Some Notes on Explanations and Inference

In some of the literature in the philosophy of science you can find a term of art that is sometimes alleged to refer to a special variety of inference that is not deductive in form but that is supposedly stronger than mere induction. The term "abduction" is due to Charles Sanders Peirce, a 19th century American chemist, mathematician, and logician who, along with William James, is credited with making seminal contributions to that distinctively American style of philosophy known as pragmatism. Abductions, he maintained, represent a kind of scientific inference involving explanations intended to connect samples to populations. Suppose, for example, that I have a small pond in my back yard, and I decide to do some fishing there one day. I spend the whole afternoon pulling small bass from the pond and putting them into a bucket, and at the end of the day I take my catch home and put the bucket on the front porch. Along comes my buddy Earl, who is in charge of stocking my pond. He sees the bucket and my fishing equipment and reasons to himself, "All of the fish in this bucket are bass; I stocked that pond over yonder myself with nothing but bass, knowing that there were no other fish in it; hence, the fish in this bucket must have come from that pond over yonder."

Peirce claimed that this is not a typical induction, because instead of reasoning from sample to population ("The fish in this bucket are all bass and came from that pond, hence that pond is stocked mostly with bass") or from population to sample ("That pond is stocked mostly with bass, so the probability of pulling bass from it is greater than the probability of pulling other kinds of fish from it, and that's why this bucket is full of mostly bass"), an abduction infers a certain relationship between a sample and a population. Peirce envisioned the scientific method as starting with abductions (basically, the "educated guessing" that goes into hypothesis formation), continuing with deductive inferences connecting an initial hypothesis to possible experimental results given certain initial conditions, and finally to hypothesis modification in light of new evidence. In his mature philosophy Peirce used the word "induction" to refer to this entire methodology.

Now imagine the following scenario. I come into my kitchen one morning to find that the big hunk of cheese I left out last night has little bite marks in it, and there are bits and pieces of it all over the counter, along with tiny little black things that look like the sort of chocolate sprinkles one gets on ice cream. As I stand there looking at the cheese, I hear a strange skittering and scratching sound coming from the kitchen wall. I reason to myself this way: "My little brother is always trying to lamplight me--obviously he has messed around with my cheese and sprinkled little chocolate sprinkles all over the counter and even now he's in the next room scratching on the wall to make me think that there's a mouse in my house." In comes my wife, who looks around, hears the sounds, and says, "We've got a mouse in the house."

Two possible explanations, but presumably they can't both be right, so which one is the "best" explanation? Abduction is sometimes called "inference to the best explanation", since one hopes, when formulating a scientific hypothesis, that one is "guessing" correctly about what will adequately explain the observable phenomena. In the case of my kitchen scenario, there are certain sorts of tests my wife and I could do to try to distinguish the one hypothesis from the other as a contender for the "best" explanation (e.g., see if my little brother is in town; check for mouse holes; see if the "chocolate sprinkles" are really made of chocolate), but to do so would be to move away from the stage of abduction and into the stage of deductive testing. The thing about abduction is that it takes place at the beginning of the investigative process, not in the middle or at the end, so what is the normative criterion at play in an abduction?

By "normative criterion" here I mean, what mark do we use to distinguish a good abduction from a bad one? Notice that in the kitchen scenario the question I posed was about which abduction was the best explanation, not which abduction was the best qua abduction. Presumably, the procedure to find out which abduction was the best explanation would have involved testing; what I'm asking here is, what sort of criteria would go into forming an abductive inference in the first place? It seems to me that in the kitchen scenario, the abduction that I came up with is clearly not as good as the one my wife came up with, but what marks that difference? Why is mine not as good as hers, and how can we know the difference independently of any testing? Someone might say something like "Your wife's abduction was better because it was simpler: it only involves a mouse, which many houses have; it does not involve a weirdo brother trying to lamplight you, which has got to be a lot rarer. In short, in similar sorts of cases, it seems much more likely that the mouse would be the cause than that a weirdo brother would be the cause, since the one cause is far more common than the other."

