This won't convince everyone, but it is very good:
To the transphobes, “what is a woman?” is never treated as a serious question. It is only a rhetorical device meant to “own the libs” or whatever. This is a shame, because it’s an excellent question. As a trans woman myself, I love this question because if treated seriously, it yields some surprising and uplifting insights into the nature of identity itself.
So that’s what we’re going to do today: take it seriously. And for the sake of clarity, the rest of this article will refer to “what is a woman?” as The Question.
If you took any philosophy classes in college, you may recognize The Question as fundamentally an ontological one. It is a question about categories, which are sufficiently interesting that an entire branch of philosophy dedicates itself to examining them and how they work.
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The broad strokes of ontology are about how categories are defined and how you determine which things in the world do or don’t belong to a given category. In that sense, The Question is clearly ontological because it implicitly posits that a category called “women” exists, and then asks for a definition of that category.
Why? Because we would presumably like to have a rigorous way of knowing which people belong to that category and which do not. That is, we would like to be able to use that definition in a social context to do useful things like decide who gets to marry whom, who gets to use which bathroom, and who might get sent off to fight in foreign wars.
Keen readers will observe that there is a circularity problem here: to define a category, we must examine members of that category to see what traits they have. But without an a-priori definition of the category, how do we know that the things we’re examining actually belong to the category? Ontologists take a variety of approaches to this circularity problem. The ones that are most relevant for our purposes are prototype theory and iterative refinement.
Prototype theory takes the existence of the category itself for granted and builds a definition of the category around uncontroversial examples. If examining the category of “birds”, the prototype theorist more or less says, “look, we’re not sure about penguins, but we all agree that crows and robins and sparrows are birds, so let’s just start there, ok?”
Iterative refinement takes a prospective category definition and refines it by examining additional candidate members of the category, to see whether they should be rejected from the category or whether the category definition itself should be refined to properly recognize them. The iterative refiner says “Ok, so penguins don’t fly, but they do lay eggs. Should we refine the category definition to exclude flying as a necessary attribute, or should we reject penguins from the category of birds?” And they probably decide to exclude flying from the definition, because a broken-winged sparrow is still a bird.