Sex is obviously a continuum
P1. It is not quite clear what sex and/or gender is in the first place. The essentialist/gender critical crowd usually just denounces the existence of gender and say there is only sex. I think it doesn't even matter for the argument, that's why I put sex in the title as well instead of the (in my opinion) more salient term gender. So what is sex? The arguments are usually via some arbitrary biological descriptor such as chromosomes, hormones, primary/secondary sex characteristics, or some combination there of. That's a nice start.
P2. Assume you're the staunchest biological essentialist and say that it's just the chromosomes that matter, okay? Without going too deep into the metaphysics of objects, just on a very basic level: it's not quite clear where a chromosome starts and where it ends. From a materialist point of view, you might say the Y chromosome is literally just the 57,227,415 base pairs that we map onto it and everything else is not a Y chromosome. It sounds super pedantic and we don't have to dwell on this point for too long. But I think it illustrates the point that it is not quite trivial to define what a chromosome is. At every stage when it gets copied into another cell at which point is it just a blob of DNA and where does it begin to become a Y chromosome? Stepping a bit back from the materialist perspective and maybe analyzing the information content on the chromosomes it gets even more hairy, since on the X and Y chromosome there seem to be about the same number of bits stored yet with less density on the X chromosome, obviously. If we step back further and leave the ultra-essentialist position and say that other biological factors play a role, it just gets more difficult. Whereas in the chromosomal case we can argue that sex is a continuum with two extremely sharp peaks at XX and XY, with small variances around it for random mutations of single base pairs, as well as a bunch of smaller very sharp peaks on all the different sex chromosome variations (anomaly seems like a loaded term), it gets more moot if we include let's say hormones. Every factor that is included will (almost as a statistical law) broaden the peaks because we increase the granularity.
C1. Sex is a continuum with most of the probability mass on XX and XY for a not really useful essentialist view with some probability mass in other places. At a reasonable (given a sex centric view) granularity including a variety of sexual indicators, most probability mass becomes a blob, where it gets quite difficult to distinguish between who ought to be of what sex.
A1. Nature is discrete from a quantum mechanical perspective; you could argue sex is discrete from that view point but it's obviously moot and no one argues for it in honesty.
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