Sexual symmetry and asymmetry

I want to think a bit about conservative Christian views of sex and gender, but before that I want to offer two stories to motivate a crucial distinction.

Electrons and Positrons

Electrons and positrons (a positron is a positively charged anti-particle to the electron) are very different in one way but not so much in another. If you take some system of electrons and positrons, and swap in a positron for an electron, the system will behave very differently—it will be attracted to the things that the electron was repelled by and vice versa. But if you replace all the electrons by positrons and all the positrons by electrons, it won’t make a significant difference (technically, there may be some difference due to the weak force, but that’s dominated by electromagnetic interaction). Similarly, a cloud of electrons behaves pretty much like a cloud of positrons, but a mixed cloud of electrons and positrons will behave very differently (electrons and positrons will collide releasing energy).

Electrons and positrons are significantly pairwise non-interchangeable, but globally approximately interchangeable.

We might conclude: electrons and positrons significantly differ relationally but do not differ much intrinsically.

On the other hand, if you have a system made of photons and electrons, and you swap out a photon and replace it by an electron, it will make a significant difference, but likewise typically if you swap out all the photons and electrons, it will also make a significant difference (unless the system was in a rare symmetric configuration). Thus, photons and electrons are significantly pairwise and globally interchangeable, and hence significantly differ both relationally and intrinsically.

Heterothallic Isogamous Organisms

Isogamous sexually-reproducing organisms have equally sized gametes among their sexes, and hence cannot be labeled as “female” and “male” (biologists define “female” and “male” in terms of larger and smaller gametes, respectively). Instead these sexes get arbitrarily labeled as plus and minus (I will assume there are only two mating types for simplicity). In heterothallic organisms, the sexes are located in different individuals, so two are needed for reproduction. Humans are heterothallic but not isogamous. But there are many species (mostly unicellular, I believe) that are heterothallic and isogamous.

We can now suppose a heterothallic and isogamous species with pretty symmetric mating roles. In such a species, again, we have significant individual non-interchangeability in a system. If Alice is a plus and Bob is a minus, they can reproduce, but if you swap out Bob for a plus, you get a non-reproductive pair. But if the mating roles are sufficiently similar, you can have global approximate interchangeability: if in some system you put pluses for the minuses and minuses for the pluses, things could go on much as before. A group of pluses may behave very much like a group of minuses (namely, over time the population will decrease to zero), but a mixed group of pluses and minuses is apt to behave very differently. We thus have pairwise non-interchangeability but approximate global interchangeability.

We might similarly say: pluses and minuses in our heterothallic and isogamous species significantly differ relationally but do not differ much intrinsically. On the other hand, cats and dogs significantly differ both relationally and intrinsically.

The Distinction

We thus have a distinction between two kinds of differences, which we can label as relational and intrinsic. I am not happy with the labels, but when I use them, please think of my two examples: particles and isogamous organisms. These two kinds of differences can be thought of as denying different symmetries: intrinsic differences are opposed to global interchange of the types of all individuals; relational differences are opposed to pairwise interchange of the types of a pair of individuals.

Conservative Christian Views of Sex and Gender

Conservative Christians tend to think that there are significant differences between men and women. In addition to cultural traits, there are two main theological reasons for thinking this:

1. Marriage asymmetry: Men and women can marry, but men cannot marry men and women cannot marry women.

2. Liturgical asymmetry: Only men can serve in certain liturgical “clerical” roles.

Of these, the marriage asymmetry is probably a bit more widely accepted than the liturgical asymmetry. (Some also think there is an authority asymmetry in the family where husbands have a special authority over wives. This is even more controversial among conservative Christians than the liturgical asymmetry, so I won’t say more about it.)

We could suppose an arbitrary divine rule behind both asymmetries. But this is theologically problematic: a really plausible way of reading the difference between the Law of Moses and the Law of the Gospel is at that in the Law of the Gospel, we no longer have arbitrary rules whose primary benefit is obedience, such as the prohibition on eating pork.

If we are to avoid supposing an arbitrary divine rule, we need to suppose differences between men and women to explain the theologically grounded asymmetries. And this is apt to lead conservative Christians to philosophical and theological theorizing about normative differences such as women being called more to “receptivity” and men more to “givingness”, or searching through sociological, psychological and biological data for relevant differences between the behavior and abilities of men and women. The empirical differences tend to lie on continua with wide areas of overlap between the sexes, however, and the normative differences are either implausible or likewise involve continua with wide areas of overlap (men, too, are called to receptivity).

