Wednesday, December 20, 2006

Again With the Non-ampliative Inference!

Dr. Mike Liccione of Sacramentum Vitae has taken issue with my post Further Notes on Ampliative and Non-ampliative Inference. In particular, he wants to dispute my claim that doctrine always develops, when it develops, in accordance with deductive rather than inductive principles. If he is right, then doctrine will develop ampliatively (in my sense of the term). I'm not altogether sure I follow his reasoning, but assuming that I do at least to a certain minimal extent, here is what I would say in reply.

To begin, I'm not sure that we are really talking about precisely the same situation. Consider the following, from Mike's post:
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.
Technically, the term "validity" refers to a property that applies strictly to deductions only, so it seems to me one of two things is going on here. Either Mike is using the word "valid" in a non-technical sense to mean something along the lines of "rationally warranted inference" or else he has something rather unorthodox in mind when he refers to an inductive inference. Since he goes on immediately to give a perfectly orthodox example of an inductive inference, I must assume the former.

So far, so good: after many years of teaching logic I know only too well that most people, when they say that an inference is "valid", do not intend to say that it is valid in the technical sense. Most folks are happy just to say that they think they can see where a particular inference comes from, and that is generally what they mean by the word "valid". Technically, every inductive inference is invalid, since it is always possible for the truth of an inductive inference to be false even if all of the premises are true. For this reason we do not characterize inductive inferences as either valid or invalid; they are characterized rather as being either strong or weak.

This is an important point, because nobody is claiming that inductive inferences should not be persuasive--a well-constructed induction should have certain properties that persuade rationally disposed hearers to believe its conclusion to be true with a certain degree of confidence less than 100% but greater than, let's say, 50%. But there is a huge difference between persuading somebody that a particular claim is true and proving that it must be true of necessity. Only a deductive inference can accomplish the latter, and only when it is sound (that is, it is valid in form and all of its premises are indisputably true).

My claim in Further Notes was that doctrine only develops in accordance with deductive principles. I confess that at least part of the motivation behind my claim was political in an ecumenical sense: I want to set at ease the hearts and minds of those Orthodox who worry that the principle of the development of doctrine warrants introducing radically new (and possibly heretical) belief-statements into the corpus of beliefs that must be held de fide. I think that this is a "valid" worry (non-technical use of "valid" here), and it is one that I share. The difficulty with any and all inductive inferences is that they are subject to (often massive) underdetermination, that is, the evidence can never establish the truth of any particular inference to the exclusion of all competing, non-consistent inferences. This is not a situation in which we want to find ourselves when trying to discover what must be believed de fide.

Certain kinds of scientific realists have suggested that this worry is overblown. They characterize certain kinds of inductive inferences as having far greater warrant than others. In order to give a certain cache of respectability to this claim they have actually come up with a special name for this kind of inductive inference: abduction. An abductive inference is one that is supposedly more likely to be true than its competitors, even though the same evidence is available to all candidate inferences. It is sometimes called an "inference to the best explanation" on the grounds that it posits an explanation that is inherently more plausible than its competitors. For example, suppose I find little teeth-marks in the chunk of cheese on my kitchen counter, and I hear little scratching sounds in the walls, and I find little tiny turds all over the floor and counter-tops. Now imagine two explanations. According to explanation (A), there is a mouse in my house. According to explanation (B), my evil little brother is trying to freak me out and drive me batty by setting things up in my kitchen to make it look as though I have a mouse in there when he knows that I have a very important dinner party coming up. Both explanations are consistent with all the known (and knowable) evidence (assume that my little brother really is such a person as to do such a thing), yet (A) seems, somehow, more plausible than (B), if only because it seems less ad hoc. But an abduction is just an induction by another name, and it suffers from all the same problems that plague induction generally. I might commit myself to (A) only to discover that it was, indeed, my little brother all along, and nothing about the evidence itself favored (A) over (B)--the only thing that makes (A) more likely than (B) is a set of theoretical presuppositions that I bring to bear on the inference-drawing process itself.

