A consistent demand of so-called “gender critical” feminists has been to posit that a definition for “woman”. “How can trans women be women?” they ask. At first, one might consider this an eminently reasonable demand. If woman is to mean something, obviously, then it must have a definition. If we don’t, well, how are we to fight the oppression of women? And those evil transactivists have refused, positively refused, to provide a definition, or at least a coherent definition.
There are several layers to the actual question at hand. First, the question of whether a definition is even necessary. For me, I see two plausible answers. The first is that while it may seem intuitive that a definition is necessary to actually liberate women, it may be more deleterious to the cause to actually fix the subject. This is one of Judith Butler’s main points in Gender Trouble – it actually starts the book off! I’ll now quote quippets of the first section at length
Recently, this prevailing conception of the relation between feminist theory and politics has come under challenge from within feminist
discourse.The very subject of women is no longer understood in stable
or abiding terms. There is a great deal of material that not only questions the viability of “the subject” as the ultimate candidate for representation or, indeed, liberation, but there is very little agreement after all on what it is that constitutes, or ought to constitute, the category of women
If this analysis is right, then the juridical formation
of language and politics that represents women as “the subject” of feminism is itself a discursive formation and effect of a given version of
representational politics. And the feminist subject turns out to be discursively constituted by the very political system that is supposed to
facilitate its emancipation.This becomes politically problematic if that
system can be shown to produce gendered subjects along a differential axis of domination or to produce subjects who are presumed to be masculine. In such cases, an uncritical appeal to such a system for the
emancipation of “women” will be clearly self-defeating.
The political assumption that there must be a universal basis for
feminism, one which must be found in an identity assumed to exist
cross-culturally, often accompanies the notion that the oppression of
women has some singular form discernible in the universal or hegemonic structure of patriarchy or masculine domination
My suggestion is that the presumed universality and unity of the
subject of feminism is effectively undermined by the constraints of the
representational discourse in which it functions. Indeed, the premature
insistence on a stable subject of feminism, understood as a seamless category of women, inevitably generates multiple refusals to accept the
category. These domains of exclusion reveal the coercive and regulatory
consequences of that construction, even when the construction has
been elaborated for emancipatory purposes
Indeed, the fragmentation within feminism and the paradoxical opposition to feminism from “women” whom feminism claims to represent suggest the necessary limits of identity politics.The suggestion that feminism can seek wider representation for a subject that it itself constructs has the ironic consequence that feminist goals risk failure by refusing to take account of the constitutive powers of their own representational claims. This problem is not ameliorated through an appeal to the category of women for merely “strategic” purposes, for strategies always have meanings that exceed the purposes for which they are intended.
In the course of this effort to question “women” as the subject of feminism, the unproblematic invocation of that category may prove to preclude the possibility of feminism as a representational politics. What sense does it make to extend representation to subjects who are constructed through the exclusion of those who fail to conform to unspoken normative requirements of the subject? What relations of domination and exclusion are inadvertently sustained when representation becomes the sole focus of politics? The identity of the feminist subject ought not to be the foundation of feminist politics, if the formation of the subject takes place within a field of power regularly buried through the assertion of that foundation. Perhaps, paradoxically, “representation” will be shown to make sense for feminism only when the subject of “women” is nowhere presumed.
Butler’s argument here is multifaceted and could serve as the subject of entire essays and even a class, but the gist of her point is that the destabilization of the concept of woman threatens to force us to reconceptualize the relationship between “women” and feminism as a political project itself. If we recognize that “woman” does not exist independently of a sociohistorical process, then what does it say that feminism is a “movement for women”? Moreover, how can feminism claim to “speak for women” or “represent women” if the progenitors of feminism as a particular social movement come predominantly from a particular background, geographic location and social class – does it make sense to say that “feminism” can be found in pre-modern China? If feminism no longer requires the type of proclaimed universality critiqued in “Under Western Eyes“, then what does the alleged universality of womanhood or a single subject “woman” do for feminism either?
