What is a Woman, Anyway?

Fuzzy Sets, Family Resemblances, and Conceptual Truths

“Two Ages” / “Profiles.” Medium: Soapstone from the Berkshires. Carved in Lennox, MA in 1955 by Franc Epping, the author’s aunt. Author’s collection.

In his 1953 book Philosophical Investigations the philosopher Ludwig Wittgenstein introduced the concept of “language-games,” in which he argued that concepts do not need perfect clarity for meaning to be found in them, with “games” as his type specimen. We speak of board games, card games, dice games, arcade games, athletic games, war games, betting games, drinking games, and even multiplayer online battle arena games, but just try to find the common denominator of the conceptual category of “games” that runs through all of them.

Many games involve physical activity, such as tennis and bowling, but most board, card, and dice games do not (beyond moving pieces, flipping cards, or rolling dice). Games are usually something one does for fun, but as often as not people play them with an intensity reserved for the most serious of life’s challenges. Games often involve competition against others, but not so for contests against the clock, or against your previous best performance, or even solitaire. Many games involve winning and losing, but party games are designed to encourage social interaction, not zero-sum victory and defeat. Games sometimes involve skill, but many board games depend on the randomness of die roll or a spinner. And so forth.

Wittgenstein’s broader point is that rules of language are analogous to rules of games, in which meaning depends on common agreement among players of games or users of words. For example, the concept of “game” cannot be reduced to a necessary and sufficient set of features that cover all specific examples, but we know one when we see one. How? Family resemblance, or a loose confederation of characteristics that applies to most examples most of the time. Such meanings are not demarcated by sharp and well-defined borders, but instead blend into one another across blurred boundaries. Call them fuzzy sets. Arguably the most famous example comes from the United States Supreme Court Justice Potter Stewart in the 1964 case Jacobellis v. Ohio over what, exactly, constitutes pornography:

I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description [“hard-core pornography”], and perhaps I could never succeed in intelligibly doing so. But I know it when I see it, and the motion picture involved in this case [Louis Malle’s The Lovers] is not that.

In his 2021 book Rationality, psychologist and linguist Steven Pinker invokes the offspring of Robert Kardashian and Kristen Jenner as literal examples of family resemblance, because even though not every scion “has the pouty Kardashian lips or the raven Kardashian hair or the caramel Kardashian skin or the ample Kardashian derriére,” “most of the sisters have some of them, so we can recognize a Kardashian when we see one, even if there is no true proposition ‘If someone has features X and Y and Z, that person is a Kardashian’.”

Kris Jenner, Kendall Jenner, Kylie Jenner, and Kim Kardashian. Photo by Dimitrios Kambouris/Getty Images.

Most concepts have exceptions, yet we can agree on a flexible set of characteristics that roughly represents the category. Chairs are seats with legs and backs, allowing for exceptions like barstools with a seat and legs but no back. Exceptions don’t refute the rule; they help demarcate the thickness of the fuzzy boundaries. “Some apples are not red; some dogs do not bark; some birds do not fly. But all the instances of a concept do share a family resemblance,” explains the social psychologist Carol Tavris, elaborating:

When we need to decide whether something belongs to a concept, we are likely to compare it to a prototype, a representative instance of the concept. Which dog is doggier, a golden retriever or a Chihuahua? Which fruit is more fruitlike, an apple or a pineapple? Which activity is more representative of sports, football or weight lifting? Most people within a culture can easily tell you which instances of a concept are most representative, or prototypical.

Family resemblance concepts by themselves are not enough, Tavris adds, noting that “we must also represent their relationships to one another” in the form of propositions, or “units of meaning that are made up of concepts and that express a unitary idea.” These, in turn, “are linked together in complicated networks of knowledge, associations, beliefs, and expectations” that psychologists call cognitive schemas, that “serve as mental frameworks for describing and thinking about various aspects of the world.” Gender schemas, for instance, “represent a person’s beliefs and expectations about what it means to be male or female.” A “mother” is a woman who gives birth to a child, but what about adoptive mothers, surrogate mothers, and egg donor mothers? And, Pinker cautions, “you can get in a lot of trouble these days if you try to lay out necessary and sufficient conditions for ‘woman’.”

Naked Woman / Mother and Child. Medium: Plaster / Marble. Sculptures by Franc Epping. Author’s collection.

Indeed, just ask Matt Walsh, the Daily Wire conservative host and writer whose new documentary film asks What is a Woman?