But I think we are now in a position to see that there is a logical shortcoming behind the focus of this search. For differences between men and women can be relational or intrinsic, and the search has tended to focus on the intrinsic.

However, I submit, purely relational differences are sufficient to explain both the marriage and liturgical asymmetries. One way to see this is to pretend that we are a heterothallic isogamous species (rather than heterothallic anisogamous species that we actually are), consisting of pluses and minuses rather than females and males.

Then, if marriage has an ordering to procreation, that would neatly explain why pluses and minuses can marry each other, but pluses can’t marry pluses and minuses can’t marry minuses. No intrinsic difference between pluses and minuses is needed to explain this. Thus, as soon as we accept that marriage has an ordering to procreation, we have a way to explain the marriage asymmetry without any supposition of intrinsic differences.

Likewise, if there is going to be an incarnation, and only one, and the incarnate God is going to be incarnate as a typical organism of our species, then this incarnation must happen as a plus or a minus. And if married love is a deep and passionate love that is a wonderful symbol for the love between God and God’s people, then if the incarnation is as an individual of one of the sexes, God’s Church would then symbolically have the opposite sex. And then those whose liturgical role it is to stand in for the incarnate God in the marriage-like relationship to the Church would most fittingly have the sex opposite to that of the Church. Thus, if the incarnate God is incarnate as a plus, the Church would be figured as a minus, one can explain why it is fitting that the clergy in the relevant liturgical roles would be pluses; if the incarnate God is incarnate as a minus, we have an explanation of why the clergy in these roles would be minuses as well. (Interestingly, on this story, it’s not that the clergy are directly supposed to be like the incarnate God in respect of sex, but that their sex is supposed to be the opposite to that of the Church, and given that in the species there are only two sexes, this forces them to have the same sex as the incarnate God: the clergy need to have a sex opposed to the sex opposed to that of the incarnate God.)

Now, we are not isogamous, and we have female and male, not plus and minus. But we can still give exactly the same explanations. Even though in an anisogamous species there are significant intrinsic biological differences between the sexes, we need not advert to any of them to explain either the marriage or the liturgical asymmetry. The marriage asymmetry is tied to the pairwise non-interchangeability of the sexes and explained by the procreative role of marriage. The liturgical asymemtry is tied to the marriage asymmetry together with the symmetry-breaking event of God becoming incarnate in one of the sexes.

As far as this story goes, there need not be any morally significant intrinsic differences between male and female to explain the marital and liturgical asymmetries. The relational difference, that you need male and female for a mating pair, is morally significant on this story, but in a way that is entirely symmetric between male and female. And then we have one symmetry-breaking event: God becomes incarnate as a male. We need not think that there is any special reason why God becomes incarnate as a male or a female—it could equally well have been as a female. The decision whether to become incarnate as a male or a female could be as arbitrary as the decision about the exact eye color of the incarnate God (though, of course, eye color does not ground either significant intrinsic or significant relational differences). But if it were an incarnation as a female, other changes would be fitting: the clergy who symbolize the nuptial role of the incarnate God would fitting be female, in the exodus story it would fitting be female lambs and goats that would be sacrificed, and it would be fitting that Sarah be asked to sacrifice her first-born daughter.

I am not saying that there are no morally significant intrinsic differences between male and female. There may be. We are, after all, not only heterothallic but also anisogamous, and so there could turn out to be such intrinsic differences. But we need not suppose any such to explain the two asymmetries, and it is safer to be agnostic on the existence of these intrinsic differences.

Nothing in this post is meant as an argument for either the marriage asymmetry and the liturgical asymmetry. I have argued for the marriage asymmetry elsewhere, but here I am just saying that it could be explained if we grant the procreative ordering of marriage. And my arguments for the liturgical asymmetry are based on fittingness. But fittingness considerations do not constrain God. While we can explain why the clergy are of the same sex as the incarnate God by the nuptial imagery story that I gave above, God could instead have chosen to make the clergy be of the opposite sex as the incarnate God, in order to nuptially signify the people with the clergy, or God could chosen to make the clergy be of both sexes, to emphasize the fact that salvation is tied to the humanity (see St. Athanasius on this) and not the sex of the incarnate God. But when many things are fitting, God can choose one, and we can then cite its fittingness as a non-deterministic explanation.

Though, I suppose, I have at least refuted this argument:

3. The only way to explain the marriage and liturgical asymmetries is by supposing morally significant intrinsic differences between female and male.