This sort of answer just reduces abduction to a post-inductive inference based on evidence. That is, it treats an abduction as a case of reasoning from population to sample (in the world overall, there are far more mice than there are weirdo brothers, hence it is more probable that this scenario was brought about by a mouse"). Can the same be said about the fishing scenario? Suppose Earl's brother, Homer, was with him when he found the bucket of fish, and when Earl tried to connect the fish to the pond, Homer responded by saying "No way, Earl, them fish was bought at the Wynn Dixie just this mornin', and they's a settin' there 'cause the boss is fixin' to cook 'em later today on yonder grill." In this case, again, we can imagine methods of testing the two hypotheses (see if Wynn Dixie sold a bucket o' bass recently; ask the boss where he got the fish), but the question isn't about how we can find out which one really is the best explanation, but rather how we can tell, from the get go, which one is better as an abduction, as an attempt to come up with the best explanation. In this case, however, the question is complicated by the fact that both explanations seem plausible in a way that just wasn't the case in the kitchen scenario, where one of the explanations seemed quite possible, while the other one seemed downright nutty, and it was easy to choose between them.

What does any of this have to do with anything? Believe it or not, I've been thinking about this in light of some posting at Sacramentum Vitae and Crimson Catholic on the development of doctrine. Both Mike Liccione and Jonathan Prejean seem to think that when doctrine develops, it does so abductively. Possibly all they mean by this is that, when doctrine develops, what the Church is trying to do is to come up with the "best explanations" for its doctrines. Indeed, Mike explicitly says that this is what he means:

I have long argued that a species of induction, namely "abduction" or "inference to the best explanation," is the standard form of DD's context of justification—as distinct from its context of discovery, which cannot and should not try to eliminate the charismatic element. It is the quality of the abduction, seen in light of the analogia fidei and thus to some extent charismatically, which suggests the difference between mere theological opinions and development of the Church's collective understanding of the DF.

If the "context of justification" means something like the texts that are used to promulgate and explain the church's teachings, as opposed to the actual process by which the content of those teachings is revealed to the church, then there is something of a mystery here, since abduction is not a method of justification in this sense but the beginning point of a method of discovery that seeks to explain. Perhaps the term "justification" is what is giving me trouble: what is meant by it, precisely? I tend to think of "justification" as encompassing such things as the giving of reasons with the aim of proving or "justifying" some claim or other, but this is not what an abduction is. When I posit the existence of a mouse in my house, or decide that a bucket of fish came from a pond, I am not trying to justify anything in that sense, I am trying to figure something out, to put together some pieces of a puzzle that are not linked by any matters of necessity.

Therein lies what I take to be a very important difficulty. Deductive inference always ensures truth when the premises are true; abduction, like induction, can offer no such assurance. Indeed, an abductive inference is as likely to be wrong as to be right unless one makes antecedent assumptions about what is more plausible. A mouse is more plausible than a weirdo brother--who would dispute that? But which is more plausible, a pond or a store, and who determines which is more plausible, who lays down the normative criterion?

Mike suggests a number of healthy criteria:

In general, explanations are evaluated in terms of a certain set of criteria: e.g., consistency (is the explanation consistent with what we already know?), capaciousness (does it cover everything that calls for explanation?), parsimony (does it avoid making assumptions and positing entities beyond what's necessary?) and other criteria depending on the subject matter.

As he quickly notes, however, such criteria are largely subjective. (He doesn't actually use the word "largely", but he ought to have.) Hence, an arbiter is needed even of the applicability of the normative criteria. This faculty he grants to the sensus ecclesiae, a deus ex machina if ever there was one from an explanatory point of view. On this sort of a view, there are almost no constraints on what sorts of "abductions" will count as normatively better than others. I say "almost" because, of course, formal contradictions are ruled out even on a subjective reading of the criteria, since there's really no nuancing that sort of thing. But it's not always all that easy to tell when to assertions are formally contradictory. In the end, Mike may be right about the role of the sensus ecclesiae, but not, I think, in quite the way he intends, if he intends that role to be part of an abductive process.

"When you hear hoof beats in Central Park, don't expect zebras." That piece of advice, sometimes given by Gregory House to his ducklings, seems to sum up the problem pretty well. When it comes to formulating abductive inferences, you have to already know a lot of stuff. You need to know already that there are no zebras in Manhattan, but that there are horses, even though it is a huge urban area with no large game to speak of. You have to know that Central Park is patrolled by police on horseback. In short, you have to already know what the relevant components of the explanation are before you formulate them as an abductive hypothesis. The only reason why "horses" is a better explanation of the sound of hoof beats in Central Park than "zebras" is, is because "horses" is the right answer. But there is literally no reason to believe that it is the right answer, independently of already knowing the facts I mentioned above: there are no zebras in Manhattan, but there are horses, and the cops ride them in Central Park.

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. This is one of the principal differences between inductive and deductive inference patterns, and it is why inductions, unlike deductions, can never guarantee the truth of their conclusions--just as abductions cannot.

