I'm having a bit of a back and forth with @bowserwife about gender and radical feminism, some of the points I'll e repeating here, so hopefully in future discussions I can use this as a reference and this might spark the discussion with other people.
Preamble
About this discussion, I'll just point out some notions for the debate.
I'm going to engage in good faith and I'll assume you're engaging in good faith too, but I'll match your energy, if you wanna go blood sports let's dance.
I'll assume you disagree with me because you might have heard some argument that I did not or because you haven't heard one I did.
English is not my first language, I'd something sounds uncanny it might be that.
Hypothesis
Let's start with a brief list if things I will not debate, if you disagree with any of those this post ain't for you.
We live in a patriarchal society
Sex is a biological category that follows a binormal distribution (most of us are either male or female)
Gender is a biopsychosocial category informed by gender but not defined by gender
Sex and gender are different things
The whole debate space between trans folk and radfem can have some nasty people saying mean things to each other, those things do not make anyone right nor wrong
Any definition of woman that includes Buck Angels failed
Any definition of woman that excludes cis woman failed
Any definition of woman that includes cis man failed
The arguments
Part 1 - rigorous definitions
I do have some background in math and I used to have a professor who said that there are three important things in math:
Rigour; rigour; and rigour. Some say you need a forth one, rigour, but I find it unnecessary.
I'll agree that rigorous definitions are valuable tools to understand the world, so let's express clearly what is meant by a rigorous definition. Some criteria one can use to identify if some object belongs to some class of objects such that the criteria includes in the category all the things that it should (no object is missed) and that the criteria do not introduce anything that it should not (no object is miss classified).
I'll provide one example, the natural numbers as defined by Peano:
1 (one) is a natural number.
For every two natural numbers a it's successor, a+1 is a natural number.
OBS: Peano did not include zero as a natural number, this is by design.
You'll notice that the definition is separated into two parts a base case and a recursive case. The definition leaves nothing to be interpreted, either something is a natural number or it is not, there is no context influence, no conditionals.
Or does it? It is pretty easy to overlook, but the Peano definition of natural numbers depends on the definition of the + (plus) operator. It might seem trivial but it is not. Peano natural numbers only work under the hypothesis that any numbers plus one is different then the original number, i.e. a+1 /= a.
Then, we can point that we need to define what equality means, so we can define what difference means... This'll run down until we need to define axioms, statements that can't be proven and we assume as true.
If math cannot rigorously define natural numbers without axioms, what hope do we have of defining anything as rigorously in the real world? We'll see.
Before we continue and leave this dreaded land of math, let me raise some other properties of definitions.
If two categories have the same definition, e.g. the non null absolute values of the integers is another definition of the natural number (a pretty round about way to define them but still). Those two categories can be viewed as being the same.
If two different categories of objects, with different definitions, can have their objects translated from the first category to the second one without losing any structural properties, it is a homomorphism. A pair of homomorphisms such that the translation can be undone is an isomorphism. Two categories between which there is an isomorphism are said to be equal up to isomorphism, or in plain English, equivalent.
The equivalence itself is contextual to what we mean by lost structural properties, and it can be distilled further, but we can specify those as we find it necessary later.
Part 2 - definitions in the real world
In the real world definitions are much more loose than in math, just as an example to hammer this home, we cannot define if things are equal without some leniency and good faith. Is two blank A4 sheets of paper equal? In that sense? They for sure are not maid by the same atoms. They for sure do not have the same thickness down to a piconometer scale... Whenever, this point forward, I say something is equal or equivalent to something else, I mean equal or equivalent up to a good faith interpretation.
In other words, let's not occupy ourselves with petty word games, please.
The, "what is a woman?" discourse have the this trope of degrading into "what is a chair?" Questioning. For everyone who ever tried to respond to this kind of questioning, you misunderstood the argument. There are no objective answers to what is a chair that do not rely on a sea of unlisted axioms, and with the axioms being, by definition of axiom, unproven but assumed as true, any two definitions, as unequivalent as possible, have the same validity.
There will be a more lengthy discussion about what I'd argue should be the criteria of choice for differentiation between definitions, but for now let's assume that given two different valid definitions we'd all agree on what'd be better.