In a Borat-like series of conversations and encounters Walsh can’t seem to get a straight answer from anyone, including the University of Tennessee Chair of the Interdisciplinary Program in Women, Gender and Sexuality, Patrick Grzanka, who answered the titular question thusly: “When someone tells you who they are, you should believe them. If a person tells you they are a woman or a man they’re telling you what their gender is.” Unsatisfied with this answer, Walsh presses his subject: “What is a woman?” This exchange is emblematic of postmodernism’s turn to obscurantism:

Grzanka: “Why do you ask that question?”

Walsh: “Because I’d really like to know.”

Grzanka: “What do you think the answer is?”

Walsh: “I’m asking you, a college professor that studies this subject.”

Grzanka: “What other answers have you gotten?”

Clearly frustrated, Walsh explains that others he’s queried are equally obfuscating.

Grzanka: “The simple answer is a person who identifies as a woman.”

Walsh: “What are they identifying as?”

Grzanka: “A woman”

Walsh: “But what is that?”

Grzanka: “As a woman.”

Walsh: “Do you know what a circular definition is?”

Of course, Grzanka perfectly well knows the answer to that question, so he pivots: “You’re seeking what we call in my profession an ‘essentialist definition’ of gender.”

That’s right, because essentialist definitions are examples of family resemblances, or fuzzy sets that must contain some agreed-upon characteristics or else the words are meaningless. But Grzanka’s dodge is not uncommon in academia today, and in exasperation with Walsh’s persistent questioning in search of the truth, Grzanka pronounces on camera, ”Getting to the truth is deeply transphobic.”

In recent years the calumny against objective truth has grown like kudzu over the ivory walls and into nearly all aspects of society, as evidenced in the many other confused subjects in Walsh’s film. There’s “Gender Affirmation Therapist” Gert Comfrey, who explains that “People are assigned a gender at birth based on genitalia: this is a girl or this is a boy. We now know that sex and gender are far more than just this binary. Some women have penises, some men have vaginas.” If so, then what do those words mean? What is a woman? “Great question,” replies the female-looking Comfrey, but “I’m not a woman so I can’t really answer that.” Oh.

A group of New York City women do no better, sputtering out through nervous laughter, “That is a tough one.” An unnamed woman offers “someone who thinks of themselves as delicate and pretty.” An unnamed cross-dressing man suggests a woman is “someone who identifies as a woman.” Walsh’s rejoinder, “But what is that?”, is met with: “I honestly don’t know.”

Marci Bowers, tagged as “the world’s preeminent ‘gender-reassignment’ surgeon” and who self-identifies as “a woman with a trans history” (i.e., a Male-to-Female [MTF] trans) defines a woman as “a combination of your physical attributes and what you’re showing to the world and the gender clues that you give. And hopefully those match your gender identity.” Hopefully? Presumably that’s what genital surgery aims to do; for example, a vaginoplasty, in which a portion of a biological male’s body is sculpted to “look and…function like female anatomy.” But as Helen Joyce points out in her book Trans: When Ideology Meets Reality, and in our conversation on my podcast, these vaginas do not work like those of a biological female so such surgeries produce what is, in essence, a fleshy tube for people who identify as male to penetrate with a penis, a very male-centric view of vaginas that objectifies women as essentially bodies for men to use. For feminists like Joyce, this is a stark reversal of a century of women struggling to be perceived as more than their body parts.

Walsh next turns to Michelle Forcier, a consultant pediatrician at Hasbro Children’s Hospital, Rhode Island, who asserts that “Gender affirmation means listening to children’s story about who they think they are” because “Telling parents that a newborn is 100% a certain gender based on the genitalia is not correct.” A woman, Dr. Forcier explains, is “someone who claims that as their identity. It could be many things to many people.” Do gametes make someone a male or female, Walsh queries? “No,” she retorts, “sperm does not make you a male” because “some women have penises, some men have vaginas.”

If so, then why does a person assigned at birth as a male but who identifies as a female need to remove the penis? Why does a person assigned at birth as a female but who identifies as a male need to add a penis? If a “woman” or a “man” is whatever anyone claims as their identity based on internal beliefs and feelings instead of external equipment—as one online influencer told Walsh, “Some people are boys, some people are girls, some are both, some are neither. Gender is all about how you feel on the inside and how you express yourself.”—then why would anyone put themselves through the ordeal of transitioning?

