be justified in a moderate empiricist scenario. This opens the possibility of arguing we do live in this scenario. Have I at least suggested how such showing could be done?
II. The problem with the above account is that it does not seem the creature could get off the ground. The creature in question would need to employ a set T1 of reasoning tools in getting from (a) its immediately-known empirical knowledge that, by using a set of reasoning tools T2, it has come to be a successful predictor and controller of reality, to (b) the conclusion that tools T2 are truth-conducive. Having established 'b', the creature would be many steps closer to being justified in the conclusions it draws out by employing T2.
Yet, a b-like statement is necessary for having epistemic justification in employing any set of reasoning tools. Thus, a b-like statement for T1 would need to be obtained (probably from an a-like statement that mentions it). Yet, that would require a previously-justified set of reasoning tools T0. Since this obviously leads to an absurd regress, it follows that the creature has no justification for any of the tools of inference it employs, and so no justification in drawing out its conclusions!
So it seems it cannot learn about moderate empiricism after all. It cannot learn about anything it does not immediately perceive. Perhaps it can barely do any interesting empirical psychology (which Quine thought was integral to empiricist epistemology), since it cannot immediately perceive many of the entities and mechanisms postulated in good psychological theories.
III. Could the above conclusion be averted for the creature? I can imagine three possibilities.
(1) Perhaps the tools' reliability can be discovered non-inferentially. Maybe just observing them work in varied situations, plus the fact that they do work, is already direct acquaintance with their truth-conduciveness. It needn't be inferred using tools of reasoning, and so regress does not surface.
(2) Perhaps a moderate coherence theory of justification is correct. Given a web of beliefs full of direct observational knowledge of the world, and given that the web is stratified by tools of reasoning, the mere fact that it managed to stay consistent, let alone coherent, is already an immense signal that such tools are correct. Coherence theories have been developed, AFAIK, in which an agent can acquire justification from coherence without being previously justified in believing the coherence theory. (The agent needn't even know that its set of beliefs is coherent or consistent, given objectively correct standards of coherence and consistency.)
(3) Maybe a holistic theory of justification is correct, and a creature's belief-system obtains justification as a whole when the creature employs it in engaging successfully with reality. This way, the reasoning tools the creature uses could acquire derivative epistemic justification, since they are an integral part of that web of beliefs.
The regress of section II might be avoidable given '1', '2', or '3'.
What do you folks think?