How a mathematical move might illuminate a cultural issue
Should we ditch gendered vocabulary to undermine patriarchy?
At the recommendation of a friend, about five years ago I read Eugenia Cheng’s X + Y: A Mathematician’s Manifesto for Rethinking Gender. Cheng is a category theorist and has all the high-powered math qualifications you’d want to see. She’s also a marvelous writer for popular audiences. (I highly recommend anything she’s written.)
In the book, Cheng tells the story of how she was able to succeed at the math game, but became uncomfortable in the persona that academic mathematical culture foisted on her. (I can relate.) She didn’t like herself in that role because in addition to systematic thinking and logic, mathematical culture is characterized by traits like competition, aggression, and individualism. She wasn’t at home in that atmosphere. So she found a way to do math and be more herself: by teaching math at the Art Institute of Chicago. She became interested in gender because she realized that traditional mathematical values are coded masculine.1
One of Cheng’s gifts is the ability to break down and explain the processes of mathematics without getting into the technicalities that unfortunately scare so many people away from the subject. Math’s two great moves, she explains, are abstraction and logic.2 “Mathematics uses these dual disciplines to do many things beyond calculating answers and solving problems. It also illuminates deep structures built by ideas and often hidden in their complexity” (6). This, she argues, is what mathematical thinking can contribute to our understanding of gender.
New vocabulary
One of the problems with using gendered language, Cheng observes, is that not all men and not all women fit the characteristics of traditional gender definitions, and not everyone behaves all the time in ways that conform to those stereotypes. Moreover, gender stereotypes and terms inflame a lot of strong emotions and knee-jerk reactions. She realized that what’s at stake in most of this kind of discussion isn’t gender as such, but a set of characteristics that are (deeply, but contingently) associated with the two gender poles. So she proposes making a mathematical move: abstracting away from gender and focusing instead on the characteristics that seem to be at issue. She proposes new terms that, she hopes, get at what’s really at stake:
ingressive: Focusing on oneself over society and community, imposing on people more than taking others into account, emphasising independence and individualism, more competitive and adversarial than collaborative, tendency towards selective or single-track thought processes.
congressive: Focusing on society and community over self, taking others into account more than imposing on them, emphasising interdependence and interconnectedness, more collaborative and cooperative than competitive, circumspect thought processes. (131)
The terms themselves come from the ideas of “going into things” and “bringing things together” respectively. Maybe there are better terms. But let’s go with it and focus on the strategy here. It’s not hard to see how “ingressive” traits are associated with masculinity—or more accurately, patriarchy—and “congressive” traits with femininity. The point, however, is to get at the real issue by abstracting away from these associations and focusing on the ways the characteristics and values get enacted in our choices and behaviors.
Cheng is clear that she doesn’t intend this to be clean dichotomy in the sense that any of us is all one or the other. Pulling gender out of the equation is meant to get us thinking in terms of more fluid and contextual behaviors rather than more fixed identities: “[People] can be somewhat one and somewhat the other under different circumstances. It’s more of a two-dimensional plane, and we can be anywhere on it, and indeed move around on it across time and in different situations” (130). That’s the point of the abstraction: to change perspectives and see more clearly.
Here’s the thing: as I noted, Cheng’s “ingressive” category looks very close to a characterization of patriarchy: a system that values a certain vision of strength—domination, aggression, hierarchy, etc. often to the exclusion of much else that’s valuable.3 It denigrates everything associated with women as being weak. It boxes everyone—men, women, and everyone in between—into ways of being they might not feel comfortable with if they were somehow able to choose freely.
More clarity
Cheng’s move is intriguing for the way it clarifies that what’s at stake in the culture wars: sets of values. Her point is that all of us behave in congressive and ingressive ways in different circumstances. Decoupling the values and behaviors from genders could help us look more carefully at how these values and behaviors are serving us.
