Aristotle, Wittgenstein, and Gender Identity

How a Philosophical confusion prolongs a political debate

There is almost no communication going on in the "debate" over transwomen in sports and other social settings. What we have are two echo chambers that constantly reinforce their animosity to each other. Check the comments on any post on this topic. There will be little or no critical response, and every other comment will be cheerleading. Every post and almost every comment on this subject I have seen on Substack says transwomen should not be allowed to compete as women. (That may be a fault of the algorithm, of course). However, if I go to Medium, Reddit, or Daily Kos, I get nothing but the other side, with all the comments cheerleading that position. Anyone who dares to take the forbidden side in either echo chamber gets showered with abuse.

This kind of impasse often arises because there is a philosophical disagreement that neither side acknowledges. Each side asserts that this philosophical disagreement has been decisively settled by certain scientific facts and/or common sense. One problem is that each side cherry-picks the facts that supports their position, and ignores the other side’s facts. But a bigger problem is that the same scientific facts can often be interpreted to support contradictory conclusions. When this happens, both side usually resort to asserting their positions over and over, mixing in rhetorical abuse with each repetition. This strategy is often called Table-pounding. It is not a kind of argument, but rather a substitute strategy for avoiding argument altogether. In this case, the table pounding “debate” consists of alternating cries of “Transwomen are women, period.” and “You have to be X to be a woman.” (born a woman, have XX chromosomes etc.)

There is a third way of avoiding both of these doomed strategies. If both sides in a dispute share certain presuppositions, it is possible to change the shape of the debate (and sometimes dissolve the debate altogether) by questioning those shared presuppositions. I will argue that this debate is a stalemate because both sides are presupposing rules established and codified by Aristotle—the inventor of common sense and traditional logic. Because almost no one but professional philosophers and Catholic priests study Aristotle today, his ideas paradoxically have an even firmer grip on how we reason and perceive than ever. That’s because it never occurs to most people that they are using his ideas, which makes it almost impossible to imagine thinking any other way. Consequently, in order to explain the assumptions that have led to this stalemate, we have to say a few words about Aristotle’s system of classification, which is the basis of his system of reasoning.

Aristotle believed that reality consisted of nothing but substances (Apples, rocks, dogs, trees etc.) and their properties or qualities (shape, color, size, weight etc.). These properties are either essential properties of a substance or accidental properties of that substance. The essential properties are those which determine what Natural kind a substance belongs to. Any substance that does not possess all the essential properties that define a kind of substance is not that kind of substance. If an alleged dog is not warm blooded, it is not actually a dog. Accidental properties are those which a substance may or may not possess. Some dogs are black, some are brown, some are white, but that has no effect on their being dogs.

Each substance can be classified into a natural kind by determining whether it possesses the essential properties of that natural kind. The essential properties are so called because all members of a natural kind allegedly possess all the essential properties of that kind. This implies that it is possible to make true statements of the forms All S is P and No S is P for any natural kind, such as All Dogs are Mammals or No Dogs are Feathered. The accidental properties are stated in sentences of the form Some S is P such as Some Dogs are brown or Some Dogs are not Brown. Once we have our thoughts arranged in this form we can make logical inferences from them to other important conclusions.

With all this in mind, we can describe the main debate over trans issues as concerned with the question “What are the essential properties that define the Natural kind “Woman” ?”(or “Man”, but we will stick with the woman example to avoid unnecessary repetition). At its best, this debate presupposes the same rules and assumptions that shaped Aristotle’s reasoning, and that of his teacher Plato. Most of Plato’s writings feature his mouthpiece Socrates asking for a definition of a widely used concept (such as “Justice” or “Rhetoric”). The definition offered in response to Socrates’ questions mentions certain qualities that are asserted to be essential properties of the category being defined. Socrates then points out that these cannot be the essential properties of that category, because this definition either 1) doesn’t apply to all members of the category, or 2) doesn’t apply to only members of the category. Either of these factors allegedly proves that the definition is unsatisfactory, which prompts the participants in the dialogue to search for another possible definition.

For better or for worse, an Aristotelian definition is what we still strive for in our heart of hearts. We want a definition to give us both necessary and sufficient conditions for the thing defined. We want it to be applicable to all things referred to by the defined word, and only to things referred to by the defined word. This is what we might call “the definition of a definition”, and it still remains the gold standard for many kinds of terminology.

