To begin, let me say that I agree with Dr. Liccione that it is unlikely for there to be any knock-down experimental test that will distinguish among the three. And I agree with Dr. Carson that abduction requires that "you already know a lot of stuff," which is to say that there is a background of factual knowledge. The reason that I have proposed an abductive model is that ISTM that the situation is therefore very similar to what we often encounter in physical science, which is that we are convinced that there is some objective reality behind observables, that we have instances of observables, but that we have no obvious way to test what is "behind" the observables so as to distinguish between the theoretical understandings. When one encounters this point in science, one doesn't ordinarily give up, particularly when there might be some possible way to distinguish among theories in the future or where there is some substantial practical value in proceeding even when you aren't quite sure why it works (I'm thinking specifically of medicine there).
Now a substantial difference arises, and it is worth quoting Dr. Carson's well-considered criticism here:
Add to this mix the fact that abduction, like induction, is an inference pattern that is aimed at explaining empirically observable phenomena, not at unpacking the meaning of assertions. It is intended to connect observables with hypotheses, not to make clear the semantic content of previous utterances. Furthermore, abduction, like induction, always requires an inference to something new. That is, the conclusion of an abduction, like the conclusion of an induction, is a linguistic representation of a fact that is not contained in the premises.
If that's true, then I concede that the completeness of revelation necessarily requires that "this immediately rules out both induction and abduction as an inferential pattern by means of which the Church may explain her teachings, since both provide conclusions in which something new is asserted, as I pointed out above." But what I would suggest is that "a linguistic representation of a fact that is not contained in the premises" should instead be "a linguistic representation of a fact not known to be contained in the premises." What I hope to make clear is why that distinction is meaningful after a quick diversion.
The diversion is to say that I am not making hay to build what I know to be a straw man. It seems that every time anyone starts speaking rigorously about doctrinal development in the Catholic tradition, he is immediately accused of reducing the Christian kerygma to dogmatic propositions, of buying into an Enlightenment-based/Cartesian desire for epistemic certainty, of replacing the Christian faith with a propositional idol, or more commonly, of all three of those things at once. I don't think either Dr. Carson or Dr. Liccione are doing anything of these things, and I find most of those accusations ridiculous. My point here is not to share some warm, fuzzy, hippy-dippy sentiment about the love of God being SO much bigger than what we can express in words blah blah blah. 'Nuff said.
On the contrary, what I have in mind is a much "harder" version of epistemic uncertainty, analogous to what we have in science. It is intended to respond to the frequently-made charge that Catholics have no more certainty than anyone else because we ourselves are not infallible in our interpretation of Catholic dogma, and further, even those in authority are not infallible in knowing the principles behind their authoritative decisions. Probably the most glaring example is the large portion of the bishops at Nicaea who signed on the doctrinal statement with extensive mental reservations, arguably interpreting the statement in a way entirely compatible with Arianism and incompatible with what would later become recognized as Nicene orthodoxy. Nor is the Pope himself infallible in terms of holding a "key of knowledge" so that whatever he says is authoritative not only insofar as it was made binding but also in terms of the particular reasons given, as was made clear by Pope John XXII. So the infallibility of the Church is not of the sort that implies infallible propositional knowledge of the content of revelation, as counter-intuitive as that conclusion might seem.
So if even the people who author the dogmas and propose them as definitive and irreformable don't know the principles behind them in their fullness, then what sort of principles are we talking about? The reason that I draw the analogy to science is that the infallibility of the Church is similar to the infallibility of the law of non-contradiction in science, which is to say that reality can't be self-contradictory. Likewise, the mind of God is not self-contradictory, meaning that God's revelation is not self-contradictory. But as in science, what we see are particular events, and those are primarily rejections of heresies as being destructive, negative propositions in some particular context. Newman's pithy statement is best: "No doctrine is defined until it is violated." The circumstances of this collision, the particle tracks they leave, form the data from which we attempt to discern principles.
I believe the analogy is apt even for the Catholic Church in the objective sense, whether or not one happens to accept (as I do) that this is defined in terms of communion with the Holy See. This is because, if we accept that revelation is real and complete without entailing full comprehension of the dogmatic principles involved, then the revelation in question must be akin to the operation of physical laws is the cosmos in terms of uniformity and consistency of operation. Like those physical laws, the principles of operation of the Church, the normative guidelines for behavior, have always been evident in what She does and how She operates. But what we directly see is what has happened in some or another situation, just as we might try to discern the biological principles in an organism in its response to stimuli.
When I speak of the Catholic HC as being abductive, I mean it in this sense of taking fixed points and positing the principles behind them. What I mean to say is that if the hypothetical structure is based on papal authority, ascribing dogmatic significance to papal decisions and illuminating principles thereby, then what emerges are clean, explanatory principles for not only distinctively Catholic events but also numerous others. Just as theories of common descent and physical unification theories explain more by taking on more to explain, so the Catholic HC is capable of cleanly subsuming not only what it uniquely sees as authoritative but also the other Christian HCs do.