Now, values are an important component of who we are both as individuals and as groups, so it’s never not going to be about identity in some sense. But detaching the sets of values from patriarchal gender norms frees us up to move around the plane a little more widely.4
Could removing the discussion from the context of gender detach us from the sensitivity of gendered language, allow us to look critically at the characteristics of ingressiveness and congressiveness, de-bundle them, and choose among them without the load of “betraying our gender” or “being a bad man/woman” clouding the issues? I don’t know. There may be reasons to want to keep the historically gendered nature of these values and behaviors in sight.
But abstracting away from gender suggests that what’s at issue is what’s going to count as a virtue, and what any given virtue means. I bet most people will agree that, for instance, strength and justice are virtues. But what do those virtues look like through congressive and ingressive lenses, respectively? They come out rather different. Justice, for instance, might look more restorative through a congressive lens, and more retributive through an ingressive one. Strength might look more like perseverance vs. domination. And so on for other virtues.
The view from the abstract plane
Perhaps there’s a time and place for each “flavor” of various virtues. A classic objection to virtue ethics, however, is how we can decide what “the” virtues are, and this is where it gets hard: as we just saw, even qualities we superficially agree are virtues seem different in different contexts, and dependent on what we happen to value. In a ingressive/patriarchal system, we’re meant to value independence, competition, etc., and this defines what virtues are within the system (some people try to opt out precisely by rejecting or redefining some values and virtues). Unlocking from gender associations might make it easier to see and implement opportunities for congressive solutions to problems rather than always assuming ingressive ones.
As Cheng describes ingressiveness and congressiveness, one looks clearly more appealing to me personally than the other. Domination and aggression are only fun for those on top; who wants to be dominated? Behind a Rawlsian “veil of ignorance” about what position you’ll get in the social lottery, would we include domination as a value we want to emphasize? I’d think not. Could this be a point of agreement when it comes to choosing our collective values?
Suppose, then, that we downplay domination out of the ingressive bundle. Independence, respect, impartiality, and many of the other qualities in that bundle do seem to have their place in many contexts (though probably fewer contexts than we currently employ them in), and they’re useful for both men and women in those contexts. But alternatives in the set of congressive qualities also have their place. Do we want to value connection or independence? Emotion or reason? Or rather, where and when do we dial up the congressive qualities and dial down the ingressive ones? Math and philosophy, the justice system, capitalism, and many other areas are currently primarily ingressive spaces. What might it look like to pull in more congressive qualities and values? Cheng—and many of my colleagues in our local math department—work to make math classrooms more congressive and thus more inclusive to people historically excluded from those spaces. Similarly in philosophy. And though I’m less plugged into bigger public contexts, I know there are those who are working to bring more congressive qualities to systems like justice and capitalism.
Like I said, maybe there are good reasons not to ignore the gendered component of the systems as we know them. One of those reasons is that it’s generally a bad idea to ignore history; truth is valuable. Even if the reasons to keep gender in sight outweigh the reasons to abstract away from it, however, I think it’s worth exploring what happens when we abstract. As I’ve said before, one of the most valuable things about humanistic study—and this is, I think, a case of a mathematical move in a humanistic domain—is that we can learn a great deal from the way different lights illuminate a subject. Even if we don’t adopt Cheng’s terms widely, looking through this lens helps us focus on the heart of the issue.
At least, this is the very strong reputation it has. One of the things we do in the Gender & Math course I team teach with a mathematician is point out that a lot of actual mathematical practice is very collaborative. (And then we dig into why that’s not more widely known or celebrated.)
In other works, she expands the list to include axiomatization and generalization, but those are less relevant for current purposes.
Gender is actually more about values and identity than it is about physiology, and while we’re getting better at recognizing that, old habits die hard.
Fascinating! Thank you!
Amazing article with so much to digest and ponder. You ask the great question, "Do we want to value connection or independence?" Is it too idealistic to answer "both?" Our freedoms are defined in terms of our place and our connections, so our independence is a product of our interdependence.
On gender, I am inclined to the view that we do well to end gender roles, admit that sex is not gender, and allow for everyone to be who they are as they are.