Yes, it is kind of arbitrary at certain point, that's why we have the debate about it in this country. I am not sure where you are going with this given the subject of the comment I was responding to.
I chose my definition from the rights-of-women perspective. My understanding is that a fetus is generally non-viable outside of a host body, and thus not "alive" by my definition.
On the other hand, we havd C-sections and incubators. If a baby can be safely extracted with a C-section, placed in an incubator, and survive, my understanding is that the choice to abort is no longer available.
Of course, I can be wrong here.
My point was that at least I can make a definition here that does not depend on a choice of an arbitrary value of a continuous variable. My definition of "alive" depends on the choice of which variables to look at, not on arbitrary thresholds. And I don't insist on it being The Truth.
Another example:
"Heart rate" is a continuous vafiable, but the distribution of its values has a large gap between 0 (no heart rate) and nonzero values (the lowest observed was 27bpm). So you don't need to make a choice for a clustering algorithm to work. You can run K-means on "heart rate" and get these 2 clusters: 0 and everything else.
This allows one to make a definition of "alive" based on heart rate. That's not my definition, but it's a usable one.
This is not feasible with race if we use the variables commonly understood to be associated with race: skin color, height, nose shape, etc. There are no gaps in those variables.
Even eye color varies continuously [2], and it's not clear how to assign labels [1].
Color in general is a good analogy for race. You see the colors vary in a rainbow. You can tell the difference between red, green, and blue.
But you can't run K-means on a rainbow to get 7 colors out. Or any number but 1, for that matter.
You need to make a call yourself where to draw those lines.
This reflects in languages. Russian has distinct words for what we'd call "blue" in English; But also English has words like cyan, turquoise, navy, etc., which other languages may not have.
Color, in end, is a social construct.
[1] https://www.edow.com/general-eye-care/eyecolor/
[2]https://udel.edu/~mcdonald/mytheyecolor.html