On that reading, simply trying to figure out "what the texts say" or "what the author intended" is inadequate, because what is really necessary is an explanation for why the texts exist in the first place. Why did the Christian community do this thing and not that thing? The underlying normative principles driving the action of the Church never change, but the question is our understanding. In that respect, our understanding assuredly can become better, even if the object of study never changes. In that respect, I sympathize entirely with those Scripture scholars who have adopted a more communitarian and less author-centered approach to Scripture (like the late Fr. Raymond Brown), but where they have gone astray is in their disregard for the supernatural in their science. They have moved their vision from identifying the principles of operation of the Church to studying narrowly mundane explanations, and thus, they have ceased to be students of Sacred Scripture, instead studying the mere Bible.
I would then interpret the closure of public revelation in the same way I would interpret the uniformitarian assumption in science. Whatever principles of operation (which might be accurately called divine energies) were operational in the Church were entirely established by the death of the last Apostle. Indeed, I would argue all such principles were documented in Scripture even if it was not immediately apparent why this or another event was so documented (such as John's vision of the Queen of Heaven in Revelation as a precursor of the Assumption). Every action of the Church qua Church is according to a divinely directed principle established from the beginning, and just as there is no such thing as half a principle, there is no such thing as divine action mixed with error.
I think this notion of finding and unifying principles is at least at home with the account of faith given in question 1 of the Second Part of the Second Part of the Summa along with the account of sacred science at the very beginning. Unlike the Apostles, we do not have the extraordinary wealth in experience of spending every day observing the actions of Christ and having our lives directly ordered by Him. Consequently, we have to muddle through synthesis and analysis of propositions (which are themselves only ulteriorly related to the unseen object of faith itself) in order to get a hazy understanding of what was presented to them as an immediate unity, although still short of the beatific vision. Even with respect to Scripture, however, the Angelic Doctor notes that even the manner of writing truths in Holy Writ requires a level of study that is frankly unattainable to many people and that much of Scripture is revealed with an ulterior purpose to illuminating some other doctrine, which isn't going to be clear without a clear vision of the unseen object of faith. What is provided to us with assurance is that there *is* such a sense, that all of the articulation does genuinely assemble the parts coherently (if we submit to them), just as the law of non-contradiction is the self-evident basis of our confidence in the physical sciences.
With respect to distinguishing as among the three hermeneutical circles that Dr. Liccione mentioned (Catholic, Protestant, and Orthodox), I agree that there can be no absolute adjudication between them, because there's is no rational argument that can compel submission by faith to the dogmatic premises. What is possible, and this is where I think I am somewhat more optimistic about the prospects, is that one can investigate what best accomplishes that sense of unification. The criteria are subjective; there is no denying that, nor could there be unless the conclusion were to be rationally compelled. But I think there is a reasonable basis for thinking that Catholicism is the best explanation for the particular dogmatic events of Christian history in that it contemplates from the very beginning the inclusion of the normative principles that cause the particular modes of rejection of heresy.
In my view, Catholicism provides a system that takes for granted the lack of immediacy to the Apostles AND the inevitable failures of human reason with respect to keeping a coherent, organized, unified picture of faith intact. Therefore, it was proposed from the very beginning to have a corrective for these things rather than depending on a bundle of propositional truths that can't possibly be maintained in perfect integrity given real human beings and the limitations of reason. Heresies and schisms will always introduce new fractures, and unless there is a built-in reason for thinking they will be repaired, there's no reason to think they will be short of the eschaton or that there is anything that can't break or isn't already broken (Scripture included, contradicting Christ's own testimony that it can't be). That argument is essentially neutral with respect to the truth of the premises; it simply looks at the mechanism of operation and the degree of reliance on ad hoc providential intervention.
What concerns me about denying the effectiveness of these sorts of techniques is that it would seem to suggest that there is no useful illumination provided by the same sorts of techniques that we use in physical science or other areas. There's no question that we're far along enough at this point that there are three dominant Christian theories, but people still have to be able to articulate the relative superiority of their theory for its chosen purposes, even if it isn't going to persuade adherents of the others. Otherwise, what's it all for? So I think that if we can at least start with some basic principles identified for divine revelation, much like the scientific conviction in the "unreasonable effectiveness of mathematics" and experimental devices, we at least have a common platform for communicating. If there's no reality in which we can point to the same objects and say that they're the same things, then I'm not sure how we stay away from religious discussions turning into a kind of rambling pseudo-science that (unfortunately) is what the general view of religion and metaphysics is.