Other than chosing between two valid definitions, we can take a step back and attack the axioms on which that definition rests, if we try and define a car as having four wheels, that depends on wheels being round and we need to ask if that holds for every case...
Than again, we can still attack a definition by pointing out edge cases, and this is where we need to have good faith, there are cars that have any number of wheels, defining it as having four is "good enough" of a definition if we agree that those outlier are too much work to deal with as a whole and that we can go on a case by case basis.
That means we lost some of our rigour on our definitions, they all now have to have an asterisk pointing that there are edge cases. This is a toll most of us are willing to pay, and only concern ourselves with for petty word games, if some wants to use only definitions without it, I'd refer that someone to the endless chair defining threads.
Then how much of the general population constitutes and edge case is another discussion, deeply linked with the discussion of which of two equally valid definitions we should use.
Furthermore, in the real world we communicate using fallible language, and words have definitions themselves. As such we should at the very least differentiate nouns and the objects they refer to. There is the word "woman" and there is the category "woman". Words have meaning but we do have word play, sarcasm, double meaning... In the definitions I'll provide, I'll try to limit how much this can influence our understanding by aiming to define woman as a category, not the word woman.
Part 3 - defining gender and sex
The three categories: female, intersex and male, are sex based. But sex, as a metacategory needs a definition to itself. We can define it in terms of genotypically male or female, hormonally male or female, anatomically male or female. All those are interlocked so someone who is in the male category on the genetic level will most probably also have hormone levels that'd classify them as male, and the anatomy of a male. The genetic aspect informs the anatomy and the endocrine aspect, they both inform each other, but they can be pretty cleanly distinguished. In the real world, we look at the anatomy.
Do a newborn have the superficial anatomy of a male? they'll be classified as a male. This early classification is the origin of the terms AGAB (assigned gender at birth), AMAB (assigned male at birth) and AFAB (assigned female at birth). Please, let's point out that those terms are not rigorous, the AGAB is not a gender, it is a sex. The Female maker on anyone's birth certificate do not refer to the biopsychosocial construction of gender. Edge cases for this will include intersex cases where a sex is not assigned, those I'll argue we should see in a case by case basis if we classify them as AFAB or AMAB. The same, I'll argue, we should do to cases where there are no birth certificate, and most other edge cases.
So male or female can be defined better by doing so by observing the anatomy of a person. To do so we need a non exhaustive list of sex markers, be they discrete or continuous. The short version of this list is: body hair; genitalia; breasts; bone structure; fat distribution; height; muscle mass; etc. Each marker indicate one or other sex, having enough markers of one sex classify one as this sex, having enough markers of both classify someone as intersex. This definition is context free in relation to social aspects, we can with this definitions, classify people into male or female regardless of the society in which they exist.
In other words, I'm defining sex purely in terms of what can be determined in a physical examination. And foreshadowing the discussion I want to have about utilitarianism later, sometimes we might need or want to classify someone with incomplete information. Mostly, you don't look at someone's genitalia before clocking then as male or female, even if you ignore gender markers, most people with hairy chests are male, and that is a safe assumption to make.
Now that we have sex, what is gender? A shallow definition could be made as "psychosocial sex". That's the idea that originates the "pink brain/blue brain" simplification. It is not an invalid definition, but it do not make as clear as desirable what is meant.
As much as sex can be broke into multiple levels, gender has multiple aspects. We can speak about gender identity, expression and roles.
Gender roles are the society archetypes in terms of expected behavior and responsibilities. Those are not written into stone, gender roles change over time, change over geography, social economic status etc...
Gender expression is the individual instances os adherence to gender roles, mostly focused into aesthetics, but not exclusively.
Lastly, gender identity is the internal alignment with the external gender division. It is how someone feels, how someone see themselves, and how someone would wish to be seen.
Differently than the sex, gender can be perceived in all levels simultaneously. Unless there is some lie involved, if someone say they identity with a gender, you can for sure know their gender identity.
Gender expression, because of its presentation quality, can be queried by looking at someone's non biological appearance markers. Make-up; clothes; posture; voice tone; etc... And gender roles you can just as easily determine by watching what do the person do, what are the roles they assume.