If we don’t have this sort of precise definition for legal terms, such as “insider trading”, “sexual harassment”, or “hate crime”, all kinds of injustices can result. If the definition doesn’t cover all such crimes, it incorrectly describes the sufficient conditions, and guilty people will go unpunished. This is one reason why after a law has been written, lawyers are often hired to find “loopholes” where the law has failed to describe all of the sufficient conditions of the behavior it was trying to prohibit. Conversely, if the definition doesn’t cover only such crimes, it incorrectly describes the necessary conditions, and innocent people will be unfairly punished. This was one of the problems that came up when governments tried to write laws that forbid the possession of drug paraphernalia. (You don’t want the law to require the police to arrest people for owning baggies.) Being a good lawmaker means being able to write laws that contain definitions that make neither of those mistakes i.e. which correctly define both the necessary and sufficient conditions of the activity being proscribed by the law. This is one reason why lawyers are still required to study Aristotelian logic.

For all these reasons, Aristotle’s categorical style of thinking, and the logic that grows out of it, is as valuable a skill now as it was 2,500 years ago when Aristotle invented it. Nevertheless, there is a serious problem with this definition: There are almost no actual categories in the real world in which all members of the category actually possess all of the allegedly essential properties. This was first pointed out by philosopher Ludwig Wittgenstein in his book Philosophical Investigations (actually a collection of unfinished notes that were not published in his lifetime). Wittgenstein was trying to understand language by comparing it to a game. At that point, any other philosopher would have set out to list a set of necessary and sufficient conditions to define a game. Wittgenstein, however, decided to question the Aristotelian assumption that such a definition was necessary or even possible. The following passage, where he first raised this question, is one of the most influential in modern philosophy.

Consider for example the proceedings that we call “games”. I mean board-games, card-games, ball-games, Olympic games, and so on. What is common to them all? — Don’t say: “There must be something common, or they would not be called ‘games’ “-but look and see whether there is anything common to all. — For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: don’t think, but look! —

Look for example at board-games, with their multifarious relationships. Now pass to card-games; here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ball-games, much that is common is retained, but much is lost. — Are they all ‘amusing’? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. In ball games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis.

Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! sometimes similarities of detail. And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear. And the result of this examination is: we see a complicated network of similarities overlapping and cries-crossing: sometimes overall similarities.
I can think of no better expression to characterize these similarities than “family resemblances”; for the various resemblances between members of a family: build, features, color of eyes, gait, temperament, etc. etc. overlap and cries-cross in the same way.-And I shall say: ‘games’ form a family.

And for instance the kinds of number form a family in the same way. Why do we call something a “number”? Well, perhaps because it has a-direct-relationship with several things that have hitherto been called number; and this can be said to give it an indirect relationship to other things we call the same name. And we extend our concept of number as in spinning a thread we twist fiber on fiber. And the strength of the thread does not reside in the fact that some one fiber runs through its whole length, but in the overlapping of many fibers. (from aphorisms 66 and 67)

When Wittgenstein says that “the strength of the thread does not reside in the fact that some one fiber runs through its whole length”, he is rejecting the distinction between accidental and essential properties. With real world categories like games or numbers or families, there will usually be no true statements of the form all S is P. Instead, you end up with something like a menu in a Chinese restaurant. In order for something to be game or a number, it must have one attribute from column A or one from column B. But that does not mean that any one item in either column is necessary, or any combination of items from both columns is sufficient. If we expand Wittgenstein’s example of a family, we can see that it works that way. In families where all members share a noticeable family resemblance, one member may have the family eyes, mouth and chin, another may have the family hair, mouth, and posture, another may have the family eyes, chin and hair and so on. If there are 30 attributes that are family attributes, it could be that everyone who shares the family resemblance may have somewhere between 8 and 12 of these 30. But it would not be necessary for there to be a single set of attributes that all members of the family have in common, which means it would be impossible to come up with a necessary and/or sufficient set of criteria that would define members of the family.

Further thought and research, however, has shown that this description is not quite enough to be the whole story. Certain attributes are usually more important than others. Some, but not all, women have ovaries and some, but not all, women like to cook. Nevertheless having ovaries is more important for determining whether a person is a woman than whether or not she likes to cook. There are, in other words, certain characteristics which need to be “weighted” as carrying more significance than others if we are to actually quantifiably determine what category something (or someone) belongs in.