Consider what’s a stake in these medical procedures. After undergoing seven surgeries to transition from a female to a male (FTM), Scott Newgent offered this forensic archaeological account: “If someone dug up my body a century from now they’d say ‘yup, that’s a woman’.” (Forensic archaeologists also employ family resemblances and fuzzy sets when identifying skeletons.) Now an educator and activist against “radical trans activism,” Newgent lists his personal reasons for caution: one pulmonary embolism, one helicopter ride to the ER, 17 rounds of antibiotics, hair on the inside of his urethra that took 17 months to eliminate, and infections every three to four months. “No one would help me, including the doctor who did this to me, because I lost my insurance,” Newgent recounted, adding “I’m probably not going to live very long.”

What about those who transition without such complications and regrets? Consider the account of Gabriel Mac, the author of the widely-read cover story of the December 2021 issue of New York magazine. Mac is a FTM trans who describes himself as “an asexual gay man with a penis and a vagina.” After a double mastectomy and a phalloplasty surgery creating a penis out of a chunk of skin carved out of his thigh, Mac explains what all is involved in the process:

While I’d been sleeping, two microsurgeons, a reconstructive urologist, a surgical fellow, and a surgical resident had, among other things, cut a seven-by-six-inch rectangle out of my right anterior lateral thigh. They’d taken all the skin and fat, plus one big nerve and some veins attached to the muscle, and connected the skin to itself in the shape of a phallus. Then they slipped the whole thing under two of my thigh muscles, pulled up out of the way with a steel retractor, dragged the phallus across my groin under the skin, and pulled it back out into the world through a hole cut in the skin over my pubic bone. They connected the new penis’s nerve to one of the nerve bundles in my native penis, which some people call a clitoris (embryologically, the cells are the same), which they’d cut free of its ligaments, then skinned, then tunneled up under the skin and out to the landing site of the new penis, the base of which they joined to the base of my pelvis, putting me all together with sutures, some finer than a human hair.

One of the film’s counter voices is the psychiatrist Dr. Miriam Grossman, author of You’re Teaching My Child What?, who articulates the importance of distinguishing between people who genuinely have gender dysphoria (her estimated rate is between 1/30,000 and 1/110,000) and what is happening today, “where kids with no history of discomfort with their biological sex seem to be getting swept up in a social contagion, in which transgender people are not merely accepted but lionized.” (In this account, one of many such stories recounted by shocked parents, a quarter [7 out of 28] of her daughter’s class claims to be trans.) Sex, Grossman explains, “is biology, sex is unchanging—99.999% of the cells in the body are marked either male or female.” By contrast, “gender is a perception, a feeling, a way of identifying, it’s an experience—that’s subjective.”

This graphic, from Gallup polling data, captures what happens when that subjective experience is shaped by social influences, in this case resulting in a 100% increase in LGBT identification in Generation Z compared to prior generations.

A new Pew survey corroborates the finding: “The share of U.S. adults who are transgender is particularly high among adults younger than 25. In this age group, 3.1% are a trans man or a trans woman, compared with just 0.5% of those ages 25 to 29.” That is a six-fold difference.

This data gainsays the hypothesis that a more tolerant society has allowed more people to come out, because if so so we should see increases in all age cohorts, but we don’t. It’s possible older cohorts will come out later as society grows more tolerant, but at the moment it appears something began to change in 2017, and that something could be a social contagion among youth to identify as something other than cisgender straight. Carl Trueman, a theologian at Grove City College and author of The Rise and Triumph of the Modern Self, explains to Walsh the psychology behind the contagion:

Trans is cool. Trans is a way of giving yourself value. All of the things that used to give us anchors of identity have become very fluid. … So new identities start to fill the void of the vacuum, whereas in the past I might have gotten my self worth from being part of a village where I grew up. Now I might get my self-worth from being part of an online community or the sexual identity community.

With selfhood itself at stake it’s no wonder otherwise rational and tolerant people tiptoe around the topic, as evidenced in the congressional hearings over Supreme Court nominee Ketanji Brown Jackson, who when asked by Republican Senator Marsha Blackburn “Can you provide a definition for the word ‘woman’?” understood the loaded question for what it was and politely declined to answer, dissembling, “I am not a biologist.”

That Ketanji Brown Jackson—along with you and me and nearly everyone else on the planet—knows perfectly well what a woman (and a man) is, tells us that something else is going on here, a semantic shift, a conceptual contrivance to shake us out of our Enlightenment liberal commitment to universal realism and the search for objective truth. Just as Force equals Mass times Acceleration (F=MA), planets travel in elliptical orbits and sweep out equal areas in equal times, entropy increases in a closed system, mass is conserved in a chemical reaction, DNA is a molecular double helical structure, and all living organisms are descended from common ancestors, in a sexually-reproducing mammalian species like ours females and males are distinctly different and should be able to be defined as such.