A similar line of questioning the necessity of such a feminist politic can be found in Richey (n.d.), who, following Haslanger (2000), identifies a normativity problem for definitions of gender terms, but sees it as fatal to the project in and of itself.
The second answer to our first question that I find myself considering is that some sort of ‘definition’ could be employed, but that it be processual, dynamic, and denying of fixity. There are several ways of doing this, and I’ll examine a few in this post.
One alternative to the typical way of thinking about defining womanhood is to see womanhood as continuously reconstituted – who is a woman is not fixed and changes from moment to moment based on factors like perlocutionary utterances. Deleuze begins such an analysis with his concept of “becoming-woman” (Dawson 2008), which makes heavy usage of Deleuze and Guittari’s thick and idiosyncratic analyses, concepts and modes of thought, while Butler’s expansion upon Austin’s theory of speech acts has been considered foundational to the field of queer theory (Butler 1988).
Consider the example of sports teams. When you are playing baseball with a group of friends and need to divide that group in half to create two teams, what are the definitions of “Team 1” and “Team 2”? Clearly, at least for the critics of self-ID definitions, we can’t define “Team 1” as “anyone who joins Team 1” or “the group of individuals who were assigned to Team 1”. But in virtue of what are members of Team 1 … members of Team 1? When we’re playing baseball, we can quite clearly distinguish members of Team 1 from members of Team 2. And this membership isn’t fixed or static – it can change. If there were initially 10 people on each team, but 2 people from Team 1 have to leave for an appointment, they are often no longer members of Team 1, and now teamless. To even the odds, you might even move someone from Team 2 to Team 1 – they changed teams. There are a number of things we might appeal to here: recursive definitions, social knowledge and performative reconstitution.
Perhaps it is a dead end to seek an intensional definition that attempts to list the factors common to women than to create ways of identifying people who are women – does it not count as a definition when one is able to identify those individuals who are women? If we go back to the typically mocked and allegedly circular “a woman is anyone who identifies as a woman”, what is the issue with the definition beyond its circularity? We are able to identify individuals who are women on this definition – they identify as women. I know I am not a woman – I do not identify as a woman. I know my brother is not a woman as he does not either. Similarly, I know my mother is because she does identify as a woman.
Yet another solution to the ‘problem’  can be grown from the seeds Tomas Bogardus sows in his polemic. In his discussion of potential ways of read Katherine Jenkins’ definition:
Someone is a woman if and only if she takes (a sufficient number of) norms about women to be relevant to herself, i.e. to be about herself
Bogardus considers the possibility that her definition has two meanings of woman. The first sense is the word in question, what she is defining – the concept on the left side of the “word equation”. The second sense is what he attempts to inquire as to its meaning – exactly what does that mean? He considers several options: that the “woman” in the definiens is the “traditional sense”, which implies that trans women can only be women in virtue of making a mistake. The second is to insert her definition as the meaning of woman in the definiens, introducing an alleged vicious circularity. He considers several others, like using Haslanger’s original ameliorative definition or becoming quietists about the meaning. To combine Bogardus’ way of specifying differing meanings of a concept to avoid circularity with the processual thinking outlined above, we can begin the construction of a non-problematic definition.
If we define womanhood recursively, by indexing acts of “womaning”, the process of becoming a woman, we can avoid circularity, and trans-exclusivity. For example, let’s consider the traditional pro-trans definition:
A woman is anyone who identifies as a woman
If we accept Bogardus’ charge that this is circular, and viciously so, to keep the “womans” the same in both uses, then we have to come up with another meaning for the second one. If we consider a recursive definition, then:
It may seem a bit confusing, and I admit this is a very rough sketch. But let’s consider a few examples. If we consider a trans woman (let’s call her A) at the moment she first realizes she considers herself a woman – at that moment, she is supposed to become a woman for trans-inclusive feminists. The moment before she does so, “woman” does not include her, but the moment after, it does. So the best way of resolving this is to say that at the moment of A’s first identification, she is identifying with the collective of individuals who were all women before her realization (let’s call this . Because of that identification , the concept of womanhood is “updated” and then includes her – . The next person to realize their womanhood then identifies (at the moment of this identification) with the “new” concept of woman, . 