Suppose we were to take a typical case of what is sometimes called the "development of doctrine", and ask whether the doctrine, as developed, represents the conclusion of an abductive inference. We will see that there are a number of reasons why this should be worrisome. There are many good examples we could choose from--the doctrine of the Trinity, the procession of the Spirit from the Son--but let's look instead at one that is often cited in polemical contexts: the teaching on usury. This is a nice example because most Catholics can agree that God is a Trinity, and that the Spirit proceeds from the Son, but there are some Catholics who think that the teaching on usury has substantially changed over time, and in this they disagree with their own Church, which maintains rather that the teaching on usury has developed over time. So the notion of the "development of doctrine", in this polemical context, must be put up against a notion of "substantial change in teaching" which is somehow quite different from mere "development". If we are to make any sense out of the inferential process by which teachings "develop", we need to make some sense out of what the difference is supposed to be between "substantial change in teaching" and mere "development" of doctrine.

The claim that the teaching on usury has "changed", if I understand it correctly, amounts to the claim that the teaching has not merely new, but different semantic content than it used to have, and that the different content constitutes an explicit, formal contradiction of the old semantic content. That is, when people claim that the teaching on usury has changed, they think that, whereas the Church used to teach x, y, and z about usury, it now teaches either (~x & ~y & ~z) or ~(x & y & z). Either of these latter two assertions would formally contradict the first, so it may not matter which of them a particular critic of the teaching claims in that regard. In order to avoid this sort of thing, the person who claims that doctrine has merely developed must claim that, whereas the Church used to teach (x & y & z), it now teaches [(x & y & z) & p], where p cannot be formally analyzed into further assertions that would contradict x or y or z. To put it less formally, whatever the Church says about usury now, she must say it without taking back any of the things she used to say about it, hence, what she says now must be new and different from but also consistent with what she said before.

This is where the real arguing starts. The Church used to say that charging any interest whatsoever on a loan was usurious and, hence, sinful. Now the Church says that there are certain forms of lending in which it would not be usurious to charge interest, just so long as the interest rate meets certain criteria, hence not all lending at interest is sinful. The critics who claim that the teaching has changed say that the Church went from saying "All lending at interest is sinful" to saying "It is not the case that all lending at interest is sinful", and that is indeed a formal contradiction of the form (p & ~p). The defender of doctrinal development says that the Church now teaches, and has always taught, that "All usurious lending is sinful", but the prudential understanding (not the formal, de fide, teaching) of what the definition of "usurious lending" is has developed in response to the rise of a capital economy beginning in the 17th century. Hence there is no formal contradiction at all, only an explicit recognition of new historical conditions under which usuriousness is present only under certain empirically testable conditions, not all of which include the presence of interest on a loan.

Suppose we want to side with the defender of doctrinal development against the critic of the teaching. Shall we say that this new way of expressing the mind of the Church is "justified" by means of an abductive process? I hope not, because if that is what we shall say then we shall be saying that, upon discovering that lots of people, including many members of the Church, are indeed lending money at interest, the Church found it expedient to redefine "usurious lending" in such a way that it is no longer sinful, just as we decided to say that it was horses that we heard in Central Park rather than zebras when we realized that there are no zebras in Central Park, though there are horses. Since abduction, like induction, requires an empirical component, we are forced to admit that the only strictly empirical considerations impinging on the developed doctrine are the historical facts regarding lending at interest. What we would like to be able to say, by contrast, is that the Church has made her position with regard to the sinfulness of lending at interest clearer: in a capital economy, money plays an entirely different sort of role than the role it plays in a feudal economy, and lending at small rates of interest will not count as sinful because it does not impose anything like the burden that it would have imposed in a non-capital economy. In making our assertion, p, clearer, we never assert ~p. Rather, we assert, either some other proposition, q, which is not inconsistent in semantic content with p but which deals with the same subject matter as p, or we assert some other proposition r, which is derivable, in some sense, from p itself.