Now, Mike suggests that there are, nevertheless, gradations of some kind among inductive inferences, and in particular he wants to claim that an inferential pattern that he thinks he has found in the Scriptures rises above the merely inductive to something like the abductive. He gives a rather intriguing example:
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.
I'm particularly concerned about Mike's claim at the end here, that the logic of deduction is always going to be something that just pops out and is obvious to everybody. Now Mike himself noted, in a post at his own blog, that he accepts Saint Anselm's argument in favor of the Filioque, and perhaps he means something non-standard when he says he buys that argument but when I say things like that I mean that I think that the argument works. Anselm's argument is a deductive argument, and it is laid out with what can only be characterized as anal-retentive precision and care, and yet it failed to persuade the Greeks. I do not think that it is the case that a deductive argument is always going to do the trick when it comes to "refuting" any particular inference, if all we mean by "refuting" is getting folks to acquiesce in our take on things. If he means something more technical by "refute"--if he means that the Arians were proven wrong, then of course they were refuted. They just didn't think that they were. In short, I think that the homoousios doctrine does follow by strict deduction. This is not to say that every premise needed for that deduction is made explicit in Scripture; some premises are themselves intermediary conclusions of other deductions. But the inference itself needs to be deductive or else there is no rationally compelling reason to believe it.

The notion of compulsion here is extremely important--it is not just a rhetorical nicety to stick in a word like that. Inductive inferences have a certain rational warrant to them--that is, if they are strong it is not irrational to accept them--but precisely because of underdetermination there is no compulsion to believe them--we may always question any inductive inference and in so doing we still act rationally. It would be irrational, by contrast, to question a sound deductive inference.

This brings me to a point that Mike makes a little later in his post. In fishing around for a description of the pattern of inference he is talking about he writes:
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.
The difficulty here is that this is not an inference at all, but an interpretation. While it is true that interpretation of data is a necessary condition on any inductive inference, it is of course also true that every deductive inference requires interpretation of data. So the fact that this pattern is to be found in the "unfolding of divine revelation" is insufficient to show that the pattern of inference involved in the development of doctrine is not deductive.

It's also worth pointing out that, in this particular case, anyway, we're dealing with scriptural claims, albeit claims separated in time. From our perspective, though, the claims of Scripture themselves do not develop, but rather our own understanding of their meaning does. To take just one of the more familiar instances of this sort of thing, consider the Church's teaching on usury. This is a favorite canard of the cafeteria catholic crowd that seems to take a perverse pleasure in saying that doctrine develops in a way that will ultimately result in new teachings on women priests, gay marriage, and a whole slew of other complaints-du-jour. It is precisely this sort of crap that a real principle of the development of doctrine must be well-constructed enough to avoid. Usury has always been condemned by the Church, but what the Church is willing or unwilling to count as an instance of usury is a prudential judgment that is contingent on certain economic and social facts. These facts, obviously, change over time, as economic and social conditions change. But the morality of usury itself never changes because it is not grounded in contingent judgments but necessary ones. (The same is true of torture, by the way, as I've pointed out in many posts. Check the archives if you're interested.)

How do we know that the Church is right about what counts as usury these days? We don't. Nor do we know for certain that capital punishment will never again be necessary for the defense of the common good. We know with certainty that usury is wrong, but we cannot know with certainty whether a particular rate of exchange is usurious in every possible case. But by becoming Christians we do place ourselves under the authority of others: we trust in the Church's authority to teach us in matters of faith and morals, even on those occasions (not rare, but not ubiquitous) when those teachings are grounded in contingent or prudential judgments. It may be in this sense that there is ampliative development of doctrine: once the deductions have been carried out, we require some authoritative source of interpretation. I said above that a sound argument cannot rationally be disputed, and a sound argument is one that is both deductively valid and its premises are all indisputably true. When was the last time you saw a premise that was indisputably true? Every premise is disputable in some sense. So in order for any teaching to be held with some degree of confidence, we must place our trust in some source of interpretive authority, and that source of interpretive authority is the Ordinary Magisterium.


Ap said...

Dr. Carson,

What about the Assumption of Mary? It seems to stem from the fact that she was the mother of God, that she was Immaculate, etc. I don't see a logical connection here. I see a probabilistic one though, which is pretty much what induction is.

DimBulb said...

You need an equalizer to balance all these ampliatives.

Vitae Scrutator said...


That's a very good question. In the case of dogmata like the Assumption, Immaculate Conception, etc., I would have to appeal to the fact that, although only explicitly declared de fide very recently, the beliefs are themselves very old. Indeed, it is possible that they go back to Apostolic times, though the historical evidence for that is very thin.

