Junia/Junias and the base rate fallacy

I think it would be useful to apply more Bayesian analyses to textual scholarship.

In Romans 16:7, Junia or Junias is described as “famous among the apostles”. Without accent marks (which were not present in the original manuscript) it is not possible to tell purely textually if it’s Junia, a woman, or Junias, a man. Moreover, “among the apostles” can mean “as being an apostle” or “to the apostles”. There seems to be, however, some reason to think that the name Junia is more common than Junias in the early Christian population, and the reading of “among” as implying membership seems more natural, and so the text gets used as support for women’s ordination.

This post is an example of how one might go about analyzing this claim in a Bayesian way. However, since I am not a Biblical scholar, I will work with some made-up numbers. A scholarly contribution would need to replace these with numbers better based in data (and I invite any reader who knows more Biblical scholarship to write such a contribution). Nonetheless, this schematic analysis will suggest that even assuming that there really were female apostles, it is more likely than not that Junia/s is one.

Let’s grant that in the early Christian population, “Junia” outnumbers “Junias” by a factor of 9:1. Let’s also generously grant that the uses of “famous among” where the individual is implied to be a member of the group outnumber the uses where the individual is merely known to the group by a factor of 9:1. One might think that this yields a probably of 0.9 × 0.9 = 0.81 that the text affirms Junia/s to be an apostle.

But that would be to commit the infamous base rate fallacy in statistical reasoning. We should think of a text that praises a Junia/s as “famous among the apostles” as like a positive medical test result for the hypothesis that the individual praised is a female apostle. The false positive rate on that test is about 0.19 given the above data. For to get a true positive, two things have to happen: we have to have Junia, probability 0.9, and we have to use “among” in the membership-implying sense, probability 0.9, with an overall probability of 0.81 assuming independence. So the false positive rate on the test is 1 − 0.81 = 0.19. In other words, of people who are not female apostles, 19 percent of them will score positive on tests like this.

But we have very good reason to think that even if there were any female apostles in the early church, they are quite rare. Our initial sample of apostles includes the 12 apostles chosen by Jesus, and then one more chosen to replace Judas, and none of these were women. Thus, we have reason to think that fewer than 1/13 of the apostles were women. So let’s assume that about 1/13 of the apostles were female. If there were any female apostles, they were unlikely to be much more common than that, since then that would probably have been more widely noted in the early Church.

Moreover, not everyone that Paul praises are apostles. “Apostle” is a very special position of authority for Paul, as is clear from the force of his emphases on his own status as one. Let’s say that apostles are the subjects of 1/3 of Pauline praises (this is something that it would be moderately easy to get a more precise number on).

Thus, the chance that a randomly chosen person that Paul praises is a female apostle even given the existence of female apostles is only about (1/13)×(1/3) or about three percent.

If we imagine Paul writing lots and lots of such praises, there will be a lot of Junia/s mentioned as “famous among the apostles”, some of whom will be male, some female, and some of whom will be apostles and some not.
All of these are the “positive test results”. Of these positive test results, the 97% percent of people praised by Paul who aren’t female apostles will contribute a proportion of 0.19 × 97%=18% of the positive test results. These will be false positives. The 3% people who are female apostles will contribute at most 3% of the positive test results. These will be true positives. In other words, among the positive test results, approximately the ratio 18:3 obtains between the false and true positives, or 6:1.

In other words, even assuming that some apostles are female, the probability that Junia/s is a female apostle is at most about 14%, once one takes into account the low base rate of women among apostles and apostles among those mentioned by Paul.

But the numbers above are made-up. Someone should re-do the analysis with real data. We need four data points:

• Relative prevalence of Junia vs. Junias in the early Christian population.

• Relative prevalence of the two senses of “famous among” in Greek texts of the period.

• Reasonable bounds on the prevalence of women among apostles.

• Prevalence of apostles among the subjects of Pauline praise.

And without such numbers and Bayesian analysis, I think scholarly discussion is apt to fall into the base rate fallacy.