Here is where the trouble begins and why we need fuzzy sets and family resemblances to properly capture the conceptual truth about women and men. Most people think that sex is defined by XX and XY chromosomes, but as the Harvard evolutionary biologist Carole Hooven notes in her 2020 book T: The Story of Testosterone, the Hormone that Dominates and Divides Us, “sex chromosomes aren’t always XX and XY. In birds, for example, males have a pair of identical sex chromosomes (‘ZZ’), and females have two different ones (‘ZW’). What’s more, many species don’t even rely on chromosomes to make males and females. In turtles and crocodiles, it’s the temperature of the eggs that determines the sex of the hatchlings. And animals don’t always stay one sex or the other. Every coral reef-dwelling clownfish is born male and some time later switch to female.”

What criteria should be used to distinguish females from males? The relative size of the sex cells or gametes, Hooven explains, echoing the definition agreed on by the vast majority of biologists. “Males produce small, mobile gametes (sperm), and females produce larger, immobile gametes (eggs),” although even here Hooven cautions readers not to take this definition too strictly, inasmuch as “my son doesn’t yet make sperm, but he’s still male. And although my ovaries are no longer regularly producing eggs, I’m no less female than when they were cranking them out on a monthly schedule. Rather, it’s the design plan for the gametes that counts.”

That design plan for producing two different types of gametes is what you would expect in a sexually reproducing species like ours, so that seems as foundational a conceptual category as we’re going to get in defining females and males, while still allowing for the rare outliers. As such, and by this definition, females can’t produce and ejaculate sperm and males can’t produce eggs and get pregnant. As these words are understood today we can say with confidence that women do not have penises and men do not have vaginas. Biological females can undergo a double mastectomy and get a penis carved out of skin folds and other body parts, and biological males can get silicon breast implants and a faux vagina, but they don’t work like the organs of their biological holotypes. The reason is that the family resemblance fuzzy set representing “female” or “woman” contains far more than breasts and a vagina. Look under the hood and you’ll find hundreds, if not thousands, of differences with men, from anatomical and physiological to cognitive and emotional. See this recent issue of Skeptic on Trans Matters for a thorough review of the scientific literature:

To complicate matters further still, what sex or gender someone identifies as is different from the equally salient issue of who they’re attracted to. Historically, heterosexual, homosexual, and bisexual represent the fuzzy sets of people who are attracted to members of the opposite sex, the same sex, or both. But now, what label should be applied to a MTF trans who identifies as a woman, retains a penis, is attracted to women, and for which sex includes traditional intercourse? Is she gay, lesbian, straight, or both/neither? What about a FTM trans who is attracted to men but retains a vagina and also enjoys intercourse? Is he gay or straight? How about a MTF trans or a FTM trans attracted to the same sex of what they were assigned at birth (but now no longer identify as)? Should the descriptor depend on the equipment they were born with, the equipment they currently have, or with just the internal identifying psychological state? And, again, if the latter, why bother with the hormone treatments and surgeries?

However the language games play out with this issue in the coming years, and whatever the science provisionally concludes about the actual rate of trans sans the social contagion element, it is good to remember that trans rights are human rights and that discrimination based on sexual or gender identity, along with sexual orientation and other protected classes, is both illegal and immoral. No one should be fired for being trans, much less treated as less than human. The fuzzy set of Homo sapiens includes all of us, regardless of how we subdivide the species.

In a cheeky ending to his film, Matt Walsh returns home from his gender-bending journey to ask the one person he is certain knows the answer to his question: his wife Penelope. What is a woman? “An adult human female…who needs help opening this,” she replies, handing him a stubborn pickle jar.

Several female reviewers who were otherwise cautiously positive about the film took mild offense at this nod to the 1950s, but I saw it as contrived humor to relieve an otherwise deadly-serious subject being driven by contemporary politics, ideological extremes, and conceptual confusions.

What would Wittgenstein say?

Michael Shermer is the Publisher of Skeptic magazine, a Presidential Fellow at Chapman University, the host of The Michael Shermer Show, and the author of Why People Believe Weird Things, The Believing Brain, The Moral Arc, Heavens on Earth, and Giving the Devil His Due. His next book is Conspiracy: Why the Rational Believe the Irrational, which you can pre-order here before the October 25, 2022 publication date.