They are certainly plausible, which is what I take it you have in mind when you say that the connection to them is "probabilistic", but the semantic content of them cannot be merely probable, in my opinion. The Papal definitions are supposed to summarize, not a new doctrine, but the evidence for believing that these teachings are very ancient and reflective of the sensus fidelium.

In other words, I take it that the dogmata you mention are not cases of the development of doctrine in the first place, but are rather instances of something else--the teaching office of the Church declaring infallibly what must be believed. These are not teachings that developed in the sense under discussion, but that have always existed and have recently been carefully defined for the faithful (in this case "defined" does not mean "stipulated").

There's probably a better answer than that that I could give, but I hope that's a good enough start to get the discussion going.

Vitae Scrutator said...


Fortunately, mine goes up to eleven.

Ap said...

Dr. Carson,

Kinda late here so let me make it quick. I think there is a distinction between development of doctrine and development of our understanding of doctrine. For example, a development of doctrine would be "logical" conclusions from premises or other doctrines. Hence, Jesus is God and Mary is the mother of Jesus. Therefore, Mary is the mother of God. In a sense, we can term it "propositional development." Then there is development of our understanding. Because of our life in the liturgy, work, and prayer, we have come to understand what original sin is and how it relates to our weakness of will and so on. It may not be as explicit and well-developed before Augustine, yet, it was "there" and we have just discovered it. Let's call this "doxastic development." I think your argument is that the IC and Assumption is an example of doxastic development and not propositional development, that is, we have only understood it fully today as taught by the Extraordinary Magisterium but it was there in the beginning. That is how I understood you. However, I don't see how the Assumption, even though it is always there in the beginning (since they are historical events), is not an example of propositional development since the event or dogma is justified from the fact that Mary is the mother of God. The predestination of Christ and Mary as the mother of God is one predestination. And in this predestination comes grace and favor which includes the Assumption. So in that sense it is a development. It also seems that the propositional development is how it came to be doxastic development. We first learn that Mary is the mother of God and then we therefore know that she is favored, and we have developed original sin first, and we understand that Mary is free from this, and so on.

Also, I don't see why development of doctrine cannot be inductive. This does not mean that one can make up developments out of no where. One can, for example, speak of development through high probability given a set of doctrines and philosophy, theology, etc. And by "probability," I did not simply mean plausibility. A premise can be plausible although cannot be shown to be probable (ex. I know I have a hand). If we take E to be evidence, A for Assumption, B for background info.,

P(A/B&E) = P(A/B) * P(E/B&A) / P(A/B) * P(E/B&A) + P(~A/B) * P(E/B&~A)

Suppose E contains the fact that Mary is the mother of God, IC, God's love for Mary, historical testimony, etc, After calculating it, it may very well be that P(A/B&E) is say .7. In that way we can see how it is developed. But it may be in another possible world where P(A/B&E) may not be .7, that there is another evidence, say, Mary's body in a grave which would make P(A/B&E) low. So it seems to me that the Assumption is not probable in that world. This shows that there is no logical development here, but only probabilistic one.

Finally, although I understand your point about not inventing new doctrine, do we really have to only hold on to deduction? Why can't we say that in order for us not to invent new doctrine, the probability of an asserted doctrine must be high given the evidences that we have?

CrimsonCatholic said...

I think that there is also a Magisterial role that is inductive, making an induction that was strong (perhaps even abductive) theologically certain.

Given what Dr. Carson pointed out about the Assumption, the Immaculate Conception might be a better example. It was admitted even by its proponents merely to be metaphysically possible. The reasoning given by William of Ware was potuit, decuit, fecit (God could do it; it was fitting; He did it). St. Thomas objected to the potuit part, but his objections were rebutted. But surely, even if those objections are overcome, this can't possibly be a deductive argument, only strongly inductive. And it can't have been something simply known from ancient times; not even the proponents claimed that to be the case.

And yet, the Immaculate Conception is dogma. I don't understand how that can be unless the Magisterium has some latitude to make some inductive arguments binding.

Mike L said...

I've got a rejoinder to this post up at my own blog.

Homily for Requiem Mass of Michael Carson, 20 November 2021

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