There are also certain kinds of individuals who are considered to be prototypes in that category. A robin is more of a prototypical bird than an ostrich, at least for those of us in North America. It appears that we acquire knowledge of a category by the first encounters we have with members of that category. We see robins, then sparrows, then blackbirds, and we eventually develop a category that is flexible enough to relate all of them to each other. With a little stretching, and some articulation of some boundaries, we can create others species in this genus, such as crows, hawks, and eventually even ostriches. When we articulate boundaries between species, we still try to use something very much like Aristotle’s accidental and essential properties. But when we try to be completely precise using Aristotle’s methods, we often discover that every necessary and sufficient definition seems to leave out individuals and species which intuitively seem like they ought to be members of that category, or include individuals that ought not to be members of that category. The necessary and sufficient criteria are usually pretty good at identifying the prototypical members of the category, but they leave out the borderline cases. We intuitively think of flight as a necessary characteristic of birds, and yet ostriches are clearly birds, because they possess many of the other properties that help define the bird family: Feathers, laying eggs, a gizzard instead of teeth etc.

The reason that Aristotle’s logic is still used is that much of the time we are thinking about the prototypical members of a category. These prototypical members usually possess most or all of what we think of as the essential properties of that category. If we assume the truth of statements like All Birds have feathers, we can usually logically argue from the presence or absence of those “essential” properties as effectively as Aristotle did. Every so often, however, we discover items which don’t belong to a category but seem to possess those properties, and/or items which intuitively belong to a category but don’t possess those properties. In these cases, we do some sort of Ad hoc patch job that enables us to put the item in question in one category or another. In Law Courts, a judge often does more than decide whether the defendant did what she is accused of. Sometimes the judge must also decide whether a defendant’s behavior could be classified as prostitution, insider trading, libel etc. That judgment becomes the basis for future judgments as case law. But on many fringe cases, the decision doesn’t have any other foundation than the judge’s intuitions.

Another example: Aristotle designed his system to apply first to biological categories, and modern biology texts still use his concepts to classify animals and plants by genus and species. But Darwinian Biology recognizes that strictly speaking the borders between species are blurry, because we now know that all life descends from a single “mitochondrial Eve”. That’s why we sometimes discover animals like the platypus, which don’t fit neatly into categories like “mammal” or “bird”. The decision was made to classify the platypus as a mammal, but that was largely because everything had to be somewhere.

No matter what you are trying to classify, there will always be items like the platypus that possess some but not all of the so called “essential” properties. Research can reveal what properties an item possesses, but it will always be up for grabs whether those properties are essential determinants of category membership. Is Pluto a planet? Is a beanbag chair a chair? Is cheerleading a sport? Is a hot dog a sandwich? Is a tomato a vegetable? Each of these items possess some of the properties of a prototypical member of the category I connected to it, but it also lacks some other prototypical properties.

This does not mean, however, that the categories we use in daily life are simply chaotic mush. Categories are not mere fairytales. We cannot divide the word arbitrarily according to our whims and impulses. We must divide the world into categories which enable us to undertake certain projects and achieve certain goals. “Essential properties” are those which are essential to the attainment of those goals and accidental properties are those which are irrelevant to those goals. Some people think that the only real categories are the ones that are necessary for doing science, because these scientific categories describe the world itself, not our ways of relating to it. But every science has different goals and purposes, each of which requires its own set of categories. For the botanist, the ability to reproduce is the essential characteristic of a fruit, and because a tomato has seeds it is a fruit. For a nutritionist, however, the essential property of a fruit is to provide certain vitamins and minerals — which the tomato does not, and is therefore a vegetable.

If this is all there is to categories, the question “Is a tomato a fruit or a vegetable?” has no single correct answer. For the botanist, the tomato really is a fruit, and for the nutritionist it really is a vegetable. Maybe there are Real Categories that carve the world up in ways completely independent of our goals and projects, maybe not. I don’t think so, but there are some philosophers that do. But even if there are no natural kinds, we cannot perform any human activity of any complexity without dividing the world up into something like Aristotle’s categories. Even if Aristotle was wrong about the existence of natural kinds, his theory of categories helps us to understand the functional kinds that we must learn (either consciously or subconsciously) before we can build bridges, bake cookies, sell real estate, or do any of the other activities that constitute our daily lives.

*****

In debates over trans issues, the trans critics usually rely on Aristotle, and the trans defenders often paraphrase Wittgenstein. Consequently, I will start by criticizing the transcritics, but I will not be letting the transdefenders off the hook. Many of their arguments are unstable hybrids of Aristotle and Wittgenstein, which don’t actually support the conclusions they are arguing for.

