Scott does an excellent job of explaining what's involved in the two types of inference. To sum up, he writes:
When the argument form is inductive rather than deductive, the information in the conclusion is actually new, and there is no guarantee that it is true even if all of the premises are true.
Inductions, then, are ampliative in the sense that they claim something above and beyond what the premises claim. Deductions, by contrast, are non-ampliative, because their conclusions do not state anything different from what the premises collectively tell us. Doctrine develops only deductively, not inductively hence, doctrine develops only in a non-ampliative manner.
The difficulty with that distinction is that, even if it's exhaustive in principle, it does not distinguish among different sorts of "induction" and therefore cannot tell us what would be distinctive about ampliative DD, if there is such a thing.
In the lingo of logicians, "inductive" inference is any type of inference that is valid, in principle and for certain purposes, but not strictly deductive. The most common sort of induction is inferring that the future will, in this or that respect, be like the past. Thus, e.g., we infer from our past experience that the sun will rise tomorrow. That's so safe an inference as to be just about ironclad. You can count on it. But from the fact that the sun has always risen each morning in the past, it does not deductively follow that it will do so tomorrow; and several billion years from now, if the astronomers are correct, the sun will cease to "rise" at all, its expansion as a red giant having vaporized this planet.
Others inductions we naturally make are somewhat less safe than that the sun will rise tomorrow. Thus, if we observe fifty ravens and find they're all black, we infer that the next raven we observe will be black too. That inference seems as safe as the first; but given the phenomenon of genetic variation, it's not quite as safe. And of course one can go down the line, identifying inferences that are progressively less and less safe objectively, but still so natural as to be almost inevitable. In my case, one example would be that the next time I check my bank balance, it will be less than I would have anticipated. I've gotten pretty good at tricking myself out and refining my inferences accordingly.
Now I consider it fairly obvious that some, perhaps even much, DD is ampliative and thus "inductive" in logicians' lingo. To take my favorite example, that the Son is homoousios (of the same substance) as the Father does not follow by strict deduction from the testimony of Scripture, the Apostles' Creed, and what the various liturgical rites of the early Church all had in common. If it did, then all it would have taken to refute the Arians decisively, once for all, would have been a logical proof of the sort that had long before been provided for, say, the Pythagorean Theorem in geometry. But that didn't happen, and it wasn't just because the orthodox weren't clever enough to do it. Such proofs, if and when possible at all, are notoriously difficult to produce in theology precisely because the objective meaning of the relevant premises is not entirely clear to everybody who holds them, unlike those supporting the Pythagorean Theorem, which are pellucidly clear to anybody of a certain mental age. That is because, in doctrine and theology, we're dealing with revealed mysteries, which are not products of the human mind or corresponding features of the natural world. Thus, what seemed obvious to the orthodox under the guidance of the Holy Spirit, and rightly so, did not seem at all obvious, but rather false, to others who claimed in all sincerity to accept the same prior media of revelation as normative. The difficulty is one of interpretation; and the sources do not interpret themselves.
Now the homoousios, if the product of valid induction, is not the result of the sort of induction we usually make. One cannot conclude that the Son is of the same substance as the Father in the same way as one can conclude that the sun will rise tomorrow or that the next raven one sees will be black. But it is a kind of inference. What kind?
I can't think of a name offhand, but I believe I can see the pattern in the unfolding of divine revelation itself. Consider how Matthew 1:23 cites Isaiah 7:14 to support the claim that Jesus was born of a virgin. Matthew was relying on the Septuagint translation of the Hebrew Scriptures into Greek, which uses the term parthenos, meaning "virgin," to translate Isaiah's almah, meaning "young woman." Why that translation? After all, not all virgins are young women and not all young women are virgins. Perhaps the "seventy" Jewish scholars in Alexandria who produced the LXX believed that the Messiah would be born of a literal virgin; but then, perhaps not. We really don't know. They may simply have chosen parthenos as a decorous synonym for 'a young woman' with the implication that the Messiah would be her first-born. At any rate, we have no evidence that first-century Jews assumed the Messiah would be born of a literal virgin. There doesn't appear to have been any consensus among Jews about how to construe Isaiah 7:14 on this particular point. Yet Matthew, or at least the early Church that received his Gospel as canonical, seems serenely confident that it prophesied that Jesus the Messiah was born of a literal virgin.
This is but one instance of how the New Testament in general treats the Old Testament. The NT even has Jesus himself explaining "the Scriptures,"—i.e., the works comprised by the LXX—as referring to him in various ways that either the original authors of the Scriptures or their audiences do not seem to have had in mind. So if Christianity is true, then the material sense of those Scriptures is far broader than what they formally say. The full material sense—what Scripture scholars call the sensus plenior—is formally brought out only in light of later events, reflections, and interpretations. And that, I believe, is how a great deal of DD also proceeds even after the complete divine revelation was fully given to the Apostles. The process of coming to understand the deposit of faith, given once-for-all to the saints, recapitulates the unfolding of divine revelation itself during the long period leading up to and including "the Jesus event."
Accordingly, if such controverted doctrines as papal infallibility and the Immaculate Conception are instances of authentic DD, they are so because they are derived from the faith-once-delivered in a way very similar to how christology is derived by the NT from the OT and by the first several ecumenical councils from the NT and other early Christian sources. They are not strictly deducible from what everybody professed formally in common during the first millennium of Christianity; they formally express what was there all along, to be sure; but they could not be derived, by any means generally acknowledged as logically reliable, from what was there all along. I don't think 'induction' is quite the right term for that. I can think of no better term than, simply, 'ampliative inference'.