Bogardus’ loop is thus broken – the concept in the definiens is not the same as the concept being defined, and it doesn’t seem to be trans-exclusive in any way.
Certainly this may introduce problems of its own. For example: on this concept of womanhood, are trans women women prior to their first moment of identification? It may seem like the easy answer is no, but I have not done the groundwork to read my own words carefully enough! Regardless, it seems that such an issue could easily be rectified by including ethical considerations in our decisions to apply gender terms (Dembroff 2019).
There are also some temporal issues to consider here. One might want to stay truer to the dynamism avowed above and claim that A is identifying as at the moment of her identification and that her act of identification ‘updates’ womanhood. But then we get stuck back in the circularity – our definition would be, for example:
I think this may be a fault of the English language and the way that we conceptualize changes in time. In programming, it is quite easy to update categories or lists. In R, one can extend a vector by combining them:
list <- c(list, addition)
One will note that list is used both in the “definition” (list is being reassigned here) and the definiens (it’s what is being combined with “addition”). Different programming languages handle this sort of reference differently – but these differences are what make each language distinct.
So perhaps it is coherent to say that one can reconstitute womanhood by identifying as a woman – that the very act of identification modifies womanhood, but that the subject of identification is itself already the modified womanhood. Perhaps what might seem like a problematic circularity ends up being the result of a flaw of natural language.
To return to the baseball team analogy, let’s consider the three proposed solutions presented earlier. Number one was recursive definitions: Team 1 is defined in terms of the previous members plus the new addition. Number two was social knowledge – perhaps we know who the members of Team 1 are … Number three was performative reconstitution: the very act of a coach saying “Team 1” to a prospective player reshapes the boundaries of “Team 1”.
One motivation for even abandoning the static, discrete definitions (Aristolean definitions as Baker (2008) points out) is that they do not comport very well with our intuitions and actual linguistic experience. Cognitive scientists have moved beyond the simplistic ways of defining concepts that involve an allegedly comprehensive list of necessary and sufficient conditions, exceptions, checking boundary cases, etc. Alternative ways of instantiating concepts (Murphy 2002) and designing social inquiry (Ragin 2008) allow us to escape analytic philosophy hellhole while retaining use of our social concepts.
Perhaps instead of Aristolean definitions, we could proffer some sort of family resemblance concept (Nicholson 1994), or a “fuzzy model” (Tauchert 2002; c.f. Joaquin & Biana 2019). The options are limitless.
 I should first note that I think Bogardus’ reconstruction of Jenkins’ definition to be grossly misrepresentation, erring on the border of libel.
 We should be more specific by what we mean by identification. It is less that identification means equation than it is a form of social expression in and of itself. To identify with a group is to join a social community, to claim membership in that community to express a desire. Personally, I am a critic of identity itself (Brubaker & Cooper 2000; Butler 1999; Moran 2014), so I don’t defend this account except provisionally.
 A commenter on this post mentioned that this account may rest on the assumption that all women will identify with , which is not going to be a part of reality. They more likely will identify with a subset of the women that they consider to be true women. This reply can be accounted for by considering a two-step reply – first we introduce the idea of the collective (Haraway 1985; Marion-Young 1994) and then connect it to our account of identification. If we posit that the collective we’re talking about needn’t be directly identified with, but connected to the perlocutionary act of identification via paradigm cases, then we can allow disparate individual concepts of womanhood to be connected to the abstract social womanhood collective despite the variability in each idiosyncratic concept’s extension.