The holiness of the Church and clerical scandals

Does gravely immoral activity by the clergy detract from the holiness of the Church as it is on earth, the Church militant? It sure seems so. But I want to argue, very speculatively (and I will withdraw the claim if it turns out that the Church teaches otherwise), that it directly detracts no more—or at least not significantly more—than equally gravely immoral activity by similar numbers of laity would.

Consider the three features we desire the Church as found on earth to have: doctrinal orthodoxy, liturgical integrity and holiness of life.

The doctrinal orthodoxy and liturgical integrity of the clergy does indeed especially contribute to the doctrinal orthodoxy and liturgical integrity of the Church. If a priest or especially a bishop is unorthodox, all other things being equal, that in itself detracts more from the orthodoxy of the Church on earth than when a lay person is unorthodox, simply because of the teaching role of the clergy. Similarly, if a priest or bishop engages in liturgical anarchy, say by changing some prayers at Mass, that detracts from the liturgical integrity of the Church more than if a lay person does so, all other things being equal.

But when a deacon, priest or bishop (including a pope) is wicked, that no more (and no less) directly detracts from the holiness of the Church than when a non-cleric person is wicked, when the degree of wickedness is the same. We can see this by considering the happier flip-side. Think of a non-cleric like St Teresa of Avila (she was a nun, of course, but a nun is a non-cleric[note 1]) and a priest like St John of the Cross. The holiness of their lives directly contributed to the holiness of the Church. But it would, I think, be mistaken to say that St John's holiness contributed more, or was a more central contribution, than St Teresa's just because St John was a priest and St Teresa was not. To say that would be to engage in clericalism, and is perhaps a species of the same error that leads to Donatism. The clergy's activity makes a special constitutive contribution to the Church's orthodoxy and liturgical integrity. But a layperson's holiness is just as constitutive of the holiness of the Church as the holiness of a deacon, priest or bishop. Mary makes a greater direct contribution to the holiness of the Church than any deacon, priest or bishop—not counting Christ the High Priest—ever did or would.

Of course, wickedness in a deacon, priest or bishop (and especially when the bishop is pope) typically has a greater negative effect on the Church's holiness, because it is more likely to scandalize others, leading them either to imitate the wickedness or abandon the faith. This indirectly detracts from the Church's holiness.

Suppose every single Catholic priest next year committed some particular grave and scandalous sin. That would be a terrible thing, would have a very unfortunate negative effect on the Church, and may God preserve us from this disaster. But it would no more directly detract from the Church's holiness than if some other group comprising 0.04% of the world's Catholic population committed an equally grave sin.

That said, a sin that is otherwise of the same sort may be graver when committed by a cleric, because (a) the cleric bears a responsibiity for avoiding the further negative effects and (b) is less likely to be excusable through ignorance. The above assumes we are dealing with sins of equal gravity.

Christ promised that the Church would be holy. The above argument shows that an argument based on clerical crimes that the Catholic Church cannot be Christ's Church because Christ's Church is holy is no stronger than argument based on equal numbers of non-clerical crimes would be. But an argument based on the crimes committed by non-clerics would fail: we do not expect the Church's holiness to imply the sinlessness of her members. The Church while holy as a body—the body of Christ—is yet a Church for sinners who need Christ's reforming grace. Thus the argument based on clerical crimes also fails.

And then, of course, there is always Boccaccio's argument.

Leviticus and a life of liturgy

I finished reading Leviticus. I had never read all of it before. It took a while to get any significant benefit from it, but finally things started coming together. Here are some unoriginal reflections. The text contains a welter of regulations about various aspects of life. In the first century AD, some heretical groups found the regulations so arbitrary that they rejected the Torah as something not fitting to a reasonable God, and some more orthodox Christians tried to find far-fetched allegorical readings of them (the Epistle of Barnabas, while well-meaning, and an interesting early witness to the Christian opposition to unnatural sexual activity, is a particularly egregious example). But textually these regulations are anchored in exhortations that the Israelites should be a priestly people, holy even as the Lord is holy.