Because Aristotle basically invented modern common sense, and the trans critics see themselves as defenders of common sense, their arguments usually paraphrase the Aristotelian principles described above. Kat Highsmith states her Aristotelian assumptions explicitly when she rhetorically asks “Why should the brain be the determining factor while chromosomes and genitalia are not? What she calls “a determining factor” is just another name for an Aristotelian essential property. The best answer to this rhetorical question is “Why should the chromosomes and genitalia be the determining factor while the brain is not?” If we try to answer either question intrinsically i.e. by leaving out all references to human goals and purpose, we are forced to say “There is no fact of the matter.” There is no such thing as a determining factor that intrinsically puts anything into any category, whether we are talking about sex or chairs or tomatoes. The brain morphology, the chromosomes, the genitalia etc. are some of the many strands that together constitute the meaning of the category of biological sex. There are no essential properties amongst those strands, only a family resemblance produced by interlocking strands.

When trans critical writers like Highsmith try to prove that trans women are not women, they mention some property which trans women lack, and assert that that is the essential property that makes a woman a woman. The trans defender then replies using the same strategy that Socrates uses in Plato’s dialogues: by pointing out that there are ciswomen which also lack that property. (e.g. women who no longer menstruate and/or can’t have children. People who were raised as women without realizing they had XY chromosomes etc.), and therefore this can’t be the essential property that makes a woman a woman. The trans critic sometimes makes a few attempts to refine her original statement in response to these objections, but then usually retreats to table-pounding surrounded by rhetorical flourishes. One of my favorite flourishes is “it’s obvious that X ” which is just another way of saying “I don’t have an argument for X.” Another is to “justify” a conclusion by paraphrasing or renaming it i.e. “There are only two sexes because sex is binary.” All of these strategies are basically retreats to common sense, which are doomed because if common sense could settle these problems, we wouldn’t be arguing about them.

Nevertheless, we shouldn’t be too hard on the gender critics, because this is really the only strategy available if you are trying to squeeze a Wittgensteinian category into an Aristotelian box. Trans defender Dayna A. Elis has the same problem when she relies on these kinds of Wittgensteinian arguments to justify the position that transwomen are women.

When we talk about biological sex, it’s tempting to look for a single defining trait — like chromosomes or genitals — and call it decisive. But in reality, it’s the combination of multiple biological factors that determines how a person’s sex is classified: chromosomes, hormones, gonads, internal and external anatomy, and how the body responds to hormonal signals. These traits can align in typical patterns, but they don’t always . . . Rather than thinking of sex as a switch with only two positions, it makes more sense to view it as a spectrum, shaped by how these factors come together in each individual. Some people fall squarely into the typical male or female range across all traits . . . Others may have a mix.

Elis is of course correct about this, but later falls back to an Aristotelian position when she insists that “gender identity is rooted in the brain”. Elis’ list of papers showing the similarities between the brains of cis and trans women is a great resource, but her insistence that the brain similarities are the real root of gender identity is as unproveable as Highsmith’s claim that the chromosomes and genitalia are the ‘determining factor” of gender identity. Both claims are a futile attempt to superimpose the outdated Aristotelian concept of essential properties on a Wittgensteinian reality of continuums and spectrums.

What these trans defenders ignore is that these Wittgensteinian arguments also require us to acknowledge that every category contains members who dwell on the fringes of its borders. The stereotypical members of the category are right in the center of the category space, because they possess most or all of the “essential” properties. Other members of the category dwell on the fringes of the category space, because they possess fewer of those properties and/or fewer or none of the “heavily weighted” properties seen as especially essential. Consequently, you can’t assume that every member of any category has a solid and unambiguous status in that category. In a world where it is not the case that “beanbag chairs are chairs, period” Or “tomatoes are vegetables, period” Or “hotdogs are sandwiches, period.” we cannot dogmatically assert that “trans women are women, period”. These other assertions are of course far more trivial than questions about the social and political rights of trans people. But for better or for worse, we are forced to use the same conceptual tools for making all of these distinctions. Transwomen are women in the same sense that all of these other examples fit into their categories i.e. only if you have a willingness to be somewhat conceptually flexible. You can plausibly draw a principled line around the category “Women” that includes them, and also plausibly draw the line somewhere else. Both sides can table-pound on behalf of their positions, but as table pounding is not argument, and this fact does not settle anything.

Each side of this controversy must thus agree to disagree: to express their opinion, and act accordingly, and permit the other side to express their opinion and act accordingly. But how does this work exactly? What happened when I act on my belief and it interferes with you acting on your belief? Where does one side’s fist end, and the other side’s nose begin? At the moment, the most extreme transcritics demand that transpeople be treated as delusional lunatics, and the most extreme trans defenders get people fired and doxed simply for expressing the belief that trans women are not women. Neither of these positions are consistent with the unresolvable nature of the ontological questions involved. Instead, compromises need to be made on a case by case basis, and considering those many cases is a job for another essay.