4. There are no such intrinsic differences.

5. So, probably, the asymmetries don’t exist either.

I have refuted it by showing that (3) is false.

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.

A reading of 1 Corinthians 14:33b-34a

1 Corinthians 14:33b-34a is one of the “hard texts” of the New Testament. The RSV translates it as:

As in all the churches of the saints, the women should keep silence in the churches.

Besides the fact that this is a hard saying, a textual difficulty is that earlier in the letter, at 11:5, Paul has no objection to women prophesying or praying (it seems very likely that praying would be out loud), though it has been suggested that this was outside of a liturgical context. Nor does later Church practice prohibit women from joining in vocal prayer during the liturgy.

I assume that the second "the churches" means "the churches of Corinth", while the first "the churches" refers to the churches more generally. And yesterday at our Department Bible study, I was struck by the fact that the “As” (Greek hōs) that begins the text can be read as “In the manner of”. On that reading, the first sentence of the hard text does not say that women should keep silent in the Corinthian churches. Rather, it says that women should keep silent in the Corinthian churches in the way and to the extent to which they keep silent in the other churches. In other words, women should only speak up in Corinthian liturgies at the points at which women speak up in non-Corinthian liturgies. This is compatible with women having various speaking roles—but only as long as they have these roles in “all the churches of the saints.”

(Note, however, that some versions punctuate differently, and make “As in all the churches of the saints” qualify what came earlier rather than what comes afterwards. My reading requires the RSV’s punctuation. Of course, the original has no punctuation.)

On this reading, the first sentence of the text is an application of a principle of liturgical uniformity between the churches, and Paul could equally well have said the same thing about the men. But the text suggests to me that there was some particular problem, which we can only speculate about, that specifically involved disorderly liturgical participation by Corinthian women, in addition to other problems of disorderly participation that Paul discusses earlier in the chapter.

The difficulty for my reading is the next sentence, however:

For they are not permitted to speak, but should be subordinate, as even the law says. (1 Cor. 14:34b, RSV)

I would want to read this with “speak” restricted to the kinds of speech not found in the other churches. Perhaps in the other churches, there was no “chatting in the pews”, or socializing during the liturgy (Mowczko in a very nice summary of interpretations notes that this is St. John Chrystostom’s interpretation).

Another interpretation is that “the law” here is Roman law or Corinthian custom (though I don’t know that in Koine Greek “nomos” can still cover custom, like it can in classical Greek), so that Paul is reprising a motif of noting that the Corinthians are behaving badly even by their own cultural standards.

I don’t know that my reading is right. I think it is a little bit more natural to read the Greek as having a complete prohibition on women speaking, but my reading seems to be grammatically permissible, and one must balance naturalness of language with consistency in a text (in this case, consistency with 11:5). And in the case of a Biblical text, I also want an interpretation compatible with divine inspiration.

A hypothesis about the origins of homophobia

Here is a hypothesis that, if correct, would explain many instances of male homophobia. Heterosexual men often objectify women, and they believe (often correctly) that other straight men do likewise. Consequently, they believe that men generally objectify those persons to whom they are sexually attracted. Therefore, such a man may believe that homosexually oriented persons objectify men, and in particular are apt to objectify him. But he has an aversion to being objectified, or at least to being objectified by persons he is not himself sexually interested in. Therefore, such a man exhibits a certain kind of aversion or even fear of men who are sexually attracted to men—he does not want to be lusted at.

The hypothesis would suggest the following predictions:

1. Homophobia is more often directed at men by men than at men by women, women by men, or women by women.
2. The incidence of homophobia is correlated with the incidence of the objectification of women (both individually and in a social circle; thus, even if x does not himself objectify women, if his friends do, this may correlate with increased homophobia).
3. Homophobic heterosexual men are likely to be averse to having a very unattractive women being sexually interested in them.
4. A significant amount of homophobia is also directed at sexually abstinent homosexual men.

I don't know if the predictions are true. I suspect on anecdotal grounds that (1) and (4) are true. I do not know if (2) and (3) are.