The expression, "in some sense", is, of course, hopelessly vague, but whatever else it might mean it certainly cannot mean "via abductive inference", for the reasons I've been rehearsing. Cardinal Newman, in the eighth, ninth, and tenth chapters of his An Essay in Aid of a Grammar of Assent, comes closer than anyone ever has, I think, to doing justice to what we need to mean by this expression "in some sense" in this context, in spite of the fact that he was by no means a professional epistemologist. He claims, first of all, that revelation was completed during Apostolic times, and this can mean only that no new doctrines can be taught by the Church; at most, the Church may express old doctrines in new ways. If Newman is right about this, 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. However, the inferential pattern need not be strictly deductive, either since, if we again assume that the Church is right to teach that not all lending at interest is usurious in a capital economy, this cannot be something that the Church has discovered by deduction, since at one time the Church taught that all lending at interest was, indeed, usurious (since at the time there was no such thing as a capital economy), and that is a direct contradiction of the proposition that not all lending at interest is usurious. They cannot both be the products of deductions working from the same premises, unless the premises themselves are inconsistent. The premises themselves, being the revealed content of our religion, had better not be inconsistent, or else our religion is just a bunch of hooey.

What has occurred, then, not only in the case of the Church's teaching on usury, but indeed in the case of the Church's teaching on slavery, the Trinity, the Procession of the Spirit from the Son, Papal infallibility, the Immaculate Conception--you name it--is that the Church has clarified the meanings of the premises in such a way as to show how it can be possible for two seemingly disparate teachings (all lending at interest is usurious; some lending at interest is not usurious) can nevertheless follow from the same premise set. Although the motivation for making this clarification arises from empirically observable facts about the world (there was no such thing as a capital economy before; now it is the norm), this process of clarification (reformulation and restatement) is not itself an empirical and, hence, not an abductive or inductive process. Since it is not a formal process, it is also not deductive. This process of clarification does not include admissions on the part of the Church that she just did not understand the premises the first time around, since that would allow for the possibility not only that the earlier teachings were just plain wrong, but also that the present ones are. In short, if there has ever been a time at which the Church herself did not understand the premises, then that time could very well be happening right now, and we have no reason to believe anything the Church teaches on the basis of her claims to authority, including the proposition that Jesus is God or, indeed, that God exists at all. The Church simply must be both infallible and consistent, otherwise the entire religion falls--there is no reason to believe in it at all, other than wishful thinking.

So a fundamental assumption of any Christian must be that the Church has always fully understood the "premises" she has been given, that is, she has always fully understood the content of the divine revelation. What changes is not that content or the Church's understanding of it, but the mode of expression the Church uses to communicate that content to the faithful. Here, by "modes of expression" I mean more than just the language and concepts that the Church deploys in exercising its teaching faculties, though those things are included in what I have in mind. I also mean something a little more complex, however, namely the change in empirically observable circumstances to which I have already alluded in the usury example. I can further illustrate what I have in mind by means of another example. The well-known phrase, extra ecclesiam nulla salus, which can be translated as "outside the Church there is no salvation", dates to the third century, a time when there was no such thing as Protestantism. Some twentieth century Catholics understood the phrase in a very literalistic sense to mean that, if you are not literally inside the Roman Catholic Church (i.e., if you are a Protestant or a Jew or an atheist or what have you), then you have no salvation, you are damned forever. The Second Vatican Council thus found it expedient to make clearer just what this catchphrase really means: it equates the concept of Salvation with the mystical understanding of the Church as the Body of Christ. As Augustine noted, just as being a member of the Church in the pedestrian sense of having been baptized does not guarantee salvation, neither does being outside of the Church guarantee damnation. The phrase means only that the Church and Salvation are one and the same thing: the Church makes Salvation possible simply by being what it is. Some regarded this "clarification" of the doctrine by the Council as evidence that either the Church was changing its teaching on salvation or that the Council was not really an Ecumenical Council--indeed, the two claims usually went together: the Council was not an Ecumenical Council precisely because it was tinkering with the Church's teachings on salvation.

Tinkering is one thing, but changing is something else. The point here is that a mistake was indeed made, but not by the Church. The mistake was made by those literalists who had misunderstood the Church's teaching on salvation in such a way as to think that the teaching demanded full-blown membership in the Church in the sense of being a communicant in good standing of some particular Roman Catholic parish or other. At the time the teaching was first articulated, such a misunderstanding was probably not possible, but whether or not it was possible it did not become a problem until relatively recently, hence the clarification, or "development", if you prefer. In short, the original statement of the teaching was directed at a particular audience in a particular time and place, and the clarification of the teaching is directed at a different audience at a different time and place. The difference is an empirically observable one, but the empirical facts only motivate, they do not enter into the formulation of, the clarification.

