> Sure, but my point is that if exogenous hormonal puberty becomes common enough (like, 50% of the population opts in to them), you can end up in a situation where in aggregate there are no measurable differences. You have equal numbers of XX women and XX men, and XY women and XY men. And all the men and all the women have equivalent heights, irrespective of their genes. In such a situation genetics cease to be predictive of height, while gender remains predictive.
This is unlikely, as you say, but in such an hypothetical situation, where half of the male population is being subjected to feminizing hormone treatments while half of the female population is being subjected to masculinizing hormone treatments, sure... you would be (artificially) reducing the difference in heights between XY and XX people. But notice that, again, the deciding factor is not at the psychosociological layer ("self-identified gender"), but still at the biological layer: what matters is whether you are genetically/chromossomally male and/or subjected to male-like hormonal profiles, and not so much whether you identify as a male.
> I acknowledge that such a situation is unlikely, but it should still cause one to second guess the "biological" nature of the differences.
If the differences are literally mediated by a combination of genetic and endocrine effects, then how could it be anything other than due to "biological" factors? Sure... if you identify as male (while not being a XY person), you're more likely to subject yourself to hormone treatments that lead to more male-like traits... the correlation is there... but the main factor, in the end, is whether or not you subject yourself to those treatments (and not so much how you identify as).
> Then I can construct sort of the opposite of the prior situation: a society where a huge number of people transitioned post-puberty, and so now identify as the opposite of the gender they went through puberty as.
This is, again, quite hypothetical. But, even in such as case, I would assume that people's physical traits would still be generally more reflective of one's genes and hormones, rather than how one identifies as or the social role they choose to perform as. Biological factors (including genetic and endocrine) would generally be more determining that psychological or sociological factors ("how I feel" or "how others perceive me").
> If we look at biology, there's a clear mapping from chromosomes to height.
There really isn't (at least not a "clear" one). You can have really good genes and still end up short due to nutrition (e.g., you're not getting enough protein and calcium in your diet) and/or epigenetic effects (e.g., your parents smoke and/or were subjected to malnourishment for a while at some point in their lives).
> If we look at gender, there's no correlation (there are tall men and short men, and tall women and short women, in approximately equal numbers and so you end up with two bimodal distributions).
This is, again, quite hypothetical and unlikely (that you end up with two bimodal distributions with no differences whatsoever in terms of mean or median-shift). Either way, it just reinforces what I've been saying: your gender (i.e. how you identify and/or how society sees you) is probably not a very important factor in determining height (once you account for confounders such as "hormonal treatments").
> In this situation, we don't really have measurable aggregate biological differences between the men and women.
Sure, in an hypothetical situation where you're giving feminizing hormones to half the men (to make them more woman-like) and giving masculinizing hormones to half the women (to make them more man-like), you could perhaps reduce differences between the two subpopulations (though not entirely... hormones don't control everything after all). But, notice that, again, you are using a purely "biological" process to achieve this and, even though you seem to be going out of your way to come up with a situation where there are no "measurable aggregate biological differences", I'm pretty sure that you would still find "aggregate biological differences" because there are non-endocrine genetic factors that affect height.
> This is really the point I'm getting at, talking about biological differences between men and women get's very complex very quickly assuming you want to consider trans people.
I don't want to sound insensitive, but if someone says "men are generally taller than women", you can probably infer from the context that they are most likely using the terms "men" and "women" to refer to biological men and women (i.e. not just someone who identifies as "man" or "woman", but someone who has the genetic and/or endocrine profile of a "man" or "woman").
To clarify, I think a "trans woman" is a "woman" and a "trans man" is a "man". But, even with hormone treatments, there are clear measurable biological differences between a XX person and a XY person (if nothing else, XY people have a shorter chromossome).
Furthermore, this overall discussion glosses over intersex people... there are plenty of people out there that are neither exactly male nor female, biologically.
Imagine there is a miracle drug that cures cancer, but it has a 95% mortality risk for men and 0.1% mortality risk for women. Should I treat a certain person according to how they identify on a psychological and social level, or according to their biological properties?
> We end up with 3 possible predictors for height: genes, hormonal-gender-at-puberty, and gender-today. Its not clear to me, when talking about biological differences, which of these three predictors we want to use, or even if we want to use biological differences, and we were seemingly assuming we'd use only one of them.
We probably want to use the predictors that are more predictive. And, as I mentioned, a person's chromossomal sex and what profile of hormones they are and were subjected to (along with environmental, nutritional, epigenetic, etc. factors), in the end, is much more determining (and, thus, a better predictor) than how a certain person identifies (or identified) themselves on a psychological or sociological level.
In the end, and as always, I think much of the disagreement has to do with the fact that people use terms that, without the proper context, could be misinterpreted (like "woman", that can be used to mean "XX person", "phenotypically female", "identifies as female", and I'm sure many other things).