Now, gender roles and gender presentation, as the set of markers, are not immutable. If you tell me that woman should not wear pants I'll tell you to fuck off, this is a marker that is waaay outdated. If you tell me man can't wear makeup I'll probe you to understand what makes you think like that... This are trivial examples, but the point is we're talking about dynamic markers that are context dependent and vary in function of the person whose perception we're considering... This is complicated.
Of course some gender marks are also sex marks. Meaning, some parts of what makes someone male or female also makes someone man or woman. Okay, that should not be that shocking, sex and gender are deeply related. It is not coincidence that most people are cis.
And now, for the fun part, let me introduce some definitions of what is a woman, in terms of the criteria one could use to classify something as a woman or not. For the sake of brevity I'll assume we're excluding everything that is nor a human and not an adult. Lastly, up to isomorphism, those definitions are equal.
Female
Someone who bears the anatomy markers that identity them as being of the female sex, is safely a woman. There will be edge cases but those ones we can treat on a case by case basis.
Someone perceived to be female
For all intents and purposes, someone whose only visible markers are ones of a female, is most certainly, a woman. There will be edge cases but those we can treat on a case by case basis.
Some who is perceived to be a woman
Now, detaching finally from the biological criteria, if someone is perceived to be a woman, they are a woman. There will be edge cases...
Someone who wants and is perceived as a woman
Well, for all intents and purposes, if someone wants to be perceived as a woman and succeed in doing so, they are a woman, and now, most of the previous edge cases are no longer an edge case.
Someone who identifies as a woman and is perceived as one
Remember that part of the gender identity having a relationship with wanting to be perceived in an specific gender? Of course there will be edge cases, but then again, in here they'll be fewer.
Now, what if the perception includes the gender identity?
Someone whose gender identity is woman
Now look of what I've done, I'm suppressing two aspects of gender to use only one as a criteria, just as we did with sex. This one is relevant because of the edge cases, in previous definitions, a butch woman whose gender expression and gender roles do not align with woman's was an edge case, now it is not.
Before we continue, you might have a problem with me saying that some of those are equivalent to the others. In specific it might seem that a pulled a fast one by going from perceived femaleness to perceived womanhood, I didn't. In the same way we defined sex in terms of its markers there I'm defining gender in terms of markers here. To be perceived as a woman is to have enough gender markers that indicate that one is a woman for the given context of this one. In a circle of trans positive friends all the necessary markers are the ones associated with the gender identity, so those definitions, in terms of gender perception, are clearly context dependent.
Part 4 - utility of definitions and inclusive language
Now, if we have all those definitions being equivalent to each other, why spend all this time if the first one is good enough? Because some are more useful then others.
Let's start by pointing out that language is mutable, and what we mean by woman changed through the last couple centuries, both in terms of what the word means and what the category women includes and excludes. Any definition of woman that'd include some trans man in a first moment but then we go and say that this buff guy with a harry chest is not actually a woman, he's female but look, he's an edge case...
Let's be honest, this type of ad hoc exclusions and inclusions is what make the definition seem less rigorous. We should choose a definition that minimizes the confusion.
Moreover, definitions can be prescriptive statements, saying "trans woman are woman" is both a description of someones beliefs and a prescription that trans woman should be seen as woman. The definition that we choose to use reflect the world we wish to create.
I, personally, want to create a world where no one has a label forcefully put on them, if a young female do not want to be seen as a woman, let them identify themselves out of womanhood. Let's not invalidate the fact that for this person, their gender identity is other than the one prescribed by the general "adult human female".
Using language so that people don't feel uncomfortable unnecessarily is preferable.
Part 5 - Lying men in dresses
Now, we have one last topic to sort, I'll be brief, if you agreed with all that I have laid until here, there is one last thing I imaging you can argue, what about a man who identify as a woman just to gain access to woman only spaces. That is, of course, the case of, if we're working with the gender identity model, the case of someone lying.
I'll be honest, I cannot see why would a man do this, but I am not one so I can't really tell. All the discomfort of being treat as some gender different of the one you identify as seems a bit too much when there exists alternatives. I won't say it never happens but those are the edge cases.
Then again, why would a man willingly identify himself into receiving misogyny? Well, this seems to me that this should be treated in a case by case basis.
Conclusions
Someone is of the woman gender if their gender identity is woman.