The problem is made rather complicated by the fact that sometimes people speaking in the name of the Church can make things seem less rather than more clear, but in the present instance the cases where this has happened only further illustrate the principal I am talking about. Popes and other bishops have said things in connection with this teaching that do, indeed, seem to contradict what the most recent Council has taught. One must then decide (a) whether there is indeed a contradiction and (b) if there is one, whether the voice of a single bishop speaking on his own, even the bishop of Rome, can outrank, as it were, the teaching of an Ecumenical Council. But even in some of the cases where it looks as though things are being made less clear rather than more clear, an argument can be made that things are not as straightforward as they seem because historical conditions are often not parallel to our own. The Bull Unam sanctam of 1302, often cited by enemies of the Council, makes the teaching clear enough. What critics of the Council tend to focus in on, of course, are the words "We declare, say, define, and pronounce that it is absolutely necessary for the salvation of every human creature to be subject to the Roman Pontiff". They take this in a very literal way to mean that, unless you are "subject to the Roman Pontiff" in the sense of being obedient to him as a literal member of the Roman Catholic Church, you are SOL. They don't even consider the possibility that there are different ways of being "subject" to the Roman Pontiff, and that a Protestant or a Jew or a Muslim is de facto subject to him whether they obey him or not, just as the atheist is subject to God whether he believes in him or not.

Was this what Pope Boniface VIII himself meant and intended when he promulgated the Bull? Intentions are notoriously slippery things--it is, in fact, impossible to know what the real intentions of another person are with any certainty, even if he tells you himself what his intentions were, since he may have been mistaken about his own motivation. However, if Unam sanctam is difficult in this way, the words of Eugene IV in Cantate Domino, 1441, are crystal clear: "none of those existing outside the Catholic Church, not only pagans, but also Jews and heretics and schismatics, can have a share in life eternal." It seems difficult to mistake what this fellow intended to say, though he does go on to say that this fate can be avoided if "before death they are joined with [the Church]", but he does not elaborate on what he thinks are the necessary and sufficient conditions of being "joined" with the Church. Presumably he means getting oneself baptized, but he does not say so explicitly, thus leaving himself wide open to all sorts of interpretations. In any case, the polemical purpose of Cantate Domino is such that its entire purpose is open to multiple interpretations. From an empirical point of view, there may very well be historical conditions that inform what interpretation is more likely, which abduction really is the "best explanation" of what the particular fellow was trying to say. But from a doctrinal point of view--a point of view that of necessity must be distinct from such historical conditions precisely because the doctrine was already definitively settled during the Apostolic age--such empirical conditions cannot settle what it is that we must believe, since it is impossible for us to experience the empirical conditions that obtained at that time.

Who is it, then, that has the authority to decide which interpretations--whether of divine revelation or of the Church's own teachings based upon those revelations--are to be regarded as authoritative in a sense that is meaningful to us and to our historical conditions? Only the Church herself can have that kind of authority. If it seems to someone, whether inside or outside of the Church, that the Church is contradicting herself, he'd better have an airtight case. If, per impossibile, he does have such a case, he'd better leave the Church right away if he is in it, or stay away if he isn't, because a case such as that would show that the Church in fact has no authority at all.

Ultimately, then, the method, if it is one, by which the Church develops her doctrines is neither inductive, nor abductive, nor deductive, but merely authoritative. She makes proclamations, and the relationship between the semantic content of her proclamations, when they are authoritative, is always one of consistency, though not always one of full clarity, if by "full clarity" what one means is complete and full understanding on the part of the target audience. That kind of clarity comes through time as the Church articulates and re-articulates the same teachings to different audiences; as audiences change, so too must the articulations of doctrine. What seems clear to us today would not have seemed clear to an audience in Thessalonica in the 4th century, nor will it seem clear to an audience in Brazil in the 25th century. This is merely a feature of the evolution of human culture. But the Church's teachings do not evolve, so they must be explained and re-explained in such a way as to make clear the original intent of the original revelation in terms that can be understood by the faithful who must assent to them.

The work of individual pastors and theologians will certainly, on occasion, take the form of inductions, abductions, and deductions, but such work, all on its own, will never be authoritative and, hence, will never constitute any part of the process whereby the teachings of the Church develop. Instead, the corporate mechanism of the Church's teaching authority, the Magisterium, will incorporate or not incorporate such work as the Spirit moves it. How that happens is entirely beyond me, but I believe that it happens, otherwise I would be acting irrationally to remain in the Church. That teachings such as those the Church proposes must be accepted by faith should come as a surprise to no one; it is a sad feature of human willfulness and pride that it does surprise many to learn that the Church's authority to teach and to interpret must also be accepted by faith.