Rudolf Otto has famously criticized the modern misunderstanding of "holy" as "superlatively morally good" for leaving out the numinous, the mysterium tremendum et fascinans. Indeed, if we read "holy" in Leviticus as "superlatively morally good", we will throw up our hands in despair, as the early groups I had mentioned did. The prohibition on eating hares surely is not in itself requires for superlative moral goodness. But neither does it appear right to read the text as simply exhorting us to be mysterious, awe-full and fascinating.

Rather, "holy" in the text tends to carry the connotation of "consecrated": holy to the Lord. A priest is, of course, consecrated to his deity, and his life is a life of liturgical service to his deity. There is no surprise if this liturgical service involves actions that are strange, for instance ordained by ancient tradition, held to be revealed by a deity, and so on. It is no surprise if a priest of a religion should be commanded to wear only certain kinds of clothes, eat only certain kinds of foods, perform special actions on special days, and so on.

What is surprising, however, is the notion of a whole people that is set apart, holy, consecrated in a priestly way, and perhaps also the notion of a service to the deity that encompasses all of the servant's time. But once we have the notion of a priestly people, and of liturgical services that encompasses all of a priestly person's time, that these people should have strange rules is no more surprising than that there should be regulations as to which direction around an altar a priest should proceed, or what material his knife should be made of. Liturgy, the priest's business, is full of rules that are not of the priest's making, rules that go beyond moral requirements. In fact, the existence of such rules seems central to liturgy—a liturgy that is created ad hoc for one occasion is either an oxymoron or at least deeply defective.

One thing we can learn from Leviticus, then, is the idea of a whole life lived as liturgy. And while the specific rules no longer literally apply in the Christian era, the idea of a whole life of service to God, a life of liturgy, is intensified in Christianity, in at least two ways. The first way is through every Christian's participation in the sacrifice of Christ, a participation more intimate than that of the Israelite in the Levitical sacrifices, because Christ the High Priest lives through us. The second, and liturgically very significant, intensification is that in the Eucharist all Christians need to participate, in a completely real way, in the quintessentially priestly action of eating of the sacrificial victim.

At the same time, we also see from Leviticus that even in a priestly people there can be distinctions between priestly roles. The priesthood of all believers does not entail that all believers are priestly in an equal way. Each Christian has a priestly role deeper than that of even the Israelite levites, but this is quite compatible with some Christians being ordained to an even deeper participation in Christ's priesthood. In fact, it seems that hierarchicality is an important part of a priestly people, just as priesthoods seem to be innately hierarchical.

The `Aqedah and the male-only priesthood

It seems to me it would have been less appropriate for God to ask Sarah to sacrifice a daughter than to ask Abraham to sacrifice a son. I don't have an argument for this—that's just how it seems to me. But if this is right, then it is not an accident that in the `Aqedah (the binding of Isaac) the two persons involved are male. But the `Aqedah is a foreshadowing of Christ's sacrifice on the cross. While with respect to the Incarnation as such, Christ's maleness might be reasonably argued to be incidental, if my intuition about the `Aqedah is right, then it is plausible that with respect to the sacrifice of Christ, the maleness is not incidental. And if so, then since what is central to the priesthood is the offering, in persona Christi and in an unbloody way, of the one sacrifice of the Cross[note 1], it seems quite appropriate that the priest be male, since he represents one whose maleness is not accidental in this context, and participates in Christ's sacrificial activity to which activity Christ's maleness is not accidental.

Is this sexist? Here is a way of thinking about this. Suppose that part of the reason God asked Abraham to sacrifice a son rather than asking Sarah to sacrifice a daughter had to do with Abraham and Isaac's maleness (leave aside the accidental fact that Sarah perhaps didn't have a daughter, since God could easily have fixed that). Would it follow that God discriminated against Sarah in asking Abraham to make the sacrifice? Surely not: one can at least equally well say that it was Abraham who was discriminated against by being asked to make the sacrifice.[note 2] The restriction of conscription to males does not discriminate against women, but against men, since it is upon men that it imposes a duty that it does not impose on women. Similarly, if God restricted who he requires to become priests to men, it is not obvious that this would be a form of discrimination against women.