I should note that I do not equate homophobia with a moral disapproval of homosexual activity or with a disgust at homosexual actions, and hence I can consistently say that homophobia is irrational (or even that some homosexual actions are disgusting—just as some unnatural heterosexual actions are), while still holding that homosexual activity is wrong. It is, after all, possible to strongly disapprove of an action, but to have no aversion or fear towards the persons who perform the action. Thus, orthodox Catholics strongly disapprove of contraception, but I think are unlikely to feel an aversion or fear towards the large majority of fellow citizens who contracept. (The case is chosen carefully: The Christian tradition classifies homosexual activity and the heterosexual use of condoms in the same moral category of "unnatural acts", and both Catholics and Protestants traditionally called both sets of acts "sodomy".) Nor can one identify disgust at an action with an aversion to the person who does it. Thus, everyone on a daily basis does disgusting and morally unexceptionable things in private, but being disgusted at these actions is not equivalent to aversion to oneself and one's fellow man. Disgust at an action can sometimes give rise to an aversion to the doer, but the disgust and the aversion are still distinct.

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.

Men and women are one species

I've always been puzzled by the following problem. The setting for it is the metaphysical Aristotelian concept of a "species", not the biological one (in the biological sense this is easy). How do we know that women and men are the same species? I.e., how do we know that the species that we belong to is human rather than there being two species, woman and man?

I think a partial answer can be given by taking into account the following observation (I've learned it from David Alexander here who attributes it Peter Geach, though neither may endorse my application): In general, from the fact that x is a good F and x is a G, one cannot infer that x is a good G.

Here, I intend "is a good F" to mean something like "flourishes at F-ness" or "is good at being an F". Moreover, I am thinking here in the context of Greek notions, so that to be a good human includes both having the virtues of the intellect and will, as well as the excellences of the body. This is at times a somewhat awkward use of "good", but I shall adopt it.

I shall be rough here. I know what I say is not exactly right. For full precision, one needs to work not with the coarse tools of entailment and necessity, but with more finegrained tools of explanation and truthmaking. But what I shall say seems approximately right.

Despite what I said above, sometimes inferences like the ones questioned above seem exactly right:
(1) If x is a good lieutenant in a military force, then x is a good officer in the same force.
(The "in the same force" condition is needed, because a spy might be an officer in more than one army, but is unlikely to be a good officer in more than one.) The converse I am less sure of, but it is also plausible:
(2) If x is a good officer in some military force and x is a lieutenant, then x is a good lieutenant in the same force.

Suppose, now, that F and G are kinds such that, necessarily, all Fs are Gs but not conversely, and necessarily x is a good F if and only if x is a G and x is a good G. I shall say that "F is normatively subordinated to G".

Conjecture 1: If F is a species and G is a higher genus, then F is not normatively subordinated to G.

Conjecture 1 embodies an Aristotelian notion of the primacy of species, in the normative realm. And I think the normative aspect of species-hood is central for Aristotelians (I would like read the characterization of the essence as to ti ên einai as normative, though it may be stretching the Greek: what [the thing] was [supposed] to be). The species encodes the normative properties for the individuals of that kind. If we can explain the normative properties of an x insofar as it is an F in terms of its aptness at fulling G-ness, then F-ness is not the normatively basic property here. F-ness specifies the x further, but does not add any nomrative force. For reasons of explanatory power, we should try to find as general a kind as we can without sacrificing any normativity when we are searching for. To be a good human is more than just being human and being a good mammal. One can be really good at mammality while being far from human flourishing. The converse, I think, is false, though: if we fully flourish at humanity, we also flourish at mammality.

Now one is a good woman if and only if one is a woman and a good human; similarly for a man. This is a controversial claim, but I think correct. Therefore woman and man are normatively subordinated to human. If woman and man were species, then human would be a higher genus, and hence Conjecture 1 would be violated. Hence, if Conjecture 1 holds, woman and man are not species.

An interesting question is whether one can come up with a full characterization of species in similar normative terms. Here is something that might come close.

Conjecture 2: A natural kind G is a species iff both (a) G is not normatively subordinated to any larger natural kind, and (b) if F is a proper natural subkind of G such that any good F is necessarily a good G, then F is normatively subordinated to G.

(The "F is normatively subordinated to G" condition in (b) can be replaced by "necessarily a good G who is an F is a good F", because more than half of the definition of normative subordination is implied by the antecedent of the conditional in (b).)

For instance, mammal is not a species. For human is a proper natural subkind of mammal such that to flourish at being a human entails flourishing at being a mammal, but human is not normatively subordinated to mammal. One can be really good at mammality while a miserable failure at all other dimensions of humanity. But one cannot be really good at humanity and a woman while being a failure at being a woman.

A different way to look at the above is to note that the flourishing of a man or a woman as such is basically no different--it is just a particular form of the flourishing of a human.